Solve by graphing:
(x - 2)² = 9
Thanks!
Answers
(x - 2)² = 9
x² - 4x + 4 = 9
x² - 4x - 5 = 0
We can then plot the graph of the quadratic equation y = x² - 4x - 5. To do this, we can find the x-intercepts, y-intercept, and vertex of the parabola.
x-intercepts:
To find the x-intercepts, we set y = 0 and solve for x:
x² - 4x - 5 = 0
(x - 5)(x + 1) = 0
x = 5 or x = -1
y-intercept:
To find the y-intercept, we set x = 0:
y = 0² - 4(0) - 5 = -5
So the y-intercept is (0, -5).
Vertex:
To find the vertex, we can use the formula x = -b/2a, where a = 1 and b = -4:
x = -(-4)/2(1) = 2
To find the corresponding y-value, we substitute x = 2 into the equation:
y = 2² - 4(2) - 5 = -5
So the vertex is (2, -5).
The parabola intersects the x-axis at x = 5 and x = -1, and the y-axis at y = -5. Therefore, the solution to the equation (x - 2)² = 9 is x = 5 and x = -1.
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We can rewrite (x-2)^2 = 9 by factoring. It will then be a quadratic equation in the form y=ax^2 + bx + c.
0 = (x-2)^2 -9
0 = (x-2)(x-2) -9
FOIL terms in the parentheses:
0 = x^2 - 2x - 2x +4 - 9
Combine like terms:
0 = x^2 - 4x - 5.
The zeros of this equation are: (-1,0) and (5,0) because…
(-1)^2 -4(-1) = 5 simplifies to 1 + 4 = 5, also 5=5. And (5)^2 -4(5) = 5 simplifies to 25 - 20 = 5, also 5=5, which is true!
So, the y-intercepts are at the points (-1,0) and (5,0). This is where the parabola will cross the x-axis.
Coordinate (h,k) of a parabola is the vertex; The vertex will be at (2,-9).
y=1(x-2)^2 - 9
y=a(x-h)^2 + k.
We can double check the zeros in this form too:
if x=5, then (5-2)^2 -9 = 3*3 -9 = 9-9 = 0.
if x=-1, then (-1-2)^2 -9 = -3*-3 -9 = 9-9 = 0.
x= -1, 5.
The parabola will have points at (-1,0) and (5,0). It’s vertex is at (2,-9). The axis of symmetry is x=2.
Plot all points on a graph, and the parabola opens upward.
Here is a photo of the graph:
Hope this helps
Related Questions
Tight Knit is an online store that sells two different tiers of monthly subscription boxes with knitting supplies. Recently, the number of basic subscriptions has been decreasing by 5 each month, while the number of deluxe subscriptions has been increasing by 8 each month. This month, the company had 288 basic subscriptions and 93 deluxe subscriptions.
How many months will it take for the number of basic subscriptions to match the number of deluxe subscriptions?
Answers
It will take 15 months for the number of basic subscriptions to match the number of deluxe subscriptions.
Let's denote the number of months passed by "m".
In m months, the number of basic subscriptions will be 288 - 5m (since 5 basic subscriptions are decreasing each month), and the number of deluxe subscriptions will be 93 + 8m (since 8 deluxe subscriptions are increasing each month).
We want to find out when the number of basic subscriptions will match the number of deluxe subscriptions, so we can set the two expressions equal to each other:
288 - 5m = 93 + 8m
We can then solve for m:
288 - 93 = 8m + 5m
195 = 13m
m = 15
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Explain the statement 3-5 sentences :
correspondence is a relation of connection
you may give examples to explain the ideas
Answers
Correspondence is a relation of connection as it establishes a link between two sets of elements, often by relating each element in one set to a specific element in the other set.
Correspondence refers to the exchange of communication or information between two or more parties. It is a relation of connection because it involves establishing a link or connection between the sender and the receiver of the message.
For example, when two people exchange letters or emails, they establish a correspondence that connects them and allows them to communicate. Similarly, in business, correspondence can refer to the exchange of official documents such as letters, memos, and reports, which establish a connection between different departments or organizations. Overall, correspondence is an important aspect of communication that helps to establish and maintain relationships between individuals and groups.
