Answers
If the line passes through the point (2,8) that cuts off the least area from the first quadrant, the slope is 8/3 and the y-intercept is 0.
To find the equation of the line that passes through the point (2, 8) and cuts off the least area from the first quadrant, we need to first determine the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
We can use the point-slope form of the equation of a line to find the slope. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line. Plugging in (2, 8) as the point, we get:
y - 8 = m(x - 2)
Next, we want to minimize the area that the line cuts off in the first quadrant. Since the line passes through the origin (0, 0), the area cut off by the line in the first quadrant is equal to the product of the x- and y-intercepts of the line.
We can express the x-intercept in terms of y by setting y = 0 in the equation of the line and solving for x:
0 - 8 = m(x - 2)
x = 2 + 8/m
The y-intercept is simply the y-coordinate of the point where the line intersects the y-axis, which is given by:
y = mx + b
8 = 2m + b
b = 8 - 2m
We can now express the area cut off by the line as:
A = x*y
A = (2 + 8/m)*8 - (8 - 2m)*2/m
A = (16 + 64/m) - (16 - 4m)/m
A = 64/m + 4m/m
To minimize the area, we can take the derivative of A with respect to m and set it equal to zero:
dA/dm = -64/m² + 4/m² = 0
64 = 4
m = 8
Plugging m = 8 into the equation for the x-intercept, we get:
x = 2 + 8/8 = 3
So the equation of the line is y = 8x/3.
To learn more about slope and y-intercept click on,
https://brainly.com/question/31684407
#SPJ1
Related Questions
PLSSS HELP AND PLEASE SHOW WORK ASWELL
Collin has 100 feet of fencing to enclose a pen for his puppy. He is
trying to decide whether to make the pen
circular or square. He plans to use all of the
fencing.
Part A.) If Collin uses all of the fencing, what
would be the area of each pen? Use 3.14
for pie. Round to the nearest hundredth if
necessary.
Part B.) To have the largest possible area for the pen, which pen should Collin build?
Answers
Answer:
A.
circular: ≈ 795.77 square feet
square: 625
Step-by-step explanation:
the circular pen would have a larger area.
Solving for the radius, we have:
r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)
Therefore, the area of the circular pen would be:
Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet
For a square pen with side length s, the perimeter is given by:
4s = 100
s = 25
The area of a square pen with side length s is given by:
A = s^2 = 25^2 = 625
Let's first consider the circular pen. The circumference of a circle is given by 2πr, where r is the radius. In this case, we have 100 feet of fencing, so:
2πr = 100
Solving for r, we get:
r = 100/(2π) = 15.92 feet (rounded to two decimal places)
The area of the circular pen is given by πr^2, so:
Area = π(15.92)^2 = 795.77 square feet (rounded to two decimal places)
Now let's consider the square pen. If we use all 100 feet of fencing, then each side of the square will be 25 feet long. Therefore, the area of the square pen is:
Area = 25^2 = 625 square feet
Part B:
To have the largest possible area for the pen, Collin should build the circular pen. We can see from the calculations above that the area of the circular pen is larger than the area of the square pen. This is because a circle has the largest area for a given perimeter, which in this case is 100 feet.
Provide appropriate commentary that will assist learner to in the completion of the sum8+(6-3)-9=
Answers
Answer:
8+(3)-9=8+3-9=11-9=2
Step-by-step explanation:
by using PEMDAS rule
Start with :
P : Paranthesis
E: exponents
M: Multiplication
D : division
A: Addition
S:Subtraction
PLEASE HELP
Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.
C=0.90, x=13.7, s =3.0, n= 10
Answers
The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is (9.7, 14.7).
Here, we have,
1. Identify the given information:
- Confidence level (c) = 0.95
- Sample mean (x) = 12.2
- Sample standard deviation (s) = 3.0
- Sample size (n) = 8
2. Determine the degrees of freedom (df) for the t-distribution:
- df = n - 1 = 8 - 1 = 7
3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:
- You can use a t-table or an online calculator for this.
- The t-value for a 0.95 confidence level and 7 df is approximately 2.365.
4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):
- ME = t-value * (s / sqrt(n))
- ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5
5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):
- Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7
- Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7
So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).
