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## Eric states that the slopes of perpendicular lines are opposite reciprocals (i.e. that the slope of one is equal to the negative of the reciprocal of the other), and Aviva states that the product of the slopes of perpendicular lines is −1. Who is correct? Why? Explain your reasoning with an example. If one of the lines is vertical and the other one is horizontal, how would your answer change?

Eric’s statement is correct that the slopes of the perpendicular lines are opposites reciprocal with each other compared to Aviva’s. Aviva’s statement is correct but is not usually the case. An example is that when you are given these functions such as y = -2x + 3 and y = 1/2x + 4. The coefficients of the x variable are 2 and negative 1/2. The slopes must be in opposite signs so that the two functions will intersect at a common point and will form a ninety degree angle. This is the very basis of a perpendicular line because if both lines have the same slopes, then both lines are just parallel with each other, they cannot intersect.

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## WHOEVER gives the CORRECT answer FIRST, gets brainliest answer and thanks Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 3 and a horizontal side of 7. The other triangle has a vertical side of 9 and a horizontal side of 21. Could the hypotenuses of these two triangles lie along the same line? (4 points) Yes, because they are both right triangles Yes, because they are similar triangles No, because they are not similar triangles No, because one is larger than the other

WHOEVER gives the CORRECT answer FIRST, gets brainliest answer and thanks Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 3 and a horizontal side of 7. The other triangle has a vertical side of 9 and a horizontal side of 21. Could the hypotenuses of these two triangles lie along the same line? (4 points) Yes, because they are both right triangles Yes, because they are similar triangles No, because they are not similar triangles No, because one is larger than the other

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## The function that represents the average cost per person, including transportation, to a museum is y= 25+8x/x Which statement is true about the graph of the function? The horizontal asymptote y = 0 means the cost approaches zero as the number of people increases. The horizontal asymptote y = 8 means the average cost approaches \$8 as the number of people increases. The vertical asymptote x = 0 means the cost approaches zero as the number of people increases. The vertical asymptote x = 8 means the cost approaches zero as the number of people increases.

The statement that is true about the graph of the function from the equation y = 25 + 8x/x which represents the average cost per person is “The horizontal asymptote y = 8 means the average cost approaches \$8 as the number of people increases.” It means that as x increases which represents the number of people, the value of the transportation to a museum averages to eight dollars.

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## Write equations for the horizontal and vertical lines passing through the point (7, -6).

Write equations for the horizontal and vertical lines passing through the point (7, -6).

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## In sunlight, a vertical stick 6ft tall casts a shadow 2 ft long. At the same time a nearby tree casts a shadow 14ft long. How tall is the tree?

In sunlight, a vertical stick 6ft tall casts a shadow 2 ft long. At the same time a nearby tree casts a shadow 14ft long. How tall is the tree?

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## Referring to a keynesian phillips curve, a reduction in inflation is likely to cause: ____________. at least a slight increase in aggregate demand. a vertical phillips curve because aggregate supply remains fixed. unemployment to remain constant in the long run. at least a slight increase in unemployment.

Referring to a keynesian phillips curve, a reduction in inflation is likely to cause: ____________. at least a slight increase in aggregate demand. a vertical phillips curve because aggregate supply remains fixed. unemployment to remain constant in the long run. at least a slight increase in unemployment.

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## PLSSSSSSSSSS HELP:)Which of the following has the two vertical probes in the proper positions to find the correct value for T?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. How many units to the right of a vertical line through (k, 0) must the fourth vertex be?

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by Therefore, the distance between the points A(8, 9) and B(x, y) is given by Since, distance between A and B is 10 units, so

d = 10.

Therefore, Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## Identify angleA and angleB as either vertical, complementary, or supplementary angles. A. Vertical B. Complementary C. Supplementary

Identify angleA and angleB as either vertical, complementary, or supplementary angles. A. Vertical B. Complementary C. Supplementary

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## Identify angleA and angleB as either vertical, complementary, or adjacent angles. A. Vertical B. Complementary C. Adjacent

Identify angleA and angleB as either vertical, complementary, or adjacent angles. A. Vertical B. Complementary C. Adjacent

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## 1). A tax that takes higher proportion from a low-income person than a rich person is known as a/an __ tax? a). proportional b). regressive c). progressive d). estate 2). Which of the following is an external factor that helps create the business cycle? a). Government spending b).Consumer spending c). Bad weather d). Psychological factors 4). Which of the following is an advantage of investing in a mutual fund? a). Guaranteed profit b). No risk c). Investments are made in only one company d). Professional management 6). A characteristic of a natural monopoly is that a). adding businesses in competition would increase cost to the consumer b). the firm is supported by the consumer and voted into existence by the voters c). the firm is dedicated to the use of natural resources d). there’s no government intervention in the market 7). How could the government fight inflation? a). raise taxes b). lower taxes c). add more unemployment insurance d). increase spending 12). A merger between a company and one of its suppliers is known as a ___ merger? a). vertical b). supply c). demand d). horizontal 15). A tax levied on inherited money is known as a/an __ tax? a). excise b). sales c). estate d). death 19). Each worker doing a small part of the overall manufacturing process is known as? a). specialization b). interchangeable parts c). automation d). appreciation 20). Which of the following is a reason for the growth of federal government spending? a). less demand for services b). growing population c). shrinking population d). deflation Please I Need Help Only With These…..

The Contribution Margin per unit (CM) can be calculated
from the difference of Selling Price per unit (SP) and Total Expenses per unit
(TE).