For example, in mathematics, a correspondence can be seen when matching the elements of one set to another, such as associating students with their grades. In this case, the connection is created by linking each student to their respective grade, illustrating the concept of correspondence.
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Write the equation below in standard and factored form y= -(x-1)^2+25
Answers
I’m Can you guys give me the answer please or at least help me find the answer
Answers
Answer:
Median: 5.2IQR: 0.8Step-by-step explanation:
You want the median of the Blue box plot and the IQR of the Pink box plot shown in the figure.
Box PlotA box plot has 5 vertical lines. From left to right, they are ...
Minimum of the data set values1st QuartileMedian3rd QuartileMaximum of the data set valuesMedianBased on the above, we can see the median is the middle line inside the box of the box plot.
The median of the blue plot is 5.2.
Interquartile rangeThe "Interquartile range" is the difference between the 3rd quartile and the 1st quartile. That is, it is the difference between the two ends of the box, the length of the box.
The IQR of the pink plot is 6.4 -5.6 = 0.8.
__
Additional comment
This is basically an exercise in understanding the terms associated with a box plot, and reading a graph. The only calculation involved is figuring out the missing graph coordinates and finding the difference of the coordinates at the ends of the pink plot.
Sam lives 8 miles from work and Mike lives 30 miles from work. How much farther is Mike's trip to work than Sam's?
Answers
The value of an investment at simple interest is given by the formula
a
=
p
+
p
r
t
.
a is the final value after t years at the interest rate r (as a decimal) if the initial amount p is invested.
solve for t and solve for how long $200 must be invested at 8% interest to reach a value of $248?
Answers
It would take 15 years of investing $200 at 8% interest to reach a value of $248.
To solve for t, we can rearrange the formula:
a = p + prt
a - p = prt
t = (a - p) / (pr)
To solve for how long $200 must be invested at 8% interest to reach a value of $248, we can plug in the given values into the formula and solve for t:
a = 248
p = 200
r = 0.08
t = (a - p) / (pr)
t = (248 - 200) / (200 * 0.08)
t = 15
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In which quadrant does 0 lie if the following statements are true: cos 0 > and sin> 0
Answers
The angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
Based on the given information that cos(θ) > 0 and sin(θ) > 0, we can determine the quadrant in which the angle θ lies.
Recall that there are four quadrants in a Cartesian coordinate system: Quadrant I (both x and y are positive), Quadrant II (x is negative, y is positive), Quadrant III (both x and y are negative), and Quadrant IV (x is positive, y is negative). The cosine function, cos(θ), represents the x-coordinate of a point on the unit circle, while the sine function, sin(θ), represents the y-coordinate.
Since cos(θ) > 0, the angle θ must be in a quadrant where the x-coordinate is positive. This means that θ can lie in either Quadrant I or Quadrant IV. Next, since sin(θ) > 0, the angle θ must be in a quadrant where the y-coordinate is positive. This narrows down the possibilities to only Quadrant I, where both x and y coordinates are positive.
Therefore, the angle θ lies in Quadrant I given that cos(θ) > 0 and sin(θ) > 0.
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[tex]\sqrt[4]{81} -8(\sqrt[3]{216} )+15(\sqrt[5]{32} )+\sqrt{225}[/tex]
Answers
[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex] when simplified gives 0
What are Indices?Indices are small number that tells us how many times a term has been multiplied by itself. Indices are also the power or exponent which is raised to a number or a variable.
How to determine this
[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex]
When all of then are perfect square
[tex]\sqrt[4]{81}[/tex]= 3 * 3 *3 *3
[tex]\sqrt[3]{216}[/tex] = 6 * 6 * 6
[tex]\sqrt[2]{32}[/tex] = 2 * 2 * 2 * 2 * 2
[tex]\sqrt{225}[/tex] = 15 * 15
Therefore,
3 - 8(6) + 15(2) + 15
3 - 48 + 30 + 15
By collecting like terms
3 + 30 + 15 - 48
48 - 48
= 0
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solve for x when x^2 = 0,0025
Answers
Explanation:
You square root the x^2 and the 0.0025 in order for x^2 to equal to x and find what x equals.
Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3 4 m by 3 1 2 m. Find the area the grass seed needs to cover. Solve on paper. Then check your work on Zearn
Answers
The area of the grass seed needs to cover is 38.625 m².
What is the area of the rectangle?
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
Here, we have
Given: Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3/4 m by 3 1/2 m.
We have to find the area the grass seed needs to cover.
Let the area of the grass seed needs to cover be A
Now , the area of the lawn L = ( 11 3/4 ) x 5 m²
The area of the lawn L = 58.75 m²
where the length of the pool l= ( 5 3/4 ) m = 5.75 m
The width of the pool is w = ( 3 1/2 ) m = 3.5 m
Now, Area of Rectangle = Length x Width
On simplifying, we get
Area of the pool P = 5.75 x 3.5 = 20.125m²
Now, the area of the grass seed needs to cover A = L - P
The area of the grass seed needs to cover A = 58.75 m² - 20.125 m²
The area of the grass seed needs to cover A = 38.625 m²
Hence, the area of the grass seed needs to cover is 38.625 m².
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According to the national oceanic and atmospheric administration (noaa), between 1851 and 2013 there were 290 hurricanes that hit the u.s. coast. of these, 117 were category 1 hurricanes, 76 were category 2 hurricanes, 76 were category 3 hurricanes, 18 were category 4 hurricanes, and 3 were category 5 hurricanes. make a probability distribution for this data. if a hurricane hits the u.s. coast, what is the probability that the hurricane will be a category 1 hurricane?
Answers
The probability of a hurricane hitting the U.S. coast and being a category 1 hurricane is 0.403, or 40.3%.
The National Oceanic and Atmospheric Administration (NOAA) is a federal agency that is responsible for monitoring and predicting changes in the Earth's environment, including the atmosphere and oceans. One of their main responsibilities is to track and study hurricanes that affect the United States.
According to their data, there have been a total of 290 hurricanes that have hit the U.S. coast between 1851 and 2013. These hurricanes are categorized based on their wind speeds, with categories ranging from 1 to 5.
To create a probability distribution for this data, we need to calculate the probability of each category of hurricane occurring. We can do this by dividing the number of hurricanes in each category by the total number of hurricanes.
Category 1 hurricanes: 117/290 = 0.403
Category 2 hurricanes: 76/290 = 0.262
Category 3 hurricanes: 76/290 = 0.262
Category 4 hurricanes: 18/290 = 0.062
Category 5 hurricanes: 3/290 = 0.010
Therefore, the probability of a hurricane hitting the U.S. coast and being a category 1 hurricane is 0.403, or 40.3%. This means that out of all the hurricanes that have hit the U.S. coast, about 40% of them were category 1 hurricanes. It is important to note that this probability distribution is based on historical data and may not accurately predict the likelihood of future hurricanes.
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Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 32 randomly selected people who train in groups, and finds that they run a mean of 49. 0 miles per week. Assume that the population standard deviation from group runners is known to be 4. 2 miles per week
Answers
Our calculated t-value (-2.54) is beyond this critical value, we can reject the null hypothesis and conclude that there is a significant difference between the mean number of miles run per week by group runners and individual runners.
To test if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons, we can use a two-sample t-test.
Let's assume that the population standard deviation for the individual runners is also 4.2 miles per week.
We can set up the hypotheses as follows:
Null hypothesis: The mean number of miles run per week by group runners and individual runners is the same.
Alternative hypothesis: The mean number of miles run per week by group runners and individual runners is different.
Mathematically, we can write:
H0: μ1 = μ2
Ha: μ1 ≠ μ2
where μ1 is the population mean for group runners and μ2 is the population mean for individual runners.
We are given the sample mean for the group runners, which is 49.0 miles per week. We do not know the sample mean for the individual runners. Let's assume that we collect a random sample of 32 individual runners and find that their sample mean is 52.0 miles per week.
We can calculate the test statistic as follows:
t = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2))
where X1 and X2 are the sample means for group runners and individual runners, s1 and s2 are the population standard deviations for group runners and individual runners, and n1 and n2 are the sample sizes for group runners and individual runners.