Know more about confidence interval here:
brainly.com/question/1136789
#SPJ1
Parametric Equations Question
A drone traveling horizontally at 100 m/s over flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground. The trajectory of the package is given by [tex]x=100t, y=-4.9t^2 +4500, t\geq 0[/tex]where the origin is the point on the ground directly beneath the drone at the moment of release. How many horizontal meters before the target should the package be released in order to hit the target? Round to the nearest meter.
Answers
the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.
what is rounded to the nearest ?
"Rounded to the nearest" means finding the nearest value of a specified degree of accuracy. For example, rounding a number to the nearest whole number means finding the closest whole number to that number. If the number is equally close to two whole numbers, it is rounded up to the higher number.
In the given question,
The trajectory of the package can be modeled using the equation:
y = -0.5 * g * x² / v² + tan(∅) * x + h
where:
y = height of the package above the ground at horizontal distance x
g = acceleration due to gravity (9.8 m/s²)
v = horizontal velocity of the drone (100 m/s)
theta = angle at which the package is released
h = initial height of the package above the ground (4500 meters)
To hit the target, we want the package to land on the ground, which means its final height should be zero. So, we can set y = 0 and solve for x to find the horizontal distance at which the package should be released. This gives:
0 = -0.5 * 9.8 * x² / 100² + tan(∅) * x + 4500
Simplifying and rearranging, we get:
0.049 * x² + tan(∅) * x - 4500 = 0
Using the quadratic formula, we can solve for x:
x = (-tan(∅) ± √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)
Since we want the package to land in front of the target, we take the positive root of the equation:
x = (-tan(∅) + √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)
Now, we need to find the value of theta that will make the package hit the target. Since the drone is traveling horizontally, the package will also have a horizontal velocity of 100 m/s when it is released. So, we can use trigonometry to find the angle at which the package should be released. This gives:
tan(∅) = 4500 / x
Substituting this into the equation for x, we get:
x = (-4500 / x + √((4500 / x)²+ 0.049 * 4500 * 4)) / (0.098)
Simplifying and rearranging, we get:
x² = 4500 * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x) / 0.098
Squaring both sides, we get:
x⁴ = 4500² * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x)² / 0.009604
Expanding and simplifying, we get:
x⁴ = 900000000 * (1 + 0.00012345679 * x² - 0.00012345679 * 4500 * x / √(x² + 202500)) / 0.009604
We can solve for x using numerical methods, such as using a graphing calculator or an online solver. Using such a method, we find that:
x ≈ 9,932 meters
Therefore, the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.
To know more about rounded to the nearest , visit:
https://brainly.com/question/1285194
#SPJ1
1. A survey conducted by a national research center asked a random sample of 920
teenagers in the United States how often they use a video streaming service.
From the sample, 59% answered that they use a video streaming service every day.
a. Construct and interpret a 95% confidence interval for the proportion of all
teenagers in the United States who would respond that they use a video
streaming service every day.
b. Based on the confidence interval in part (a), do the sample data provide
convincing statistical evidence that the proportion of all teenagers in the United
States who would respond that they use a video streaming service every day is
not 0.5? Justify your answer.
Mean Standard Deviation Sample Size
Standard care 0.57 0.26 56
New treatment 0.69 0.27 56
2. Patients experiencing symptoms of a heart attack are routinely transported to a
hospital in an ambulance. In a study of a new treatment thought to reduce damage to
the heart, patients experiencing symptoms of a heart attack were randomly assigned to
one of two groups. During transportation to the hospital, patients in one group received
standard care, and patients in the other group received the new treatment consisting of
standard care and the application of a blood pressure cuff.
The response variable measured for each patient was a number between 0 and 1,
referred to as the myocardial salvage index (MSI). A higher MSI value indicates a more
positive outcome for the patient. Summary statistics for the MSI responses of the two
groups are shown in the table.
Do the data provide convincing statistical evidence that the new treatment results in a
higher mean MSI value than does the standard care among people similar to the
patients in the study?
Answers
Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.
How to solvea. The 95% confidence interval for the proportion of teenagers using video streaming services daily is (0.5579, 0.6221). This means we're 95% confident that 55.79% to 62.21% of US teenagers use such services daily.
b. The results demonstrate that the proportion is not 0.5 because the full confidence interval is higher than 0.5.2. We obtain a t-value of roughly 2.51 with 108.52 degrees of freedom using a two-sample t-test.
At a significance level of 0.05, the critical t-value for a one-tailed test is approximately 1.66.
Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.
Read more about confidence interval here:
https://brainly.com/question/15712887
#SPJ1
The construction of copying is started below. The next step is to set the width of the compass to the length of . How does this step ensure that the new angle will be congruent to the original angle?
Answers
The first step is to copy a segment and an angle, and the second step is to fix the width of the compass to the length of the segment. Then last, draw a perpendicular line.
What is geometry?
Geometry is a branch of mathematics that deals with the study of spatial relationships, shapes, sizes, positions, and dimensions of objects. It involves the study of points, lines, angles, planes, curves, surfaces, and solids, and how they relate to each other in space.
According to the given information:
Considering that, we must define the first stage, which is the process of copying a line segment in order to ensure that the new line segment is the same length as the original line segment. In a first stage, an angle and a segment must be replicated. The illustration depicts the copying construction.
The compass width must then be changed to match the section length. The new angle is now commensurate with the old angle. This is the following step.
The next step is to draw a perpendicular line. It is shown here how to draw a line perpendicular to the specified line across a point.
As a result, the first step is to copy a segment and an angle, and the second step is to set the width of the compass to the length of the segment. Then last, draw a perpendicular line.
To know more about geometry visit :
brainly.com/question/8942537
#SPJ1
-(4-8)+(-3-7)−(−1+6) + (−2+5)=
Answers
Answer: -8
Step-by-step explanation:
Simple math. Your welcome glad to help
What is the answer?
A) Yes
B) No
Answers
Answer:
Step-by-step explanation:
No
NEED HELP ASAP PLS AND THX PIX IS ATTACHED
Answers
Sin A Cos A, and Tan A can be found respectively as follows:
1. 41.81°.
2. 44.19 degrees
2. 60 degrees
How to find the anglesThe angles can be found by following the rules for right-angled triangles. This can be achieved in the following ways:
1. sin A= opposite/hypotenuse
sin A = 6/9
Now we take the sine inverse:
sin^-1(6/9)
= 41.81°.
2. Cos 45° = Adjacent/hypotenuse
= cos 45° = x/4
x = cos 45° × 4
= 0.707 × 4
= 2.82
cos A = b2 + c2 – a2 ÷ 2bc
2.8² + 4² - a² ÷ 2×2.8×4
23.84 - 2.8² ÷ 22.4
23.84 - 7.84 ÷ 22.4
Cos A = 0.7142
= 44.19 degrees
3. tan A = Opposite/Adjacent
tan 60° = 4/x
x = 4/tan 60°
x = 4/1.732
= 2.309
Tan A = 4/2.309
= 1.732
= 60 degrees
Learn more about right-angled triangles here:
https://brainly.com/question/64787
#SPJ1
There are two spinners. The first spinner has three same-sized sectors labeled 1, 2, and 3. The second spinner has four same-sized sectors labeled 3, 4, 5, and 6. The spinners are spun once. How many outcomes do not show an odd number on the first spinner and show a 3 on the second spinner?
Answers
Answer:
The first spinner has a 1/3 chance of not showing an odd number, and the second spinner has a 1/4 chance of showing a 3. The probability of both events happening is:
1/3 x 1/4 = 1/12
Therefore, there is a 1/12 chance of an outcome showing a 3 on the second spinner and not showing an odd number on the first spinner. Since there are a total of 3 x 4 = 12 possible outcomes, the number of outcomes that meet the criteria is:
12 x 1/12 = 1
So there is only one outcome that meets the criteria.
PLEASE FIND THE AREA
Answers
Answer:
50 cm
Step-by-step explanation:
To solve this answer you can find the area of the small triangle, and multiply it by 2 to get the area of the top part.
Then you can find the area of one of the bigger triangles and multiply it by 2.
Please could I get brainiest? I'm trying to get to the Expert level.
The times to run a mile are 7,
9, 10, 11, 11, and 12.
What is the mean?
Answers
Answer:
10
Step-by-step explanation:
When you think of the mean of a data set, think of the word average. 'Mean' and 'average' are the same thing when you're talking about a set of data.
To find the mean, you have to divide the sum of all values in your data set, by the number of values.
7 + 9 + 10 + 11 + 11 + 12 = 60
60/6 = 10
Therefore, the mean of this data set would be 10.
