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Evgesh-ka [11]
3 years ago
5

15 POINTS! + BRAINLIEST.

Mathematics
1 answer:
bezimeni [28]3 years ago
8 0

Answer:

x^6 + 2 x^5 - 6 x^4 + 3 x^2 + 6 x - 18

Step-by-step explanation:

f(x) = x^2 +2x-6

g(x) =x^4+3

We want to find f*g

(f*g)(x) = (x^2 +2x-6)(x^4+3)

Distribute

          =x^2*x^4 +3x^2 +2x*x^4 +2x*3 +-6x^4 -6*3

         = x^6 +3x^ +2x^5 +2x^3 -6x^4 -18

Combine like terms

         =x^6 + 2 x^5 - 6 x^4 + 3 x^2 + 6 x - 18

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Answer:

x = 20

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3 years ago
Which values are the solutions of the compound inequality? Select all that apply.
evablogger [386]

Answer:

b, c, e

Step-by-step explanation:

First, just simplify the inequality.

-18 < 5x - 8 < 17

-10 < 5x      < 25

-2  <  x        < 5

Answers that fit this inequality:

-1, 0, 3

3 0
3 years ago
What is the value of   ?
azamat
Sure! So this is ready as "the cube root of 125". This basically means, "what number cubed can get me 125?"
Let's go through our options.
We can rule out D, as D cubed would be unreasonably big.
We can also rule out C, because 375 cubed is easily over 10000, you know this even if you haven't computed it all, just compute the 300 cubed.
We can rule out B, too. 41 squared is already over 125, therefore it can't be the answer.
Therefore our answer is A, 5. We can check that by cubing 5, and that indeed gets us 125.
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Answer:

3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21

4. The solutions are, x = -2 + √10 and x = -2 - √10

5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;

f(x) = x² - 6·x + 10

Step-by-step explanation:

3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c

The vertex form of the of a quadratic function can be presented based on the above standard form as follows;

f(x) = a(x - h)² + k

Where;

(h, k) = The coordinate of the vertex

h = -b/2a

k = f(h)

Comparing with the given equation, we have;

f(x) = a·x² + b·x + c = x² - 4·x - 17

a = 1

b = -4

c = -17

∴ h = -(-4)/(2 × 1) = 2

h = 2

k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21

k = -21

The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;

f(x) = (x - 2)² - 21

4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12

Dividing the given equation by 2 gives;

x² + 4·x = 6

Which is of the form, x² + b·x = c

Where;

a = 1

b = 4

c = 6

From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²

Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;

x² + 4·x + 4 = 6 + 4

(x + 2)² = 10

x + 2 = ±√10

x = -2 ± √10

The solution are, x = -2 + √10 and x = -2 - √10

5. Given that the value of the vertex = (3, 1), and a = 1, we have;

The vertex, (h, k) = (3, 1)

h = 3, k = 1

Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)

∴ -b = 2 × 3 = 6

b = -6

k = f(h) = a·h² + b·h + c, by substitution, we have;

k = f(3) = 1 × 3² + (-6) × 3 + c = 1

∴ c = 1 - (1 × 3² + (-6) × 3) = 10

c = 10

The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;

f(x) = x² - 6·x + 10

4 0
3 years ago
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