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Evgen [1.6K]
3 years ago
8

Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).

Mathematics
2 answers:
Trava [24]3 years ago
8 0

Answer:

 x^3 + 8x^2 + 11x-20

Step-by-step explanation:

f(x) = x^2 + 3x − 4

g(x) = x + 5

To find f(x) * g(x) we multiply f(x) with g(x)

f(x) * g(x) = (x^2 + 3x -4) * (x+5)

First multiply each term in f(x) and multiply with x+5

x^2 times x+5 becomes x^3+5x^2

3x times x+5 becomes 3x^2 + 15x

-4 times x+ 5 becomes -4x -20

so f(x) * g(x) = x^3 + 5x^2 +3x^2 + 15x -4x -20

Combine like terms

f(x) * g(x) = x^3 + 8x^2 + 11x-20

Natasha2012 [34]3 years ago
4 0

Answer:    [C]:    " x³ + 8x² + 11x − 20 " .

______________________________________________________

Step-by-step explanation:

______________________________________________________

Given:      "  f(x) =  x² + 3x − 4 " ;   and

                " g(x) =  x + 5  "  ;

Find:         "  f(x) ⋅ g(x) "  :

______________________________________________________

    f(x) ⋅ g(x) =

     " (x² + 3x − 4) (x + 5) " ;

     ↔  " (x + 5) (x² + 3x − 4) " ;

______________________________________________________

<u>Note</u>:  " (a + b) (c + d + e)  =  ac + ad + ae + bc + bd + ae " ;

______________________________________________________

 →  " (x + 5) (x² + 3x − 4)

             =  (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;

             =  (x³) + (3x²)  + (-4x) + (5x²) + (15x) + (-20) ;

             =   x³  + 3x² − 4x + 5x² + 15x − 20 ;

 →  Combine the "like terms" :

          + 3x² + 5x²  =  + 8x²  ;

           − 4x + 15x   = + 11 x ;

______________________________________________________

 → And rewrite:

______________________________________________________

        →   "  x³ +  8x²  +  11x  − 20 " ;

______________________________________________________

       →  which is:  Answer choice:  [C]:   " x³  +  8x²  +  11x  −  20 " .

______________________________________________________

     Hope this helps!

        Best wishes!

______________________________________________________

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Mila [183]

Answer:

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Step-by-step explanation:

7 0
3 years ago
8x - 2y if x=3, y=5<br> (1) 24<br> (2) 15<br> (3) 14 <br> (4) 10
ladessa [460]

Answer: (4) 14

Step-by-step explanation:

8x - 2y if x is 3 and y is 5

8x = 24

2y = 10

24 - 10 = 14

So 8x - 2y is 14.

5 0
3 years ago
Read 2 more answers
Write an equation for the sentence "The product of a number n and 7.7 equals 112.42." Solve for the variable.
pishuonlain [190]

Answer:

7.7n=112.42

n=14.6

Step-by-step explanation:

The product is the result obtained by multiplying two factors. Then, the sentence ""The product of a number n and 7.7 equals 112.42" can be expressed with the following equation:

7.7n=112.42

To solve for the variable "n", you has two apply the Division property of equality and divide both sides of the equation by 7.7

Therefore, the value of "n" is:

\frac{7.7n}{7.7}=\frac{112.42}{7.7}\\\\n=14.6

8 0
3 years ago
Please solve this thank you!
SSSSS [86.1K]

Answer:

1024x^{40}

Step-by-step explanation:

So the first step is to add like terms since you can simplify the numerator by adding the two values sine they have the same variable and degree.

Add like terms:

[\frac{8x^9}{2x}]^5

Divide by 2x (divide coefficient by 2, subtract coefficient degrees)

[4x^8]^5

Multiply exponents and raise 4 to the power of 5

1024x^{40}

The reason you multiply exponents is because you can think about it like this:

(4 * x * x * x * x * x * x * x * x) (this has one 4 and 8 x's because x is raised to the power of 8. Now if you do that 5 times which is what the exponent is doing you're going to have 40 x's and 8 4's. So it's essentially

(4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x). If you group like terms you'll get (4 * 4 * 4 * 4 * 4) *  (x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x). Which simplifies to 4^5 * x ^ (8 * 5) which further simplifies to the answer 1024x^40

6 0
2 years ago
Read 2 more answers
. help needed please​
Anastasy [175]
In order to do this, we would use order of operations. First, Parentheses, which is division with fractions, so we would do KCF,keep it, change it, flip it. keep the first fraction, change the operation to multiplication, then flip the next fraction, making it -7/9 x 3/1. the answer would be -2.33. multiply that by -2, and you would get -4.66, which is your answer. PLEASE MARK BRAINLIEST IF HELPFUL! :))
5 0
3 years ago
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