What is the solution set for −4x−38<2
Answers
The solution set for the inequality is x < -10
What are inequalities?The different signs for representing inequalities are;
< represents the sign for less than> represents the sign for greater than≥ represents greater than or equal to≤ represents less than or equal toFrom the information given, we have that;
−4x−38<2
To solve for the value of x, take the steps;
collect the like terms
-4x> 2 + 38
Add the values
-4x> 40
Divide both sides by the coefficient of x, we have;
x > -10
Learn about inequalities at: https://brainly.com/question/25275758
#SPJ1
Consider the line 6x-7y = 4. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Answers
The slope of a line parallel to this line is 6/7.
The slope of a line perpendicular to this line is -7/6.
What are parallel lines?In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
In Mathematics and Geometry, two (2) lines are parallel under the following conditions:
Slope, m₁ = Slope, m₂
Based on the information provided about this line, we have the following equation in standard form;
6x - 7y = 4
By making y the subject of formula, we have:
7y = 6x - 4
y = 6x/7 - 4
In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:
m₁ × m₂ = -1
6/7 × m₂ = -1
6m₂ = -7
Slope, m₂ = -7/6
Read more on perpendicular line here: brainly.com/question/27257668
#SPJ1
Share your own multi-step combination problem
Answers
My own multi-step combination problem is given below:
Amanda was planning a dinner party for 10 people, and she want to choose a menu of 3 fruit , 2 meat pie, and 2 desserts. Amanda have a total of 5 fruit , 4 meat pie, and 3 desserts to choose from. How many different dinner menus can Amanda create?How do you solve the multi-step combination?To solve this problem, Amanda need to use the formula for combinations and it is:
nCr = n! / (r! x (n-r)!)
where:
n = total number of items to select from
r is the number of items to select.
First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:
5C3
= 5! / (3! x (5-3)!)
= 10
Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be
4C2
= 4! / (2! x (4-2)!)
= 6
Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:
3C2
= 3! / (2! x (3-2)!)
= 3
To have the total number of dinner menus, we have to multiply these three numbers together:
= 10 x 6 x 3
= 180
Therefore, one can say that Amanda have 180 different dinner menus that she can be create.
Learn more about multi-step combination from
https://brainly.com/question/2191693
#SPJ1
14 15. A composite figure is created from a cylinder and a cone like in the image below. Use the informative given in the image to find the volume of the composite figure. Select the closest estimate for the volume of the figure. 15 7 feet h
Answers
The volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.
How to evaluate for the volume of the composite figureWe shall calculate for the volumes of the cone and the cylinder, the sum of each volume will give the volume of the composite figure
The cone have;
radius = 7 ft
height = 34ft - 16ft = 18ft
Volume of the cone = 1/3 × 22/7 × 7ft × 7ft × 18ft
Volume of the cone = (22 × 7 × 6) ft³
Volume of the cone = 924 ft³
The cylinder have;
radius = 7 ft
height = 16 ft
Volume of the cylinder = 22/7 × 7ft × 7ft × 16ft
Volume of the cylinder = (22 × 7 × 16) ft³
Volume of the cylinder = 2464 ft³
Volume of the composite figure = 924 ft³ + 2464 ft³
Volume of the composite figure = 3388 ft³
Therefore, the volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.
Read more about volume here:https://brainly.com/question/23935577
#SPJ1
Suppose that the functions and are defined as follows.
Answers
1) (f - g) (x) = f(x) - g(x) = x ≤ 1/4
Domain of the function is : [1/4, infinity)
2) → [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]
Domain of the function : (1/4, infinity)
We have the function are as follows:
f(x) = -x + 4
g(x) = [tex]\sqrt{4x+1}[/tex]
To find the f - g and f/g and also their domains using interval notation.
Now, (f - g) (x) = f(x) - g(x)
= [tex]-x+4-\sqrt{4x+1}[/tex]
= 4x + 1 ≤ 0
= x ≤ 1/4
Domain of the function is : [1/4, infinity)
→ [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]
=> 4x - 1 > 0
=> x > 1/4
Domain of the function : (1/4, infinity)
Learn more about Function at:
https://brainly.com/question/12431044
#SPJ1
see attachment
3(3m+N)
Answers
Answer:
Step-by-step explanation:
A right triangle with coordinates A (2,1), B (6,1), and C (6,4) is reflected across the Y axis, then rotated 180 degrees counter clockwise and then translated down 2 units to form triangle A'B'C'.