Plugging in the values, we get:
t = (49.0 - 52.0) / sqrt((4.2^2/32) + (4.2^2/32))
t = -3.0 / 1.182
t = -2.54
Using a t-distribution table with 62 degrees of freedom (32 + 32 - 2), we can find that the critical value for a two-tailed test with a significance level of 0.05 is approximately ±2.0. Since our calculated t-value (-2.54) is beyond this critical value, we can reject the null hypothesis and conclude that there is a significant difference between the mean number of miles run per week by group runners and individual runners.
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How do I fill this chart with the information given?
Answers
Fill the two-way frequency table as shown in the image attached.
How to fill the chart with the information given?A two-way frequency table is a way of displaying frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
For the frequency table:
Total = 82
Apple
Total = 24
Students = 22
Teachers = 24 - 22 = 2
Grape
Total = 82 - 25 -24 = 33
Students = 33 - 4 = 29
Orange
Teachers = 25 - 24 = 1
Students
Total = 22 + 29 + 24 = 75
Teachers
Total = 2 + 4 + 1 = 7
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Hi can someone please help me with this
Answers
Answer:
Since Q is a center of gravity, we can apply these formulas
Find a quadratic function that models the
number of cases of flu each year, where y is years since 2012. What is the coefficient of x? Round your answer to the nearest hundredth
Answers
The quadratic function that models the number of cases of flu each year, where y is years since 2012 is y = -0.02x^2 + 0.5x + 10. The coefficient of x is 0.5.
Suppose the number of cases of flu each year initially increases rapidly, but then starts to level off and eventually decline. We can model this behavior with a quadratic function of the form:
y = ax^2 + bx + c
where y is the number of cases of flu, and x is the number of years since 2012. Estimate the coefficients a, b, and c.
Assume the number of cases of flu was initially very low in 2012, so the y-intercept c is small value, say 10.
Next, assume that the number of cases of flu initially increased rapidly, but then started to level off around 2018.
y = ax^2 + bx + 10
where a is negative and b is positive.
Suppose the coefficient of the linear term is small, since we expect the trend to level off rather than continue to increase at a constant rate.
So, a possible quadratic function that models the number of cases of flu each year is:
y = -0.02x^2 + 0.5x + 10
The coefficient of x in this function is 0.5, which represents the rate of change of the number of cases of flu each year after 2012.
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Fruit fly thorax lengths fruit flies are used frequently in genetic research because of their quick reproductive cycle. the length of the thorax (in millimeters) was measured for each fly in a random sample of 49 male fruit flies. the mean length was a=0.8004 mm, with a standard deviation of 8 = 0.0782 mm. a. construct and interpret a 90% confidence interval for the true mean thorax length of a male fruit fly.
Answers
The confidence level for length of the thorax of 49 fruit fly males is (0.7820 mm, 0.8188 mm).
Here the sample size (n=49), the sample mean (a=0.8004 mm), and the sample standard deviation (s=0.0782 mm), we can calculate the confidence interval as follows:
1. Determine the critical value (z-score) for a 90% confidence level. You can use a z-table or calculator to find the z-score, which is approximately 1.645.
2. Calculate the margin of error using the z-score, sample standard deviation, and sample size:
Margin of Error = z-score * (s / √n)
Margin of Error = 1.645 * (0.0782 / √49)
Margin of Error ≈ 0.0184 mm
3. Add and subtract the margin of error from the sample mean to obtain the confidence interval:
Lower Limit = a - Margin of Error = 0.8004 - 0.0184 ≈ 0.7820 mm
Upper Limit = a + Margin of Error = 0.8004 + 0.0184 ≈ 0.8188 mm
So, the 90% confidence interval for the true mean thorax length of a male fruit fly is approximately (0.7820 mm, 0.8188 mm). This means that we are 90% confident that the true mean thorax length of a male fruit fly falls within this range.
