Answer: There would 20-gon
Here is the graph for one equation in a system of equations. (picture below)
Write a second equation for the system so it has infinitely many solutions.
Write a second equation whose graph goes through (0,2) so that the system has no solutions.
Write a second equation whose graph goes through (2,2) so that the system has one solution at (4,3).
After answering the provided question, we can conclude that which slope equals m = 1/2. As a result, the second line's equation is y - 2 = (1/2)(x - 2), or y = (1/2)x + 1.
what is slope intercept?In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the line's gradient and b is the más, which is the point on the line where it intersects the y-axis. Because it allows you to speedily see the line and ascertain its slope and y-intercept, the slope-intercept form is a useful way to represent a line's equation. The slope of the line indicates its steepness, while the esta indicates in which the line intersects the y-axis.
To answer these questions, we must first determine the equation of the line depicted in the graph. Assume the line is in slope-intercept form, y = mx + b, with m representing the slope and b representing the y-intercept.
where m is the slope to be found. Because we want this line to intersect the given line at (4, 3), we can plug those values into both equations and solve for m: Because y = (1/4)x + 1, we get 3 = (1/4)(4) + 1 = 2 + 2m, which equals m = 1/2. As a result, the second line's equation is y - 2 = (1/2)(x - 2), or y = (1/2)x + 1.
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7-31.
During a given week, the museum had attendance as shown in the table at right. Z-31 HW
eTool (CPM) Homework Help
a. Numerically summarize the center and spread of attendance by finding the median and
interquartile range (IQR).
b. The museum management needs to tell the staff members their work schedules a week in
advance. The museum wants to have approximately one staff member for every 150 visitors.
How many staff members should be scheduled to work each week? Explain your reasoning.
c. Why is a scatterplot not an appropriate display of this data?
a. The median attendance is 796, and the IQR is 229. b. the museum should schedule 37 staff members. c. A scatterplot is not an appropriate display of this data because it is not continuous data, but rather discrete data.
Describe interquartile range?The interquartile range (IQR) is a statistical measure that represents the spread or variability of a dataset. It is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset.
To find the interquartile range, the dataset is first arranged in order from smallest to largest. The median of the dataset is then found, and the data is split into two halves: the lower half, which contains all the data points less than or equal to the median, and the upper half, which contains all the data points greater than or equal to the median.
a. To find the median and interquartile range (IQR), we first need to arrange the attendance numbers in order from lowest to highest:
400, 593, 680, 731, 861, 870, 940
The median is the middle number, or the average of the two middle numbers. In this case, the median is:
Median = (731 + 861) / 2 = 796
To find the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data. To find Q1, we take the median of the numbers below the median:
400, 593, 680, 731
Q1 = (593 + 680) / 2 = 636.5
To find Q3, we take the median of the numbers above the median:
861, 870, 940
Q3 = (870 + 861) / 2 = 865.5
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 865.5 - 636.5 = 229
Therefore, the median attendance is 796, and the IQR is 229.
b. To find the number of staff members needed each week, we divide the total attendance by 150:
(870 + 940 + 731 + 400 + 861 + 680 + 593) / 150 ≈ 36.54
Rounding up to the nearest whole number, we get 37 staff members. Therefore, the museum should schedule 37 staff members to work each week to meet their goal of having approximately one staff member for every 150 visitors.
c. A scatterplot is not an appropriate display of this data because it is not continuous data, but rather discrete data. Attendance is measured in whole numbers of visitors, and there are only 7 data points in this set. A scatterplot is typically used to display continuous data, where there are many data points and each data point can take on any value within a certain range. Instead, a bar chart or a histogram would be a more appropriate display for this data set.
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The complete question is:
During a given week, the museum had attendance as shown in the table at right. a. Numerically summarize the center and spread of attendance by finding the median and interquartile range (IQR). b. The museum management needs to tell the staff members their work schedules a week in advance. The museum wants to have approximately one staff member for every 150 visitors. How many staff members should be scheduled to work each week? Explain your reasoning. c. Why is a scatterplot not an appropriate display of this data?
Day Attendance
1 870
2 940
3 731
4 400
5 861
6 680
7 593
ΔGHJ ~ ΔKLM . The measure of ∠L is 75° and the measure of ∠G is 45°. What is the measure of ∠M?
Step-by-step explanation:
K = G = 45°
L = H = 75 °
M = J = 180° - 45 - 75 = 60° ( because three angles sum to 180 degrees)
Find the mean, median, and mode(s) of the data. Calculator use is ok.