What is the measure of angle A'B'C', in degrees, in the resulting figure?
Answers
The measure of angle A'B'C' in the resulting figure is approximately 142.6 degrees.
How to calculate the angleThe reflection of a point (x, y) across the y-axis is (-x, y). Applying this transformation to the coordinates of A, B, and C, we get:
A' (-2, 1)
B' (-6, 1)
C' (-6, 4)
The rotation of a point (x, y) by 180 degrees counter clockwise is (-x, -y). Applying this transformation to the coordinates of A', B', and C', we get:
A'' (2, -1)
B'' (6, -1)
C'' (6, -4)
Next, we can use the law of cosines to find the measure of angle B:
A'B'C' = 180 - arccos(-7/24)
≈ 142.6 degrees
Learn more about triangles on
https://brainly.com/question/17335144
#SPJ1
The average height of young adult males has a normal distribution with standard deviation of 2.7 inches. You want to estimate the mean height of students at your college or university to within one inch with 93% confidence. How many male students must you measure?
Answers
You must measure 24 male students to estimate the mean height within one inch with 93% confidence.
How to solve for the sample sizeSince we want to estimate the mean height within one inch, the margin of error (E) is 1 inch:
E = Z * (Standard deviation / √Sample size)
Now, we can rearrange the formula to solve for the Sample size (n):
1 = 1.81 * (2.7 / √n)
Solving for n:
n = (1.81 * 2.7 / 1)²
n ≈ (4.887)²
n ≈ 23.88
Since we cannot have a fraction of a person, we round up to the nearest whole number:
n ≈ 24
So, you must measure 24 male students to estimate the mean height within one inch with 93% confidence.
Read more on Sample size here: https://brainly.com/question/30224379
#SPJ1
Each state sets its own state income tax rate. Table 1 shows 3 individuals'
incomes and taxes owed. Table 2 shows the income tax rates for several
states.
Table 1:
Name Income Taxes Owed
Beatrice $35,000
Gregory $55,000
Melinda $72,000
O $4,602.50
O $19,725
$2,450
$4,400
$3,600
O $46,025
O $61,147.50
Table 2:
State
Alabama
Georgia
Maine
If Anthony lives in Georgia and has an income of $65, 750, how much money
will he have left after he pays state income taxes?
Income Tax Rate
5%
7%
8%
Answers
From Table 2, we can see that Georgia's income tax rate is 7%.
To find the amount of state income taxes Anthony will owe, we can multiply his income by the tax rate:
State income tax = (Anthony's income) x (Georgia's tax rate)
State income tax = $65,750 x 0.07
State income tax = $4,602.50
Therefore, Anthony will owe $4,602.50 in state income taxes. To find out how much money he will have left after he pays these taxes, we can subtract the tax amount from his income:
Money left after paying state income taxes = Anthony's income - State income tax
Money left after paying state income taxes = $65,750 - $4,602.50
Money left after paying state income taxes = $61,147.50
Therefore, Anthony will have $61,147.50 left after he pays state income taxes.
Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.
Of all those who participated in the study, 80% received medication A.
Of those who received medication A, 76% reported an improvement.
Of those who received the placebo, 62% reported no improvement.
I see the other answers about the same question, but I still don't understand some of it
Answers
P(A and B) = P(A) x P(B|A)
where P(A) is the probability of event A, and P(B|A) is the conditional probability of event B given that event A has occurred.
In this case, we want to find the probability of two events occurring together: receiving the placebo and reporting an improvement. Let's use a tree diagram to organize the information:
```
A (80%)
/ \
Imp No imp
/ \
B No B
```
From the diagram, we can see that:
- P(placebo) = 1 - P(medication A) = 1 - 0.8 = 0.2
- P(improvement | medication A) = 0.76
- P(no improvement | placebo) = 0.62
Now we can use the formula to find P(placebo and improvement):
P(placebo and improvement) = P(placebo) x P(improvement | placebo)
P(placebo and improvement) = 0.2 x (1 - P(no improvement | placebo))
P(placebo and improvement) = 0.2 x (1 - 0.62)
P(placebo and improvement) = 0.2 x 0.38
P(placebo and improvement) = 0.076
Therefore, the probability of receiving the placebo and reporting an improvement is 0.076, or approximately 0.08, which means that about 8% of the participants received the placebo and reported an improvement.