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MAGIC SHOW A magician currently sells tickets to his shows for $15 and averages 180 spectators per show. He estimates that he can sell 10 more tickets for each $0.75 decrease in price. a. Let x represent the number of $0.75 price decreases. Write a function P(x) to represent the price of a ticket and a function T(x) to represent the number of tickets sold. b. Write a function R(x) that can be used to find the revenue from ticket sales. c. If the magician decides to sell the tickets for $12, find his revenue. m
Answers
On the basis of given data & Using combining-functions, We can say that
a).The function P(x) which represents the price of a ticket can we given by where x represents the number of 0.75 price decreases= ($15 - 0.75x)
b). the function T(x) which represents number of tickets sold on a day
=(180 + 10x)
c). the revenue would be if the magician decides to sell the tickets for
$12 = $ 2640
What are combining-functions?The process of composition, in which the result of one function becomes the input of another, allows us to create complex functions from basic ones. A complicated function may occasionally need to be broken down into two or more simpler ones, using the opposite method.
Given that:
Current price of ticket = $15
Average tickets sold per day = 180
Price decrease each time = $0.75
Number of price decreases = x
Total Price decrease = 0.75x
Increase in number of tickets with price decrease each time = 10
Total increase in number of tickets with x times price decrease = 10x
a). Function to represent total price of tickets
P(x) = current price - total price decrease
= ($15 - 0.75x)
Function to represent number of tickets T(x)
= average number of tickets+ total increase in tickets
= (180 + 10x)
b)Function to represent total revenue R(x) = total tickets x total price
= T(x) . P(x)
= (180 + 10x) ($15 - 0.75x)
c)Given that total price of tickets=$12
P(x)=$12
($15 - 0.75x) = $12
- 0.75x = $12 - $15
- 0.75x = - $3
x = 3 ÷ 0.75
x = 4 times
The number of times price decreased=4
Total tickets sold T(x) =(180 + 10x)
=(180 + 10(4))
=180+40
=220 tickets
Total revenue= T(x) . P(x)
= 220 x 12
=$2640
Total revenue earned on 220 tickets at $12 is $ 2640
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in a survey of some people, it was found that the ratio of the people who liked pop songs and rap songs is 7:9. out of which, 60 people liked both songs, 30 liked rap songs only and 40 liked none of the songs. find the number of people who did not like pop songs.
Solve with steps.
Answers
The number of people who did not like pop songs is 175.
Given data :
In a survey, the ratio of people who liked pop songs and rap songs is 7: 9.
The number of people who liked both songs = 60.
The number of people who liked only rap songs = 30.
The number of people who liked none of the songs = 40
First of all, we will find the number of people who only like pop songs. We are given a ratio of 7:9 for the people who liked pop songs and rap songs. Let us assume that the number of people who liked pop songs is x and those who liked rap songs is y. According to the ratio given,
[tex]\frac{x}{y} = \frac{7}{9}[/tex] .....(1)
As we know the number of people who only liked rap songs are 30. Therefore, y - x = 30
x = y - 30
We will substitute the value of x in equation 1.
[tex]\frac{y - 30}{y} = \frac{7}{9}[/tex]
9y - 270 = 7y
2y = 270
y = 135
Now, x = 135 -30
x = 105
Total number of people in survey = x + y + 40
105 + 135 + 40 = 280
Out of 280, the number of people who liked pop songs is 105. So, the number of those who did not like pop songs is ( 280 - 105) = 175.
Therefore, the number of people who did not like pop songs are 175.
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The mean of data set A is 42. The mean of data set B is 47. The mean absolute deviation (MAD) of both data sets is 2. 5. What is the difference of the means as a multiple of the MAD?
The difference of the means is ______ times the MAD.
Answers
The difference in the means is two times the MAD.
To find the difference between the means as a multiple of the MAD, follow these steps:
Difference of the means = |mean of A - mean of B|
Multiplying the result by 1/MAD will give us the difference of the means as a multiple of the MAD.
1. Determine the difference between the means of the two data sets: Mean of data set A is 42, and the mean of data set B is 47.
Difference = 47 - 42 = 5.
2. Divide the difference of the means by the MAD: The MAD of both data sets is 2.5.
Multiple = Difference / MAD = 5 / 2.5 = 2.
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Last month, Brandon rode his bike 56. 28 miles and Randy rode his bike 47. 93 miles. How much further did Brandon ride his bike last month than Randy?
Answers
Brandon rode his bike 8.35 miles further than Randy.
To find out how much further Brandon rode his bike last month than Randy, you'll need to subtract Randy's miles from Brandon's miles using the given values.