0.4, 0.6, 0.6, 0.9, 0.4, 0.5, 0.8
Mean
Median
Mode(s)
the mean of the data is 0.54,the median of the data is 0.6.and the mode(s) of the data are 0.4 and 0.6.
what is median ?
The median is a measure of central tendency that represents the middle value in a dataset when the data are arranged in numerical order. It is a value that separates the dataset into two equal halves.
In the given question,
To find the mean of the data, we add up all the values and divide by the total number of values:
Mean = (0.4 + 0.6 + 0.6 + 0.9 + 0.4 + 0.5 + 0.8) / 7
Mean = 3.8 / 7
Mean = 0.54
Therefore, the mean of the data is 0.54.
To find the median of the data, we first need to put the values in order:
0.4, 0.4, 0.5, 0.6, 0.6, 0.8, 0.9
Since there are an odd number of values, the median is the middle value, which is 0.6.
Therefore, the median of the data is 0.6.
To find the mode(s) of the data, we look for the value(s) that appear most frequently:
0.4 appears twice
0.6 appears twice
Therefore, the mode(s) of the data are 0.4 and 0.6.
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the city council has 6 men and 3 women. if we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? select the correct fractional response. hint: consider there is no replacement of an individual who is already selected.
The probability that the two chairpersons chosen are of the same gender is 9/36.
Probability is a branch of mathematics that deals with the study of random events and their outcomes. It involves quantifying the likelihood of an event or outcome by assigning a numerical value between 0 and 1.
A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.
Probabilities between 0 and 1 indicate the likelihood of the event occurring, with higher probabilities indicating a greater likelihood.
This can be calculated by looking at the number of possibilities when selecting two members from a group of nine (6 men, 3 women):
Total possibilities = 9C2 = 9!/(2!*7!) = 9*8/2 = 36
Ways of selecting two of the same gender = 6C2 + 3C2 = 6*5/2 + 3*2/2 = 15
Therefore, the probability of selecting two of the same gender is 15/36, which reduces to 9/36.
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An online retailer receives 5% of the cost of all sales made on their website. How much does the retailer make on a sale of $80?
The online retailer will make $4 on a sale of $80. This is calculated by multiplying the cost of the sale ($80) by the retailer's percentage (5%).
The first step in calculating the retailer's profit is to identify the cost of the sale. In this case, the cost of the sale is $80.
The next step is to identify the percentage of the cost that the retailer will receive. In this case, the retailer will receive 5% of the cost of the sale.
The third step is to calculate the retailer's profit. This can be done by multiplying the cost of the sale ($80) by the retailer's percentage (5%). This calculation results in $4, which is the retailer's profit for this sale. Hence, the online retailer will make $4 on a sale of $80.
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The given point P is located on the unit circle. P[24/25, 7/25}
Answer:
Yes
Step-by-step explanation:
Unit circle is the circle whose center is at origin (0, 0) and radius r = 1 unit.
equation of this circle is,
[tex]x^2 + y^2 = 1[/tex]
point P(24/25, 7/25) lies on the above curve (substitute and check).
therefore point P lies on unit circle.
Hopefully this answer have helped you!
a student takes a true-false test that has 14 questions and guesses randomly at each answer. let x be the number of questions answered correctly. find p(5) group of answer choices 0.0001 0.0611 0.1833 0.1222
The probability to answer 5 questions correctly from 14 true or false questions is 0.1222
The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:
P(x)= nCx × p^x × q^(n-x)
Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.
n = 14 (total number of questions)
p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).
To find P(5), we substitute these values in the formula
P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222
Therefore, the answer is option D, 0.1222.
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What is the value of x in the equation ½ x- Zy = 30, when y = 152
Please help me answer the following question :)
Answer:
y = x - 1
Step-by-step explanation:
to determine the equation of the line we require to find the slope of the line and its y- intercept, where it crosses the y- axis.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0-(-1)}{1-0}[/tex] = [tex]\frac{0+1}{1}[/tex] = [tex]\frac{1}{1}[/tex] = 1
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = x - 1
Write a word problem that involves adding or subtracting two fractions. Draw a model and describe how you would act out the problem to solve it.
After simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 so the answer is 19/15.