Need answers to this by 20 min please!
Dividing cubic polynomials by linear divisor
Answers
The solution to each of the given polynomials are:
1) x² + 3x - 4
2) x² - 4x + 4
3) x² - 7x + 8
4) x² - 13 - (15/(x + 3)
How to carry out polynomial division?1) We want to divide the polynomial. Thus:
x² + 3x - 4
x + 2| x³ + 5x² + 2x - 8
- x³ + 2x²
3x² + 2x
- 3x² + 6x
- 4x - 8
- -4x - 8
0
2) We want to divide the polynomial. Thus:
x² - 4x + 4
x - 2| x³ - 6x² + 12x - 8
- x³ - 2x²
- 4x² + 12x
- -4x² + 8x
4x - 8
- 4x - 8
0
3) We want to divide the polynomial. Thus:
x² - 7x + 8
x + 3| x³ - 4x² - 13x + 24
- x³ + 3x²
- 7x² - 13x
- -7x² - 21x
8x + 24
- 8x + 24
0
4) We want to divide the polynomial. Thus:
x² - 13
x + 3| x³ + 3x² - 13x - 15
- x³ + 3x²
- 0x² - 13x
- -7x² - 13x
0 - 15
Read more about Polynomial Division at: https://brainly.com/question/25289437
#SPJ1
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen.
34
9-ft
3-A
15 ft
3 ft
Answers
The total surface area of this countertop is 522 square feet.Once all of these factors are taken into account, Mrs. Miller can then calculate the total cost of the countertop.
What is surface area?Surface area is the total area of the visible surface of an object, such as a cube or a sphere. It is measured in square units such as square inches, square feet, or square meters. It is important in mathematics, science, and engineering because it is used to calculate the amount of material needed to cover an object, the volume of a container, and other measurements. Surface area is also helpful in solving problems involving friction, heat transfer, and air flow.
Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen. The total surface area of this countertop is 522 square feet. This is calculated by multiplying the length of the countertop (34 feet) by the width of the countertop (15 feet), which yields 510 square feet. Then, the total surface area of the countertop is increased by adding the surface area of the 3-ft by 3-ft corner (9 square feet). Therefore, the total surface area of the countertop is 522 square feet.
Part B
To determine the cost of the countertop, Mrs. Miller would need to consider several factors, such as the material used, the labor required to install the countertop, and any additional fees associated with the purchase. Generally speaking, countertops made of granite, quartz, and marble tend to be more expensive than countertops made of laminate and solid surface. The installation labor cost will vary depending on the complexity of the installation, as well as the type of material used and the size of the countertop. Additionally, there may be additional fees associated with the purchase, such as the cost of delivery and taxes. Once Mrs. Miller has determined all of these factors, she can then calculate the total cost of the countertop.
Conclusion
In conclusion, Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen. The total surface area of this countertop is 522 square feet. To determine the cost of the countertop, Mrs. Miller would need to consider several factors, such as the material used, the labor required to install the countertop, and any additional fees associated with the purchase. Once all of these factors are taken into account, Mrs. Miller can then calculate the total cost of the countertop.
To know more about surface area click-
http://brainly.com/question/16519513
#SPJ1
The reciprocal of h.C.F and lcm of two number are 1/12 and 1/312 respectively. If one of the number is 24. Find the other number?
Answers
The other number is 156.
Let a and b be two numbers, with a = 24.
We know that the product of two numbers' HCF and LCM is equal to the product of the two numbers.
So, we have:
HCF × LCM = a × b
We are given that the reciprocal of HCF is 1/12.
So, HCF = 1 / (1/12) = 12.
We are also given that the reciprocal of LCM is 1/312.
So, LCM = 1 / (1/312) = 312.
12 × 312 = 24 × b
Simplifying, we get:
b = (12 × 312) / 24 = 156
Therefore, the other number is 156.
Learn more about LCM and HCF here
https://brainly.com/question/16881805
#SPJ1
A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).
Answers
The height of the person on the ferris wheel can be modeled by the equation:
h = 20sin(π/4*t) + 21
where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.
Use the general form of the equation for an ellipse with center (0,0) with a vertex at (5,0) and a co-vertex at (2,0)
Answers
(x^2/a^2) + (y^2/b^2) = 1
Since the vertex is at (5,0), we know that a = 5. Since the co-vertex is at (2,0), we know that b = 2.