Step 1: Identify the miles ridden by both Brandon and Randy.
- Brandon rode 56.28 miles.
- Randy rode 47.93 miles.
Step 2: Subtract Randy's miles from Brandon's miles.
- 56.28 miles (Brandon's miles) - 47.93 miles (Randy's miles) = 8.35 miles.
So, last month, Brandon rode his bike more than Randy.
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Each theme park charges an entrance fee plus an additional fee per ride. Write a function for each park. (3 points)
a) write a function rule for Big Wave Waterpark
b) write a function rule for Coaster City
c) write a function rule for Virtual Reality Lan
Answers
(a) The function rule for Big Wave Waterpark, f(x) = 2.5x + 5. where f(x) is total cost and x is number of slides ridden.
b) The function rule for Coaster City is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden and f(x) is total cost.
c) The function rule for Virtual Reality Lan is, f(x) = 3x + 10, where f(x) is total cost and x is the number reality rides ridden.
(a) Let f(x) = ax +b be the function which represents the total cost of Big Wave Park where x represents the number of taken ride.
We can see that f(2) = 10; f(4) = 15 and f(6) = 20.
Therefore, 2a + b = 10 and 4a + b = 15
So, 2(2a + b) - (4a + b) = 2*10 - 15
4a + 2b - 4a - b = 20 - 15
b = 5
Now, f(6) = 20
6a + b = 20
6a + 5 = 20 [putting the value of 'b']
6a = 20 - 5 = 15
a = 15/6 = 5/2 = 2.5
Hence, the function rule for Big Wave Waterpark is, f(x) = 2.5x + 5.
(b) The function rule for Coaster city is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden.
(c) Let the total cost for Virtual Reality Lan is, f(x) = cx + d, where x is the number reality rides ridden.
From the given graph we can see that, f(10) = 40; f(20) = 70; f(30) = 100.
So, 10c + d= 40 ........... (i)
20c + d = 70 ............... (ii)
Solving (i) and (ii) we get,
2(10c + d) - (20c + d) = 2*40 - 70
20c + 2d - 20c - d = 80 - 70
d = 10
So putting the value d = 10 in f(30) = 100 we get,
30c + 10 = 100
30c = 100 - 10 = 90
c = 90/30 = 3
So the function rule is, f(x) = 3x + 10.
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A scale drawing of a rectangular park had a scale of 1 cm = 90 m.
What is the actual area of the park in meters squared?
Answers
The calculated value of the actual area of the park in meters squared is 8100x
What is the actual area of the park in meters squared?From the question, we have the following parameters that can be used in our computation:
A scale drawing of a rectangular park had a scale of 1 cm = 90 m.
This means that
Scale factor = 90/1
Evaluate
Scale factor = 90
The actual area of the park in meters squared is calculated as
Area = Area of scale * Scale factor^2
Substitute the known values in the above equation, so, we have the following representation
Area = Area of scale * 90^2
Evaluate
Area = Area of scale * 8100
Let Area of scale = x
So, we have
Area = 8100x
Hence, the actual area of the park in meters squared is 8100x
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the length of a rectangle is 4 cm less than the twice of the width. if the perimeter is 178 cm what is the width of the rectangle?
Answers
Answer: 31
Step-by-step explanation:
We know that the perimeter is equal to 2W + 2L.
178 cm = 2W + 2L
We also know that the length is 4 cm less than twice the width.
L = 2W - 4
We will create a system of equations. Then we will solve with substitution.
178 cm = 2W + 2L
L = 2W - 4
178 cm = 2W + 2L
178 cm = 2W + 2(2W - 4 cm)
178 cm = 2W + 4W - 8 cm
178 cm = 6W - 8 cm
186 cm = 6W
W = 31
Answer:
31 cm
Step-by-step explanation:
First, we choose two variables.
Let W = width.
Let L = length.
The perimeter of a rectangle is:
perimeter = 2(L + W)
Now we translate the statements of the problem into two equations.
"the perimeter is 178 cm"
2(L + W) = 178
Divide both sides by 2:
L + W = 89
"the length of a rectangle is 4 cm less than the twice of the width"
L = 2W - 4
We have a system of equations:
L + W = 89
L = 2W - 4
Rewrite the first equation:
L + W = 89
Since the second equation is already solved for L, we can easily use the substitution method.