First, let’s calculate the value of SP:

SP = Sales / Units sold

SP = \$1,043,400 / 22,200 units sold

SP = \$47

Second, calculate all expenses:

Direct materials per unit = \$234,948 / 27,970 units
manufactured = \$8.4

Direct labor per unit = \$131,459 / 27,970 units
manufactured = \$4.7

Variable manufacturing overhead per unit = \$240,542 / 27,970
units manufactured = \$8.6

Variable selling expenses per unit = \$113,220 / 22,200
units sold = \$5.1

TE = \$26.8

Therefore the CM is:

CM = SP – TE

CM = \$47 – \$26.8

CM = \$20.2 per unit

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## The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 22. If the vertical distance from the bottom to the top of the mountain is 689 feet and the gondola moves at a speed of 130 feet per minute, how long does the ride last? Round to the nearest minute.

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by Therefore, the distance between the points A(8, 9) and B(x, y) is given by Since, distance between A and B is 10 units, so

d = 10.

Therefore, Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## If a 70 inch television's diagonal forms a 29° angle with the base of the screen, what is the vertical height (h) of the screen to the nearest inch? 34 in 39 in 51 in 61 in

If a 70 inch television’s diagonal forms a 29° angle with the base of the screen, what is the vertical height (h) of the screen to the nearest inch? 34 in 39 in 51 in 61 in

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## What is the equation of a vertical line passing through (-5,-2)

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## Which statement is true about the graphs of the two lines y = –6 and x =1/6 ? The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope that is undefined, and the graph of x = 1/6 is a vertical line with a slope of 0. The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope that is undefined, and the graph of x =1/6 is a horizontal line with a slope of 0. The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope of 0, and the graph of x =1/6 is a horizontal line with a slope that is undefined. The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope of 0, and the graph of x =1/6 is a vertical line with a slope that is undefined.

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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## Which statement is true about the graphs of the two lines y = –6 and x = ? a The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope that is undefined, and the graph of x = is a vertical line with a slope of 0. b The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope that is undefined, and the graph of x = is a horizontal line with a slope of 0. c The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope of 0, and the graph of x = is a horizontal line with a slope that is undefined. d The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope of 0, and the graph of x = is a vertical line with a slope that is undefined.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## A toy rocket with a mass of 300 g takes off in a vertical direction under the influence of gravity. it burns fuel at the rate of 25 g/s. the exhaust speed of the gases is 80 m/s. what is the speed of the rocket at the end of 10 seconds?

The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

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## Why might vertical systems be a business ethics issue? ? a. ?they threaten the existence of large multinational corporations. b. ?they can increase consumerism and planned obsolescence. c. ?they can result in a channel member having too much control. d. ?they cut out the need for retailers and wholesalers. e. ?they can result in lower wages for factory workers?

Why might vertical systems be a business ethics issue? ? a. ?they threaten the existence of large multinational corporations. b. ?they can increase consumerism and planned obsolescence. c. ?they can result in a channel member having too much control. d. ?they cut out the need for retailers and wholesalers. e. ?they can result in lower wages for factory workers?

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## A tennis ball traveling horizontally at 22.0 m/s suddenly hits a vertical brick wall and bounces back with a horizontal velocity of 18.0 m/s

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## Arms that are longer than legs, and a short stable lumbar spine are traits associated with a. full-time bipedalism b. brachiation c. arboreal quadrupedalism d. vertical clinging and leaping

The correct option is 1.

Step-by-step explanation:

It is given that Inez has to pay 4 percent in closing costs and 16 percent for the down payment on a purchase of \$225,500 with an ARM.

So, Inez has to pay 20% of \$225,500. Therefore Inez has to pay \$45100 as closing cost and down payment.

Over the life of the loan, she will pay \$262,072.72.

The total cost of her house is the sum of \$262,072.72 and \$45100. Because the total cost is the sum of down payment, closing cost and the payments over the life of the loan. Therefore the correct option is 1.

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## A merger between a company and one of its suppliers is known as a _______ merger. A. supply B. demand C. horizontal D. vertical Supply is not the answer

Depreciation=(equipment cost-salvage value)/useful life

Depreciation=(16,950−4,200)÷6
=2,125 per year

Book value after 3 years
=16,950−2,125×3
=10,575

Now find the amount of depreciation to be charged against the equipment during each of the remaining years of its useful life
Depreciation=(equipment cost-salvage value)/useful life

Depreciation=(10,575−1,695)÷3
=2,960

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## If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.

If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.

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## Let theta denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the Bob is m, then the tension in string is

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## A building 300 feet tall casts a 100 foot long shadow. if a person looks down from the top of the? building, what is the measure of the angle between the end of the shadow and the vertical side of the building?

Answer: If two angles are equal to the same measure, then
the angles are congruent.

That is actually the definition of congruent. Whenever they
throw the same value, they are called congruent.

There is something that proves that PTR and STQ will always
be equal to the same measure, and it was not among the given options:

Acording to the construction protocol, one side of PTR (the
PT side) is opposite to one side of STQ (the TQ side). We call two rays opposite
when they belong to the same line but they have different directions (for example,
one goes to the left and the other one goes to the right). Try building it and
you will see it! The same happens with the other sides: TR is opposite to ST. Whenever
this happens, we call those two angles a vertical pair and they are
always the same size. You can prove that tying it up with linear pairs,
which sum 180°. An angle forms a linear pair with another angle whenever they share a side
and the other two sides are in the same line.

If a and b are supplementary angles, then a+b=180°

So a=180°-b

If b and c are adjacent angles, then b+c =180°

So c=180°-b

This proves that c and a are the same size.

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