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3 years ago

Factor the polynomial: 462 + 15b - 4

Mathematics

1 answer:

kirza4 [7]3 years ago

8 0

Answer:

15( $\frac{458}{15}$ +b) or

15(b+ $\frac{458}{15}$ )

Step-by-step explanation:

First we can subtract the 4.

458 + 15b

Now we need to find the GCF, but they do not share any kinds of factors together. This might look ugly, but it is what it is. We factor out 15 to get b by itself.

15( $\frac{458}{15}$ +b) or

15(b+ $\frac{458}{15}$ )

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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

4 0

3 years ago

What is -8 -10 ÷ 2+8=?

jek_recluse [69]

is 3

because like terms

-10/2=-5

-5+8=3

so, 3 is your answer

4 0

3 years ago

What is the slope of the line? -2/5 2/5 5/2 1/3

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

(0, 3) (5, 1)

(1-3)/(5-0) = -2/5 is the slope

6 0

3 years ago

Read 2 more answers

Determine sun or difference -3 1/3 + 2 2/5

Artist 52 [7]

Answer:

-14/15

Step-by-step explanation:

First, you want to turn each mixed number into an improper fraction. So you get -10/3 + 12/5. Then you want to get the same denominator, and the LCD happens to be 15. You get -50/15 + 36/15. Addition is commutative, so you can do something like this: 36/15 - 50/15. You can do 36-50=-14, and then add the denominator to get -14/15.

8 0

3 years ago

M is the midpoint of CF (line over it) for the points C(3,4) and F(9,8). Find MF

elena55 [62]

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\(\frac{3 + 9}{2}, \frac{4 + 8}{2}) \\(\frac{12}{2}, \frac{12}{2}) \\(6, 6)$

Midpoint of CF: (6, 6)

3 0

3 years ago