Substitution Property of Equality

Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ?

vitfil [10]

Assume that f(5)=8. So, (5, 8) is a point in the graph of f.

For g(x) to give us 8, we need x to be 12, because in that case we would have:

g(12)=f(12-7)=f(5), which is 8. Thus, (12, 8) is a point on the graph of g.

Comparing (5, 8) in f, and (12, 8) in g, we can see that the graph of g is the graph of f shifted 7 units to the right.

Answer: <span>C) The graph of g(x) is the graph of f(x) translated 7 units right.</span>

6 0

3 years ago

42 of the 150 employees at Carlo's Car Repair wear contact lenses. What percent of the employees wear contact lenses?

antiseptic1488 [7]

$\frac{42}{150}$ ÷ 2 = $\frac{21}{75}$

$\frac{21}{75}$ ÷ 3 = $\frac{7}{25}$

$\frac{42}{150}$ = $\frac{7}{25}$

Then, divide 7 by 25 because 25 is the divisor

7 ÷ 25 = 0.28

28% is the answer (:

6 0

3 years ago

Peter works at Silly's and makes $33.19 an hour. He also collects a 5.3% commission on final weekly sales. Last month, he worked

Romashka-Z-Leto [24]

Answer:

$10,318.62

Step-by-step explanation:

We have been given that works at Silly's and makes $33.19 an hour. He also collects a 5.3% commission on final weekly sales. If he works over 40 hours during any week, he earns double his hourly wage.

Peter's hourly charges during 1st and 2nd week would be $33.19 and hourly charges during 3rd and 4th week would be 2 times $33.19.

First of all, we will find total hourly income as:

$\text{Total hourly income}=\$33.19(30+40)+2\times \$33.19(49+55)$

$\text{Total hourly income}=\$33.19(70)+\$66.38(104)$

$\text{Total hourly income}=\$2323.3+\$6903.52$

$\text{Total hourly income}=\$9226.82$

Now, we will find income from commission on sales as:

$\text{Income from commission on sales}=\frac{5.3}{100}(4500+5500+3800+6800)$

$\text{Income from commission on sales}=0.053(20600)$

$\text{Income from commission on sales}=1091.8$

Peter's total earnings is the last month: $\$9226.82+\$1091.8=\$10,318.62$

Therefore, Peter's total earnings in last month was $10,318.62.

5 0

3 years ago

A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of

Ivenika [448]

The equation for the height of the rocket at time t given

$h= -16t^2+192t$

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

$h= -16t^2+192t$

$560 = -16t^2+192t$

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

$560 = -16(t^2 - 12t)$

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

$560/-16 = -16(t^2-12t)/-16$

$-35 = t^2 -12t$

Now we will move -35 to the righ side by adding 35 to both sides.

$-35+35 = t^2-12t+35$

$0 = t^2 -12t+35$

$t^2-12t+35 = 0$

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

$t^2-12t+35 =0$

$(t-5)(t-7) =0$

So by using zero product property we will get

$t-5 =0$

$t-5+5 = 0+5$

$t=5$

Also $t-7 =0$

$t-7+7 = 0+7$

$t=7$

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

$h= -16t^2+192t$

$0= -16t^2 + 192 t$

$0 = -16(t^2-12t)$

$-16(t^2-12t) = 0$

We will move -16 to the other side by dividing it to both sides.

$-16(t^2-12t)/-16 = 0/-16$

$t^2-12t = 0$

We will take out the common factor t from the left side. By taking out t we will get,

$t(t-12) = 0$

We will use zero product property now. By using that we will get,

$t = 0$

ans also $t-12 = 0$

$t-12+12 = 0+12$

$t = 12$

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0

3 years ago

Rob is saving to buy a new MP3 player. For every $14 he earns babysitting, he saves $6. On Saturday, Rob earned $28 babysitting.

ddd [48]

He saved $12 from Saturday babysitting

7 0

3 years ago

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