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3 years ago

If f(x)=4x-2 and g(x)=-8x+7, find h(x)=f(x) - g(x)

Mathematics

1 answer:

user100 [1]3 years ago

3 0

Answer:

$h(x)=12x-9$

Step-by-step explanation:

We are given the two functions:

$f(x)=4x-2\text{ and } g(x)=-8x+7$

And we want to find:

$h(x)=f(x)-g(x)$

So, by substitution:

$h(x)=(4x-2)-(-8x+7)$

Simplify. Distribute:

$h(x)=(4x-2)+(8x-7)$

Rearrange:

$h(x)=(4x+8x)+(-2-7)$

Combine like terms. Hence:

$h(x)=12x-9$

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A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $13.50, and the price

timofeeve [1]

Answer:

165 student tickets and 435 adult tickets were sold

Step-by-step explanation:

In this question, we are asked to calculate the number of students and adults tickets sold.

since we do not know these numbers, let the number of student tickets sold be s and the number of adult tickets sold be a

From the question, we are told that a total of 600 tickets were sold.

mathematically, this means that;

a + s = 600 •(i)

The price of students ticket sold is $13.5, this means the total money realized from sales of student ticket = $13.5s

The price of adult ticket sold is $15, this means the total money realized from the sales of adult ticket is $15a

Adding both yields a total of $8,587.5

Hence, mathematically;

13.5s + 15a = 8,587.5. ••••••••(ii)

From equation 1, a = 600 - s , we can input this in the second equation to yield;

13.5s + 15(600-s) = 8,587.5

13.5s + 9,000 - 15s = 8,587.5

2.5s = 9,000 - 8587.5

2.5s = 412.5

s = 412.5/2.5

s = 165 student tickets

Number of adult tickets = 600 - s = 600 - 165 = 435

4 0

4 years ago

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Aleksandr [31]

Answer:

x = 9

Step-by-step explanation:

$a^{2} = c^{2} - b^{2}$

$a^{2} = 15^{2} - 12^{2}$

$a^{2} = 225 - 144$

$a^{2} = 81$

$\sqrt{a^2} = \sqrt{81}$

$a = 9$

7 0

3 years ago

A consumer is considering two different purchasing options for the car of their choice. The first option, which is leasing, is d

Otrada [13]

Answer:

y=250x+4000
y=400x+400

Step-by-step explanation:

Given that:

x represents the number of months of ownership; and
y represents the total paid for the car after ‘x' months.

First Option (Leasing)

250x - y + 4000 = 0

Expressing the equation in the Slope-Intercept Form y=mx+b, we have:

y=250x+4000

Second Option (Financing)

$400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400).

First, we determine the slope of the line joining (0,400) and (10,4400)

$Slope, m= \dfrac{4400-400}{10-0}= \dfrac{4000}{10}=400$

We have:

y=400x+b

When y=400, x=0

400=400(0)+b

b=400

Therefore, the Slope-Intercept Form of the second option is:

y=400x+400

Significance

In the first option, there is a down payment of $4000 and a monthly payment of $250.
In the second option, there is a down payment of $400 and a monthly payment of $400.

Part B

We notice from the graph that after 24 months, the cost for leasing and financing becomes the same ($10,000). Therefore, a consumer will be better off financing since the downpayment for leasing is higher.

i.e

When x=0, y=$4000 for leasing
When x=0, y=$400 for financing

5 0

3 years ago

Write a formula for the distance between a point (x, y) on the graph of y = x^4 and the point (3, 6). Express your answer in ter

Mariana [72]

Distance between points is given by the formula:
$D = \sqrt{(x1-x2 ) ^{2}+ ( y1 - y2) ^{2} }$
We will plug in the coordinates:
$D = \sqrt{( 3-x) ^{2} + ( 6- x^{4} )^{2} }$

5 0

3 years ago

This diagram can be used to prove the Pythagorean theorem.

KatRina [158]

Answer:

D) See that the red and purple triangles can be subtracted from both pictures

Step-by-step explanation:

I just did answered this question on USATestprep

3 0

3 years ago

Read 2 more answers