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3 years ago

If a polynomial function f(x) has roots 4 - 131 and 5, what must be a factor of f(x)?

Mathematics

1 answer:

pantera1 [17]3 years ago

5 0

Answer:

(x - 4), (x + 131), and (x - 5) must all be factors of f(x).

Step-by-step explanation:

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Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

3 years ago

If 5x = 30 then x is equal to

max2010maxim [7]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Can someone please help if you can you are amazing and awesome

Ainat [17]

Answer:

domain(-4,6) and range(-1, 8)

Step-by-step explanation:

domain is an imput on x axis, and range on y

4 0

3 years ago

What is y=-3x written in standard form

nataly862011 [7]

This would be 3x + y = 0.

I hope this helps!

5 0

3 years ago

What properties makes the equation ture?

Oksi-84 [34.3K]

Answer:

A.2z+5=5+2z

Associative properties

Distributive properties

Commutative properties

Indentity propertie

5 0

3 years ago