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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.

You might be interested in
Factor completely 2x^3 + 6x^2 + 10x + 30
andrezito [222]

Answer:

The factored expression is 2(x² + 5)(x + 3).

Step-by-step explanation:

Hey there!

We can use a factoring technique referred to as "grouping" to solve this problem.

Grouping is used for polynomials with four terms as a quick and easy factoring method to remove the GCF and get down to the initial terms that create the expression/function.

Grouping works in the following matter:

  1. Given equation: ax³ + bx² + cx + d
  2. Group a & b, c & d: (ax³ + bx²) + (cx + d)
  3. Pull GCFs and factors

Let's apply these steps to the given equation.

  1. Given equation: 2x³ + 6x² + 10x + 30
  2. Group a & b, c & d: (2x³ + 6x²) + (10x + 30)
  3. Pull GCFs and factors: 2x²(x + 3) + 10(x + 3)

As you'll see, we have a common term with both sides of the expression. This term, (x + 3), is a valuable asset to the factoring process. This is one of the factors for our expression.

Now, we use our GCFs to create another factor.

  1. List GCFs: 2x², 10
  2. Create a term: (2x² + 10)

Finally, we'll need to simplify this one by taking another GCF, 2.

  1. Pull GCF: 2(x² + 5)

Now that we have this term, we need to understand that this <em>could</em> also be factored further using imaginary numbers, but it is also acceptable to leave it in this form.

Therefore, we have our final factors: 2(x² + 5) and (x + 3).

However, when we factor, we place all of our terms together. This leaves us with the final answer: 2(x² + 5)(x + 3).

7 0
2 years ago
Gabriel divides 64 grapes among his 15 friends. How many grapes does Gabriel give each friend?
kirza4 [7]

each friend would get 4 grapes, there will be some loftover at the end

8 0
3 years ago
Consider the equation 2x+1=16
Aliun [14]

Step-by-step explanation:

2x + 1 = 16

2x = 15 (subtract 1 on both sides)

x = 7.5 (divide 2 om both sides)

Since 7.5 is not an integer, (a) is No.

However 7.5 is rational, therefore (b) is Yes.

6 0
2 years ago
Read 2 more answers
. Ramu took a loan of 50000 rupees from a bank which charges 10% interest, compounded an- nually. He repaid 10000 rupees after o
Setler79 [48]

Answer:

= 30,550 rupee owed

Step-by-step explanation:

yr1 = 50000 x 0.10^1 = 5000

5000 - 10000 = 5000 credit from debt.

yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt

yr 3 = 50000 x 1.10^3 = 50 debit from debt

5000 + 500 = 15000 where 50,000 owed initially and yr1 and yr 2 paid in full interest of 5500 and we deduct this from his payment = 25000-5500 =

19500 paid of initial and nothing owed on interest.

50000-19500= 30,500 rupees owed + 50 rupee interest.

= 30,550 rupee owed

4 0
2 years ago
Read 2 more answers
30 POINTS please help me!
Stels [109]
To prove a similarity of a triangle, we use angles or sides.

In this case we use angles to prove

∠ACB = ∠AED (Corresponding ∠s)
∠AED = ∠FDE (Alternate ∠s)

∠ABC = ∠ADE (Corresponding ∠s)
∠ADE = ∠FED (Alternate ∠s)

∠BAC = ∠EFD (sum of ∠s in a triangle)

Now we know the similarity in the triangles.

But it is necessary to write the similar triangle according to how the question ask.

The question asks " ∆ABC is similar to ∆____. " So we find ∠ABC in the prove.

∠ABC corressponds to ∠FED as stated above.
∴ ∆ABC is similar to ∆FED

Similarly, if the question asks " ∆ACB is similar to ∆____. "
We answer as ∆ACB is similar to ∆FDE.

Answer is ∆ABC is similar to ∆FED.
7 0
3 years ago
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