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3 years ago

11

A recreation center offers a membership for $75.Members may take classes for $10 each.Nonmembers pay $15 for these classes.how m

any classes could a nonmember take pay the same total amount as a member?

1 answer:

antoniya [11.8K]3 years ago

8 0

75 +10n = 15n
75 = 5n
15 = n

Therefore 15 classes

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SOLVE THE QUESTION BELOW ASAP

qwelly [4]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) 16 feet

Part C) see the explanation

Step-by-step explanation:

Part A) Graph the function

Let

h(t) ----> the height in feet of the ball above the ground

t -----> the time in seconds

we have

$h(t)=-16t^{2}+98$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

To graph the parabola, find the vertex, the intercepts, and the axis of symmetry

<em>Find the vertex</em>

The function is written in vertex form

so

The vertex is the point (0,98)

Find the y-intercept

The y-intercept is the value of the function when the value of t is equal to zero

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98$

The y-intercept is the point (0,98)

Find the t-intercepts

The t-intercepts are the values of t when the value of the function is equal to zero

For h(t)=0

$-16t^{2}+98=0$

$t^{2}=\frac{98}{16}$

square root both sides

$t=\pm\frac{\sqrt{98}}{4}$

$t=\pm7\frac{\sqrt{2}}{4}$

therefore

The t-intercepts are

$(-7\frac{\sqrt{2}}{4},0), (7\frac{\sqrt{2}}{4},0)$

$(-2.475,0), (2.475,0)$

Find the axis of symmetry

The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

so

$x=0$ ----> the y-axis

To graph the parabola, plot the given points and connect them

we have

The vertex is the point $(0,98)$

The y-intercept is the point $(0,98)$

The t-intercepts are $(-2.475,0), (2.475,0)$

The axis of symmetry is the y-axis

The graph in the attached figure

Part B) How far is the artifact fallen from the time t=0 to time t=1

we know that

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98\ ft$

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

Find the difference

$98\ ft-82\ ft=16\ ft$

Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?

we know that

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

For t=2

$h(t)=-16(2)^{2}+98$

$h(2)=34\ ft$

Find the difference

$82\ ft-34\ ft=48\ ft$

so

The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1

therefore

The distance traveled from t=1 to t=2 is greater than the distance traveled from t=0 to t=1

8 0

2 years ago

What is the equation of the graph shown?

OlgaM077 [116]

<em>Greetings from Brasil...</em>

As we have a line, the function will be given by the expression:

F(X) = AX + B

where

<em>A = ΔY/ΔX</em>

<em>B = where the line intersects the Y axis</em>

Looking at the graph we have already concluded that

B = - 3

A = ΔY/ΔX

A = (5 - 3)/(4 - 3) see attached picture

A = 2

So,

F(X) = AX + B

<h2>F(X) = 2X - 3</h2>

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2 years ago

Emily is buying a new mountain bike on layaway for $324 if she pays $54 each week how many weeks will it take Emily to pay for t

Lapatulllka [165]

Answer: 6 weeks

Step-by-step explanation: $54 x 6 = $324

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2 years ago

A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 5/4 .

Andrei [34K]

The volume of the original prism is calculated by multiplying the area of the base by the height,
volume = (8 cm²)(6 cm) = 48 cm³
By the word dilated we mean to say that the dimensions of the new prism is 5/4 times that of the original solid. If we let x be the volume of the new solid,
x / 48 cm³ = (5/4)³
The value of x from the equation above is equal to 93.75 cm³.

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Answer:

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Step-by-step explanation:

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