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Rainbow [258]
1 year ago
14

I need to know the new equation, I’ve provided a picture

Mathematics
1 answer:
Juli2301 [7.4K]1 year ago
3 0

Hello there. To solve this question, we'll simply have to make x => x + 5 in the function.

Given the function:

f(x)=4x^2-3^{}

We have to determine f(x + 5)

By making x => x + 5 in this function, we get:

f(x+5)=4\cdot(x+5)^2-3

Now remember the binomial expansion of order 2:

(a+b)^2=a^2+2ab+b^2

Therefore we have:

f(x+5)=4\cdot(x^2+2\cdot x\cdot5+5^2)-3

Multiply the terms inside parentheses and calculate the square.

f(x+5)=4\cdot(x^2_{}+10x+25)-3

Apply the distributive property

f(x+5)=4x^2+4\cdot10x+4\cdot25-3

Multiply and add the numbers

\begin{gathered} f(x+5)=4x^2+40x+100-3 \\ \boxed{f(x+5)=4x^2+40x+97} \end{gathered}

This is the answer we're looking for.

A way of showing this is the correct answer is to make x = 1 and x = 6 in the former function:

\begin{gathered} f(1)=4\cdot1^2-3=4\cdot1-3=4-3=1 \\ f(6)=4\cdot6^2-3=4\cdot36-3=144-3=141 \end{gathered}

Then making x = 1 in the expression we found after:

f(1+5)=f(6)=4\cdot1^2+40\cdot1+97=4+40+97=141

As expected.

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zubka84 [21]

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7 0
3 years ago
As an incoming college freshman, Tina received a 10-year $9,900 Federal Direct
Ksju [112]

The amount charged on the loan which is the loan interest rate, increases as the time after the initial amount is credited into the account increases.

  • The interest on the Federal Direct Unsubsidized Loan after 4 years 6 months is <u>$1,911.195</u>

Reasons:

The given parameter are;

Loan amount, the principal, P = $9,900

Duration of the loan = 10 years

Loan interest rate, R = 4.29%

Required:

The amount of interest that will accrue while she is still in school and over the 6-months grace period for the freshman loan.

Solution:

Based on a similar question on an online source, we have;

Interest, I = P × R × T

Where;

T = The time = The time the freshman is in school + 6 months

Therefore, normally, we have;

T = 4 years + 6 months = 4.5 years

R = 4.29% = 0.0429

Therefore;

Interest, I = 9,900 × 0.0429 × 4.5 = 1911.195

The interest that will accrue while she is still in school and over the 6-months grace period for the loan,<em> I</em> = <u>$1,911.195</u>

Learn more about the interest rate here:

brainly.com/question/1368015

6 0
2 years ago
The coordinate (1,3) is a solution to 2x-3y=-7<br><br> True <br><br> False
Natalija [7]
True because just plug in (1,3) for x and y and solve it out.
Plugging it in gives you 2(1)-3(3)=-7 which simplifies to 2-9=-7, which is true.
5 0
4 years ago
5x - 12 = 13, solve using algebra.
ella [17]

Step-by-step explanation:

5x-12=13

5x -12 =13

+12=+12

<u>5x</u>= <u>25</u>

5 =. 5

x=5

3 0
3 years ago
Read 2 more answers
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