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3 years ago

Factor the equation.

Mathematics

1 answer:

goblinko [34]3 years ago

3 0

Answer:

$(5t+3), (t+3), (t-3)$

Step-by-step explanation:

Reorder terms.

$5t^3+3t^2-45t-27$

Factor out the greatest common factor from each group

$t^2(5t+3)-9(5t+3)$

Factor the polynomial by factoring out the greatest common factor, $5t +3$

$(5t+3)(t^2-9)$

Factor.

$(5t+3), (t+3), (t-3)$

hope this helps :)

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A car park has no parking spaces on the first floor. The second floor has double the amount of spaces on the first floor. The th

Artist 52 [7]

Answer:

85 parking spaces

Step-by-step explanation:

Given that :

Parking spaces on floors :

Let first floor = x

Second floor = 2x

Third floor = 2x + 3

Total parking spaces = 428

THEREFORE ;

x + 2x + 2x + 3 = 428

5x + 3 = 428

5x = 428 - 3

5x = 425

x = 425 / 5

x = 85

Hence, there are 85 parking spaces on the first floor

7 0

3 years ago

If f(x) = x^2 -5x +1 and g(x) =5x+4 what is the value of g•f (-2)

Arlecino [84]

Answer:

The value of $gof (-2)=79$

Step-by-step explanation:

We have

$f(x) = x^2 -5x +1 \\\\f(-2) = (-2)^2 -5\times-2 +1 \\\\=15$

Now we need to find

$gof (-2)=g(15)$

$g(15) =5\times15+4\\\\=79$

5 0

2 years ago

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Alex17521 [72]

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7 0

3 years ago

Did ari and Cal walk the same distance? Explain

Setler [38]

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3 years ago

The equation for the ellipse given is 4x^2+9y^2-16x+18y-11

natita [175]

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

$\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) = 25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

$\dfrac{4\cdot (x - 2)^2}{36} + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}$

$\therefore \dfrac{ (x - 2)^2}{9} + \dfrac{ (y + 1)^2}{4} = \dfrac{ (x - 2)^2}{3^2} + \dfrac{ (y + 1)^2}{2^2} = 1$

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

8 0

3 years ago

Factor the equation.​

Factor the equation.