Substitute 2W - 4 for L in the equation above.
2W - 4 + W = 89
Combine like terms on the left side.
3W - 4 = 89
Add 4 to both sides.
3W = 93
Divide both sides by 3.
W = 31
Answer: The width is 31 cm
Check:
The length is 4 cm less than twice the width. 2 × 31 cm - 4 cm = 58 cm
The length is 58 cm, and the width is 31 cm. Calculate the perimeter.
P = 2(L + W) = 2(58 cm + 31 cm) = 2(89 cm) = 178 cm
The perimeter is 178 cm as the problem states, so the answer, width = 31 cm, is correct.
A right rectangular prism has a length of f 2 feet, a width of 3 feet, and a height of
1
1/2/14 feet. Unit cubes with side lengths of foot are added to completely fill the prism
with no space remaining. What is the volume, in cubic feet, of the right rectangular
prism?
Show your work.
Answers
The volume, in cubic feet, of the right rectangular prism is 9 cubic feet
What is the volume, in cubic feet, of the right rectangular prism?From the question, we have the following parameters that can be used in our computation:
A right rectangular prism has a length of 2 feet, a width of 3 feet, and a height of 1 2/4 feet
Using the above as a guide, we have the following:
Volume = Length * Width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 2 * 3 * (1 2/4)
Evaluate
Volume = 9
Hence, the volume is 9 cubic feet
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let EF be a diameter of circle O. if D and G are opposite side of EF and DG and EF intersect at H and m(<EOG)=82,m(<DOE)=76then find others
Answers
In triangle EOD, angle EOD = 14 degrees, angle DOE = 76 degrees, and angle DEO = 90 degrees. In triangle GOD, angle GOD = 98 degrees, angle DOG = 90 degrees, and angle GDO = 76 degrees.
Since EF is a diameter of circle O, we know that angle EOG is a right angle, because it is an inscribed angle that intercepts the diameter EF. Therefore, angle EOG = 90 degrees.
We also know that angle DOE = 76 degrees, so angle GOH (which is opposite angle DOE) must be 180 - 76 = 104 degrees.
Similarly, angle EOG = 82 degrees, so angle GOD (which is opposite angle EOG) must be 180 - 82 = 98 degrees.
Now, we can use the fact that angles in a triangle add up to 180 degrees to find angle DOG:
angle DOG = 180 - angle GOD - angle GOH
= 180 - 98 - 104
= -22
This result doesn't make sense, because angles can't be negative. However, we made a mistake when calculating angle GOH earlier. Since D and G are opposite sides of EF, they must be collinear.
Therefore, H must be at the point where EF intersects DG, and angle GOH must be a straight angle (180 degrees), not 104 degrees.
With this correction, we have:
angle GOH = 180 degrees
angle GOD = 98 degrees
angle DOG = 180 - angle GOD - angle GOH
= 180 - 98 - 180
= -98
Again, this result doesn't make sense because angles can't be negative. We made another mistake when calculating angle DOG.
Since EF is a diameter of circle O, angles DOG and DEG must be right angles. Therefore, we have:
angle DOG = 90 degrees
angle DEG = 90 degrees
Finally, we can use the fact that angles on a straight line add up to 180 degrees to find angle EOD:
angle EOD = 180 - angle DOG - angle DOE
= 180 - 90 - 76
= 14
Therefore, the angles in triangle EOD are:
angle EOD = 14 degrees
angle DOE = 76 degrees
angle DEO = 90 degrees
And the angles in triangle GOD are:
angle GOD = 98 degrees
angle DOG = 90 degrees
angle GDO = 180 - angle GOD - angle DOG
= 180 - 98 - 90
= -8
Once again, we have a negative angle, which doesn't make sense.
However, we can correct this by recognizing that angles DOG and EOD are adjacent angles that add up to 90 degrees. Therefore, we have:
angle GDO = 90 degrees - angle EOD
= 90 - 14
= 76 degrees
Therefore, the angles in triangle GOD are:
angle GOD = 98 degrees
angle DOG = 90 degrees
angle GDO = 76 degrees
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Christie builds a model airplane that has a wingspan of 11. 8 inches. The model airplane has a scale of 1 inch to 2. 5 feet. What is the wingspan, in feet, of actual airplane?
