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3 years ago

What are the Factors of -18

Mathematics

1 answer:

postnew [5]3 years ago

7 0

The factors of -18 are 1, 2, 3, 6, 9, 18 and their negative counterparts :)

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Determine the awnser to (-5) +4 and explain the steps using a number line

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-5 0 4

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(-5) + 4 = -1 = 5 - 4 = 1

(But take the symbol of the bigger number, which is 5) (-)

Hope helps!-Aparri

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Find an nth-degree polynomial function with real coefficients satisfying the given conditions.

lesya692 [45]

Answer:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

Step-by-step explanation:

We want to find a third degree polynomial with zeros x = 2 and x = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since x = 2i is a root, x = -2i must also be a root.

Hence, we will have the three factors:

$\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))$

Where a is the leading coefficient.

Expand and simplify the second and third factors:

$\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}$

Hence:

$\displaystyle f(x) = a(x-2)(x^2+4)$

Since f(-1) = 30:

$\displaystyle \begin{aligned} f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}$

In conclusion, third degree polynomial function is:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

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3 years ago

4. Miguel is helping his mom paint his home. He finished 2 rooms in ⅓ of an hour. How many rooms can he paint in 1 hour?

lilavasa [31]

Answer: 6

Step-by-step explanation:

Let's use a rule of three here.

2 rooms in 1/3 h

x rooms in 1 h

$\frac{2}{x}=\frac{\frac{1}{3} }{1}$

Solve for x;

$x=\frac{2*1}{\frac{1}{3} }$

Remember that when you divide by a fraction, you invert the fraction and multiply by the numerator.

1/3 inverted is 3/1 or 3

$x=(2*1)*3$

$x=(2)*3\\x=6$

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2 years ago

Can someone please help me on this question

Anastasy [175]

$(7,-3)$
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3 years ago