Suppose there are two pizza slices on a plate. One slice is divided into 3 equal parts, and the other slice is divided into 5 equal parts. If you eat 2 out of the 3 parts of the first slice and 3 out of the 5 parts of the second slice, what fraction of the total pizza have you eaten?
To solve the problem, we need to add the fractions together. The fraction of the first slice eaten is 2/3, and the fraction of the second slice eaten is 3/5. We must identify a common denominator in order to add these fractions. In this case, the least common multiple of 3 and 5 is 15. So we need to convert both fractions so that they have a denominator of 15.
To convert 2/3 to a fraction with a denominator of 15, we need to multiply both the numerator and denominator by 5. This gives us 10/15. To convert 3/5 to a fraction with a denominator of 15, we need to multiply both the numerator and denominator by 3. This gives us 9/15.
We can now put the two fractions together because they both have the same denominator. This results in:
10/15 + 9/15 = 19/15
By dividing the denominator and numerator by their 1 greatest common factor, we may simplify this fraction. The final response is thus: 19/15
To act out this problem, we can draw a pizza with two slices, one divided into 3 parts and the other divided into 5 parts. We can then shade in the parts that have been eaten (2 out of 3 for the first slice and 3 out of 5 for the second slice), and count the total number of shaded parts. We can then convert this count into a fraction and simplify it if necessary.
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A seed sprouted and grew
2
3
of a foot in 3 months. What was its rate of growth?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
feet per month
After calculation, we know that rate of growth of the seed is 2/9 feet in 1 month which is in proper fraction.
What is the rate of growth?Take the current number and subtract it from the prior value to determine the growth rate.
The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.
The three types of growth identified by the Harrod-Domar model are warranted growth, real growth, and the natural rate of growth.
The economy cannot continue to develop at this rate indefinitely or without experiencing a downturn, which is known as the warranted growth rate.
The annual increase in a country's real GDP rate is known as actual growth.
So, we know that the seed grows:
2/3 foot in 3 months
Then, the rate of growth in 1 month was:
= 2/3 ÷ 3
= 2/3 ÷ 3/1
= 2/3 * 1/3
= 2/9 foot
Therefore, after calculation, we know that rate of growth of the seed is 2/9 feet in 1 month which is in proper fraction.
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If 6x + 2y = 18, but 8x + 3y also equals 25, what are the values of x and y?
Answer: x=1 y=6
Step-by-step explanation:
Translate the images by (3x-1,y+5)
Answer:(3x−y+5)(3−+5)
Step-by-step explanation:
answer i will give u a lot of points 100
Answer:
25.1
Step-by-step explanation:
formula for circumfrance is 2piR
so (2pi)(4)= 25.1
:)
The rectangular board below is to be cut at an angle of 36 and 32 as shown.When you cut out ABC,what is the measure of A
The measure of angle A is 112 degrees. Hence, option d is correct.
What is a rectangle?Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Similarly, since the angle of the cut is 36 degrees, the angle opposite it (angle BCD) is also 36 degrees. Since angles BCD and BDC add up to 90 degrees (because triangle BCD is a right triangle), angle BDC measures 54 degrees (90 - 36 = 54).
Now, we can find angle BDA by subtracting angle ADB and angle BDC from 180 degrees:
angle BDA = 180 - angle ADB - angle BDC
= 180 - 58 - 54
= 68
Finally, we can find angle A by subtracting angle BDA from 180 degrees:
angle A = 180 - angle BDA
= 180 - 68
= 112
Therefore, the measure of angle A is 112 degrees. Hence, option d is correct.
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Complete question:
I and m are in direct proportion.
The equation of proportionality is = = 9m.
If m increases from 4 to 7, how much will
increase by?
If your answer is a decimal, give it to 1 d.p.
Since I and m are in direct proportion, we can write:
I = km
where k is the constant of proportionality.
From the given equation of proportionality, we have:
I/m = 9
Multiplying both sides by m, we get:
I = 9m
So, the constant of proportionality is k = 9.
If m increases from 4 to 7, then we can find the increase in I as follows:
ΔI = I2 - I1
where I1 is the initial value of I when m = 4, and I2 is the final value of I when m = 7.
From the equation of proportionality, we have:
I1 = km1 = 9(4) = 36
I2 = km2 = 9(7) = 63
Therefore, the increase in I is:
ΔI = I2 - I1 = 63 - 36 = 27
So, if m increases from 4 to 7, then I increases by 27.
Help please for brainliest 20 points
The value of x in the similar triangles are:
a. x = 80 ft.
b. x = 16 ft.