Plugging these values into the equation, we get:
(x^2/5^2) + (y^2/2^2) = 1
Simplifying, we get:
x^2/25 + y^2/4 = 1
Therefore, the equation of the ellipse with center (0,0), a vertex at (5,0), and a co-vertex at (2,0) is x^2/25 + y^2/4 = 1.
In a recent test cricket match, Steve made 286 runs in both innings which represented 37% of the team total. How many runs did the team make in the match
Answers
The team made approximately 773 runs in the match.
How to find How many runs did the team make in the matchLet's start by setting up an equation to represent the information given in the problem.
Let's call the total runs made by the team "T".
37% of T = 286
To solve for T, we can start by converting the percentage to a decimal:
37% = 0.37
0.37T = 286
Now we can solve for T by dividing both sides of the equation by 0.37:
T = 286 ÷ 0.37
T ≈ 773.0
Therefore, the team made approximately 773 runs in the match.
Learn more about equations at https://brainly.com/question/22688504
#SPJ1
Select the correct answer from each drop-down menu. A system of linear equations is given by the tables. x y -1 1 0 3 1 5 2 7 x y -2 -7 0 -1 2 5 4 11 The first equation of this system is y = x + 3. The second equation of this system is y = 3x − . The solution of the system is ( , ).
Answers
The first equation of this system is y = 2x + 3, the second equation is y = 3x - 1, and the solution of the system is (4, 11).
a) The first equation of this system can be found by using the points given in the first table. We can use the two points (-1, 1) and (0, 3) to find the equation of the line passing through them using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
The slope of the line passing through (-1, 1) and (0, 3) is (3-1)/(0-(-1)) = 2/1 = 2.
Substituting one of the points in the slope-intercept form, we get 1 = 2(-1) + b, which gives us b = 3. Therefore, the equation of the line is y = 2x + 3.
b) Similarly, we can use the points given in the second table to find the equation of the second line. Using the points (0, -1) and (2, 5), we get the slope as
(5-(-1))/(2-0)
= 6/2
= 3.
Substituting one of the points in the slope-intercept form, we get
-1 = 3(0) + b, which gives us b = -1.
Therefore, the equation of the second line is y = 3x - 1.
c) To find the solution of the system, we need to find the point of intersection of the two lines. We can do this by solving the two equations simultaneously.
Substituting the second equation in the first, we get:
2x + 3 = 3x - 1
Simplifying, we get x = 4.
Substituting x = 4 in either of the equations, we get y = 11. Therefore, the solution of the system is (4, 11).
To learn more about equations click on,
https://brainly.com/question/29017443
#SPJ1
please help with an explanation
Answers
It is financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model, as it has a net benefit of $12,000 compared to continuing to use the old boat.
To determine whether Harris Fishing Tours should replace the old boat with the new fuel-efficient model, we need to compare the costs and benefits of each option.
Option 1: Replace the old boat with the new fuel-efficient model
If Harris replaces the old boat with the new fuel-efficient model, they will have to pay $80,000 for the new boat. They can sell the old boat for $32,000, so the net cost of the new boat will be $48,000 ($80,000 - $32,000).
The new boat is expected to be extremely fuel efficient, which means that the fuel costs will be $15,000 per year lower than the old boat. Over the remaining four years of the old boat's useful life, this represents a total savings of $60,000 ($15,000 x 4).
Therefore, the total cost of replacing the old boat with the new fuel-efficient model is $48,000 - $60,000 = -$12,000, which means that this option has a net benefit of $12,000.
Option 2: Continue to use the old boat until it wears out
If Harris decides to continue using the old boat until it wears out, they will not incur the $80,000 cost of purchasing the new boat.
However, they will continue to pay $15,000 per year more in fuel costs than they would with the new boat. Over the remaining four years of the old boat's useful life, this represents a total cost of $60,000 ($15,000 x 4).
In addition, at the end of the four years, the old boat will have no salvage value since it will have reached the end of its useful life.
Therefore, the total cost of continuing to use the old boat until it wears out is $60,000, which means that this option has a net cost of $60,000.
Conclusion
Based on the analysis above, it is more financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model. This option has a net benefit of $12,000, while continuing to use the old boat until it wears out has a net cost of $60,000.
For more questions like Costs click the link below:
brainly.com/question/31041508
#SPJ1