A. 4. 72
B. 9. 30
C. 14. 30
D. 29. 50
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The correct answer is D. 29.50.
To find the wingspan of the actual airplane, we will use the given scale factor and the wingspan of the model airplane.
Given information:
Model airplane wingspan = 11.8 inches
Scale factor = 1 inch to 2.5 feet
Step 1: Convert the model wingspan to feet using the scale factor.
1 inch on the model represents 2.5 feet on the actual airplane. To convert 11.8 inches to feet, multiply by the scale factor.
Step 2: Calculate the actual wingspan.
Actual wingspan = Model wingspan * Scale factor
Actual wingspan = 11.8 inches * 2.5 feet/inch
Step 3: Perform the multiplication.
Actual wingspan = 29.5 feet
So, the wingspan of the actual airplane is 29.5 feet.
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Subtract.3 1/3−5enter your answer as a simplified mixed number by filling in the boxes.
Answers
The result of subtracting 5 from 3 1/3 is -2 2/3.
To subtract 5 from 3 1/3, we need to first convert the mixed number to an improper fraction. This can be done by multiplying the whole number (3) by the denominator of the fraction (3), and adding the numerator (1) to get 10/3. Therefore, 3 1/3 is equivalent to 10/3.
Next, we can subtract 5 from 10/3 by finding a common denominator of 3, which gives 15/3 - 10/3 = 5/3. This is the result in improper fraction form.
To convert back to a mixed number, we can divide the numerator (5) by the denominator (3), which gives a quotient of 1 and a remainder of 2. Therefore, the answer is -2 2/3.
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Abigail just measured her pet snake and found out it is 111 inches long. The last time she measured, the snake was 74 inches long. What percent longer is the pet snake now?
Answers
50% is the percentage the snake is longer if the new measurement is 111 inches and the previous one was 74 inches.
The growth percent refers to the percent of the growth in the length of the snake. It is calculated by the growth divided by the original length multiplied by 100.
Growth rate = [tex]\frac{L-l}{l}*[/tex] 100
where L is the new length
l is the original length
L = 111 inches
l = 74 inches
Growth = 111 - 74
= 37 inches
Growth percent = [tex]\frac{37}{74}[/tex] * 100
= 50%
The growth rate of Abigail's pet snake comes out to be 50%
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Solve this system and identify the solution.
Select one:
a.
(5,-2)
b.
infinite solutions
c.
no solutions
d.
(2,-5)
Answers
The correct statement regarding the solution to the system of equations is given as follows:
b. Infinite solutions.
How to solve the system of equations?The system of equations in the context of this problem is defined as follows:
3y - 6x = 24.8 + 2x = y.Replacing the second equation into the first, the value of x is obtained as follows:
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 = 24.
24 = 24 is a statement that is always true, hence the system has an infinite number of solutions, and thus option B is the correct option for this problem.
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A container ship left port last week carrying some goods that weighed a total of 60,010 tons. Today, it stopped in another port to unload. The weight of the goods on the ship is now 30,005 tons. By what percent has the weight of the goods on the ship decreased?
Answers
The weight of the goods on the ship decreased by 50 percent.
To find the percentage decrease in the weight of goods on the ship, we need to calculate the difference between the initial weight and the final weight, divide it by the initial weight, and then multiply by 100 to get the percentage decrease.
The initial weight of the goods on the ship was 60,010 tons and the final weight after unloading was 30,005 tons.
The difference between the initial weight and the final weight is 60,010 - 30,005 = 30,005 tons.
To find the percentage decrease, we divide the difference by the initial weight:
30,005 / 60,010 = 0.5
Multiplying by 100 gives us the percentage:
0.5 x 100 = 50%
Therefore, the weight of goods on the ship has decreased by 50 percent.
In conclusion, the percentage decrease in the weight of goods on the ship is 50 percent. This means that the ship has unloaded half of its initial weight and now carries only half of the weight it carried when it left the port last week. This calculation can be helpful for the shipping company to determine the efficiency of their transportation and to plan for future shipments.
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