What are similar triangles?Similarity among two or more triangle is a common relations when the properties of the triangles are compared. But in this case, the triangle are NOT congruent.
Considering the triangles in the given question,
1. Comparing the properties of the similar triangles, we have;
So that,
30/ x = 50/ 80
50x = 4000
x = 4000/ 50
= 80
x = 80 ft.
2. Comparing the properties of the two triangles, we have;
4.5/ 12 = 6/ x
4.5x = 72
x = 72/ 4.5
= 16
x = 16 ft
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i am in 7th grade trying to do this pls helpp
Check the picture below.
so the volume of each green box will be 1x1x1, and the volume of the whole rectangular prism on the back of Nico's truck is 7x4x8.
Now, let's get the volume of the containing rectangular prism, and then the volume of each box and do a division, namely, "how many times does the volume of a box go into the volume of the prism?"
[tex]\stackrel{\textit{volume of the prism}}{(7)(4)(8)}\div \stackrel{\textit{volume of one box}}{(1)(1)(1)}\implies \cfrac{(7)(4)(8)}{(1)(1)(1)}\implies \cfrac{224}{1}\implies \stackrel{ boxes }{\text{\LARGE 224}}[/tex]
In the accompanying diagram, tangent PA and secant PBC are drawn to circle O from point P. If the measure of arc AC = 90° and the measure of arc AB = 26°, what is the m/P? plsss helps
The measure of angle P in the accompanying diagram is 0.072, when the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees. This is determined by using the formula for the measure of a central angle: M/P = (arc measure)/(360°).
What is angle?Angle is a measure of the amount of turn between two straight lines or planes that have a common point or line of intersection. It is usually measured in degrees, radians, or gradians. An angle can be measured in different ways, such as the angle between two lines, the angle between two planes, or the angle between two points. Angles are important in mathematics, engineering, and physics as they help describe the shape and size of objects.
Since the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees, we can use the formula for the measure of a central angle:
M/P = (arc measure)/(360°)
Therefore, the measure of angle P is:
M/P = (26°)/(360°) = 0.072
Therefore, the measure of angle P is 0.072.
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Male and female students were surveyed about dancing and playing sports. They had the following preferences:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.25 0.27 0.52
Female students 0.17 0.31 0.48
Column totals 0.42 0.58 1
Which of the following is a two-way conditional relative frequency table for gender?
Do you prefer dancing or playing sports?
Playing sports Dancing
Male students 0.60 0.47
Female students 0.40 0.53
Column totals 1 1
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.48 0.52 1
Female students 0.35 0.65 1
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 25% 27% 52%
Female students 17% 31% 48%
Column totals 42% 58% 100%
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 50 54 104
Female students 34 62 96
Column totals 84 116 200
The option that shows a two-way conditional frequency table is option B as shown in the image attached.
What is a two-way conditional frequency table?A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:
Gender.Preferred activity.Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.
Which option is correct?The correct option is option B because it meets the following requirements:
It displays the two variables: gender and preferred activities.It uses frequency values such as 0.48 rather than percentages or the number of people, which would be incorrect.The row totals are displayed in a third column than in a new row.A pet store sells puppies and kittens in the ratio 5:4.
If their sales of puppies and kittens combined came to 36, how many puppies did they sell?
Let us consider the ratio to be x
So, as per the question's statement, we can write it as;
[tex]5x+4x=36[/tex]
[tex]\implies 9x=36[/tex]
We will divide 9 on both the sides, we get;
[tex]\implies x=\dfrac{36}{9} =4[/tex]
So, for getting the number of puppy sold we have to multiply it with 5, we get:
[tex]5x=5\times4=20[/tex]
They have sold 20 puppies.
Hence, the answer is [tex]20[/tex] puppies.
How do you calculate a ratio?Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.
How to simplify a ratio?Ratios can be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more.
a gift has the dimensions shown .what is the volume of the gift box? the length is 14 1/4 the width is 9 1/4 and the height is 1 7/8 write your answer as a mixed number in simplest form
To find the volume of the gift box, we need to multiply the length, width, and height together.First, let's convert all the dimensions to improper fractions:
Length: 14 1/4 = 57/4,
Width: 9 1/4 = 37/4,
Height: 1 7/8 = 15/8
Now we can multiply them together:
57/4 * 37/4 * 15/8 = 31,635/128
To write this as a mixed number in simplest form, we need to divide the numerator by the denominator and express the result as a mixed number:
31,635/128 = 247 with remainder of 19
So, the volume of the gift box is 247 19/128
A group of friends wants to go to the amusement park. They have $152.75 to spend on parking and admission. Parking is $10.25, and tickets cost $14.25 per person, including tax. Write and solve an equation that can be used to determine
�
x, the number of people who can go to the amusement park.
