A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function? y =

A line is drawn on a coordinate grid by the equation y = 4. Which of the following lines would represent a row parallel to it?

dedylja [7]

Y = and then any number you want to put there

8 0

3 years ago

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Kendra dives off of a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation

il63 [147K]

Answer:

1) How high is the diving board?:  6 feet above the water surface

2) How deep does the diver dive into the water?: 6.5feet into the water

3) At what horizontal distance from the board does the diver enter the water? 1 feet from the board

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive? 6 feet from the board

Explanation:

The dive is modeled by the equation h(x) = x² - 7x + 6.

Two important features that you must notice quickly are:

That is a quadratic function, which is a parabola.

Since the leading term, x², is positive, the parabola open upwards, and the vertex is a minimum.

As for the questions:

1) How high is the diving board?

The diving board is the place from which Kendra dives off. At this point, the horizontal distance, x, from the diving board is 0.

Then, the height will be given by h(x) with x = 0. Substitute into the equation and compute:

h(0) = 0² - 7(0) + 6

h(0) = 0 - 0 + 6

h(0) = 6

Therefore, the diving board is 6 feet above the water surface.

2) How deep does the diver dive into the water?

This is the minimum heigth given by the function h(x).

As explained above, this is the vertex of the parabola.

You can find the x-coordinate of the vertex with the equation:

x-coordinate of the vertex = -b/(2a)

Where b and a are the coefficients of the linear term and the quadratic terms in the equation for h(x), respetively:

a = 1
b = -7

x-coordinate = - (-7) / (2 × 1) = 7/2 = 3.5

Now you can find h(x) for x = 3.5

h(3.5) = (3.5)² - 7(3.5) + 6 = 12.25 - 24.5 + 6 = - 6.25

That is 6.25 feet below the water surface.

3) At what horizontal distance from the board does the diver enter the water?

That is the x-intercept of the function. This is, the value of x when h(x) = 0.

Thus, solve the equation 0 = x² - 7x + 6.

You can factor the equation:

Find two numbers that add up -7 and their product is +6. Those are - 6 and -1:

0 = (x - 1) (x - 6)

Using the zero product property:

(x - 1) = 0 or (x - 6) = 0

x = 1 or x = 6

Thus, you have two solutions, which are the two x-intercepts of the funtion.

x = 1 represents the horizontal distance from the board where the diver enters the water.

The other solution is the answer to the next question.

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?

As explained above, the equation has two x-intercepts. They both are the points where the parabola crosses the x-axis, which is when the height, h(x) is 0. That height is the surface of the water level.

The first x-intercept is the point (horizontal distant from the board) where the diver enters the water, such as asserted above.

The other x-intercept is where the diver comes to the surface of water after the dive and after being submerged in the water: the diver enters the water, dives 6.5feet into the water, and returns to the surface.

Thus, this is the solution x = 6 for h(x) = 0.

Hence, Kendra comes to the surface of water at 6 feet from the board.

7 0

3 years ago

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Write the equation of a line perpendicular to y=1/2x + 8 that passes through ( 4, 9 ).

iogann1982 [59]

Answer:y = - 2x + 17

Step-by-step explanation:

The equation of a line, represented in the slope-intercept form, is

y = mx + c

Where

Slope = m

c = intercept

Looking at the equation given,

y=1/2x + 8

Slope,m = 1/2

If a line is perpendicular to a another line, then the slope of one line is equal to the negative reciprocal of the other line. It means that the slope of the perpendicular line that passes through that passes through ( 4, 9 ) will be -2

To determine c,

We will substitute m = -2, y = 9 and x = 4 into the slope intercept equation,

y = mx + c. It becomes

9 = -2 × 4 + c

9 = -8 + c

c = 9 + 8 = 17

The equation becomes

y = - 2x + 17

4 0

3 years ago

Fuel economy. Although the Environmental Protection Agency (EPA) establishes the tests to determine the fuel economy of new cars

never [62]

Answer:

95% confidence interval for the mean city mpg for the model is 28.156±0.791 that is (27.365,28.947)

Step-by-step explanation

Confidence Interval can be calculated using M±ME where

M is the mean miles per gallon (mpg) values for the models the EPA investigated

ME is the margin of error from the mean

And margin of error (ME) from the mean can be calculated using the formula

ME= $\frac{t*s}{\sqrt{N} }$ where

t is the corresponding statistic in the 95% confidence level

s is the standard deviation of the sample

N is the sample size (16)

mean miles per gallon (mpg) values can be calculated dividing the sum of the samples by sample size, which yields 28.156

standard deviation of the sample distribution can be calculated by adding square differences from the mean and dividing by sample size, which yields 1.437

statistic in the 95% confidence level with 15 degrees of freedom is 2.131

Then ME= $\frac{2.131*1.437}{\sqrt{15} }$ ≈ 0.791

95% confidence interval would be 28.156±0.791 that is (27.365,28.947)

8 0

4 years ago

Sa se determine masurile unghiurilor formate de doua inaltimi ale unui triunghi echilateral

Inessa [10]

Let's determine the
measures of the angles
formed by two heights of an equilateral triangle.

7 0

4 years ago

A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function? y = –x