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3 years ago

Solve the expression for x: (4-2)(x-2)=4x-8

1 answer:

ivann1987 [24]3 years ago

5 0

First, distribute the left side. You should get 4x-8-2x+4=4x-8. Then, get all the xs on one side.

4x-2x-4x-8+4=-8

Then, put the numbers on one side.

4x-2x-4x=-8+8-4

Then, add it up.

-2x=-4

Then, solve for x.

(-2x)/(-2)=(-4)/(-2)

x=2

Hope that helps!

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Your family goes to a Southern-style restaurant for dinner. There are 5 people in your

AURORKA [14]

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3 years ago

Find the slope passes through (-5,2) and (3,3)

kykrilka [37]

Answer:

1/8

Explanation:

y2-y1/x2-x1

3-2/3-(-5) = 1/8

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2 years ago

Thomas bought a desk with a retail sales price of $128 and paid $10.37 for sales tax. What is the sales tax rate where Thomas bo

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10.37/128 = 8.1%. Is the rate of tax

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3 years ago

The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

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

The vertex represent a maximum

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long.

givi [52]

<h2>Hello!</h2>

The answer is: There are a total of 16 skits in the video.

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

$TotalDuration=Introduction+n*Skit$

Second equation:

$Skit=6Minutes$

Where,

$TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes$

So, replacing and substituting the second equation into the first equation we have:

$101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16$

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

$101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes$

Have a nice day!

8 0

3 years ago