The group of friends can consist of up to 10 people if they want to stay within their budget of $152.75 for parking and admission.
Total cost = parking cost + ticket cost
The ticket cost for x people can be expressed as:
Ticket cost = x × $14.25
the cost of each ticket is $14.25.
the total cost for x people can be expressed as:
= $10.25 + x × $14.25
the group has a budget of $152.75 to spend on parking and admission, so we can set up
$152.75 = $10.25 + x × $14.25
Now we can solve for x by first subtracting $10.25
$152.75 - $10.25 = x × $14.25
Simplifying:
$142.50 = x × $14.25
Finally, we can solve for x
x = $142.50 ÷ $14.25
x = 10
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I need help, please say the right answers!
A. Define variables and write an equation to represent the relationship between the quantities.
B. How far would the biker travel in 20 minutes?
C. If the biker traveled 48 miles, how many minutes did he bike? Round to the nearest tenth.
A. The equation d = s * t shows relationship between the quantities.
B. They would cover a distance of 10 miles in 20 minutes.
C. Rounded to the nearest tenth, the biker would bike for 96.0 minutes.
What is distance?
Distance is the measure of the physical space between two objects or points. It is a scalar quantity that is usually measured in units such as meters, kilometers, miles, etc. In physics, distance is considered to be a fundamental concept and is often used in conjunction with time to calculate other physical quantities, such as speed and acceleration.
a. We can define the following variables:
t: time in minutes
d: distance traveled by the biker in miles
s: speed of the biker in miles per minute
Using these variables, we can write the equation d = s * t to represent the relationship between them.
b. If the biker rides for 20 minutes, we can use the equation d = s * t to find the distance traveled. Assuming the biker's speed is 0.5 miles per minute, we get:
d = 0.5 * 20 = 10 miles
Therefore, the biker would travel 10 miles in 20 minutes.
c. If the biker traveled 48 miles, we can use the equation t = d / s to find the time taken, where s is again assumed to be 0.5 miles per minute:
t = 48 / 0.5 = 96 minutes
Rounded to the nearest tenth, the biker would have ridden for 96.0 minutes to cover 48 miles.
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Please show working out
Perimeter of quadrilateral: P = 20 m and Total area = 18 sq. m.
Explain about the quadrilaterals:Quadrilaterals have the following two qualities:
A closed quadrilateral should have four sides.A quadrilateral's internal angles add up to 360°.Using Pythagorean theorem in two given right triangles for finding the missing sides.
In triangle PQR
PR² = QR² + QP²
PR² = 8² + 1²
PR² = 64 + 1
PR = √65
Now,
In triangle PRS
PR² = PS² + RS²
PS² = PR² - RS²
PS² = 65 - 16
PS = 7
Perimeter of quadrilaterals:
P = sum of all exterior sides
P = 8 + 1 + 4 + 7
P = 20 m
Total area = area of triangle PQR + area of triangle PRS
Total area = 1/2 *QR*PQ + 1/2 * PS *SR
Total area = 1/2*8*1 + 1/2*7*4
Total area = 18 sq. m
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What is the perimeter? 3 mi. Il mi.
Perimeter = 2(3 mi + 1 mi) = 8 miles.
What is coefficient?A coefficient is a numerical factor that is multiplied by a variable or a term in an algebraic expression. In mathematics, coefficients are commonly used in polynomial functions, where they determine the degree of the polynomial and the specific values of the function.
For example, in the polynomial function [tex]f(x) = 3x^2 + 2x - 1[/tex], the coefficients are 3, 2, and -1. The coefficient 3 is multiplied by the variable [tex]x^2[/tex], the coefficient 2 is multiplied by the variable x, and the coefficient -1 is the constant term.
by the question.
If you are referring to a rectangle, then the perimeter would be:
Perimeter = 2(length + width)
Assuming the 3 mi and 1 mi are the length and width respectively, then the perimeter would be:
Perimeter = 1 mile + 1 mile + unknown length of the third side
Perimeter = 2(3 mi + 1 mi) = 8 miles
perimeter = 8 mi.
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Complete question -
Find the perimeter of following -
3 mi. 1l mi.
Which of the graps below best displays this situation?
Which expression can be used to calculate the area of the smaller square?
For the first question, the correct graph would be option B (b-a)², as the water level decreases at a constant rate and then remains constant, which would result in a diagonal line followed by a horizontal line on a graph.
Define the term expression?An expression is a combination of symbols and/or numbers that can be evaluated or simplified to obtain a numerical or symbolic result. Expressions can be composed of one or more terms, which are separated by arithmetic operations, such as addition, subtraction, multiplication, or division.
For the second question, the area of the smaller square can be calculated using the expression (c - b)² or option C. This is because the length of the side of the larger square is c, and one side of the smaller square is equal to the difference between the side length of the larger square and the length of the smallest side of one of the congruent triangles, which is c - b.
Taking the square of this difference gives the area of the smaller square. Option D (a-b)² and option E b(c-b) are not correct expressions for the area of the smaller square, and option A does not provide enough information to calculate the area of the smaller square. Option (c - b)² is equivalent to option F.
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29. The correct graph would be option B (b-a)², as the water level decreases at a constant rate and then remains constant.
30. The area of the smaller square can be calculated using the expression (c - b)² or option C.
Define the term expression?An expression is a combination of symbols and/or numbers that can be evaluated or simplified to obtain a numerical or symbolic result. Expressions can be composed of one or more terms, which are separated by arithmetic operations, such as addition, subtraction, multiplication, or division.
For the first question, the correct graph would be option B (b-a)², as the water level decreases at a constant rate and then remains constant, which would result in a diagonal line followed by a horizontal line on a graph.
For the second question, the area of the smaller square can be calculated using the expression (c - b)² or option C. This is because the length of the side of the larger square is c, and one side of the smaller square is equal to the difference between the side length of the larger square and the length of the smallest side of one of the congruent triangles, which is c - b.
Taking the square of this difference gives the area of the smaller square. Option D (a-b)² and option E b(c-b) are not correct expressions for the area of the smaller square, and option A does not provide enough information to calculate the area of the smaller square. Option (c - b)² is equivalent to option F.
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Three people Sagar, Basanta and Krishna are walking on the two edges of a straight road of 6 m width. Their position on a fixed time is found to be S(4, 6), B(6,-2) and K(4, 2). Find the equation of Basanta's walking route.
The equation of Basanta's walking route is: y = -2x + 10
How to find the equation of Basanta's walking routeWe can find the equation of Basanta's walking route by using the slope-intercept form of a linear equation:
y = mx + b
where m is the slope of the line and
b is the y-intercept.
To find the slope of Basanta's walking route, we can use the coordinates of two points on the line, namely B(6, -2) and K(4, 2):
slope = (y2 - y1) / (x2 - x1)
= (2 - (-2)) / (4 - 6)
= 4 / (-2)
= -2
To find the y-intercept, we can use the coordinates of one of the points on the line, for example, B(6, -2):
y = mx + b
-2 = (-2)(6) + b
-2 = -12 + b
b = 10
Therefore, the equation of Basanta's walking route is: y = -2x + 10
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Find all polar coordinates of point P where P = (9 , -pi/5)
the polar coordinates of P are: (r, θ) = ([tex]\sqrt{(81 +\pi ^{2} /25)}[/tex], -0.3586 + 2πk) for all integers k. There are an infinite number of polar coordinates for P, corresponding to different values of k.
To express the point P = (9, -π/5) in polar coordinates, we need to find its distance from the origin and the angle it makes with the positive x-axis.
The distance from the origin to P can be found using the formula:
r = [tex]\sqrt{(x^2 + y^2)}[/tex]
where x and y are the Cartesian coordinates of the point. Substituting the values for P, we get:
r = [tex]\sqrt{9^2}[/tex]
The angle θ that P makes with the positive x-axis can be found using the formula:
θ = atan(y/x)
where atan is the arctangent function. Substituting the values for P, we get:
θ = atan((-π/5)/9) ≈ -0.3586 radians
Note that the angle is negative because the point is in the fourth quadrant.
Therefore, the polar coordinates of P are:
(r, θ) = ([tex]\sqrt{(81 +\pi ^{2} /25)}[/tex], -0.3586 + 2πk) for all integers k.
There are an infinite number of polar coordinates for P, corresponding to different values of k.
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