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Svet_ta [14]
3 years ago
14

Factor completely 15x^5 + 12x^4-24x^3-3x^2

Mathematics
1 answer:
diamong [38]3 years ago
7 0

Answer:

3x^2 (5x^3 + 4x^2 - 8x - 1)

Step-by-step explanation:

The given expression is 15x^5 + 12x^4-24x^3-3x^2

Here we have to find the GCF of all the above terms.

The GCF is 3x^2, let's take out 3x^2 and write the remaining terms in the parenthesis.

15x^5 + 12x^4-24x^3-3x^2

=3x^2 (5x^3 + 4x^2 - 8x - 1)

Therefore, the factors are 3x^2 and (5x^3 + 4x^2 -8x -1).

15x^5 + 12x^4-24x^3-3x^2 = 3x^2 (5x^3 + 4x^2 -8x -1)

Thank you.

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(cotx+cscx)/(sinx+tanx)
Butoxors [25]

Answer:   \bold{\dfrac{cot(x)}{sin(x)}}

<u>Step-by-step explanation:</u>

Convert everything to "sin" and "cos" and then cancel out the common factors.

\dfrac{cot(x)+csc(x)}{sin(x)+tan(x)}\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)}{1}+\dfrac{sin(x)}{cos(x)}\bigg)\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg[\dfrac{sin(x)}{1}\bigg(\dfrac{cos(x)}{cos(x)}\bigg)+\dfrac{sin(x)}{cos(x)}\bigg]\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)}{cos(x)}+\dfrac{sin(x)}{cos(x)}\bigg)

\text{Simplify:}\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)+sin(x)}{cos(x)}\bigg)\\\\\\\text{Multiply by the reciprocal (fraction rules)}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)cos(x)+sin(x)}\bigg)\\\\\\\text{Factor out the common term on the right side denominator}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)(cos(x)+1)}\bigg)

\text{Cross out the common factor of (cos(x) + 1) from the top and bottom}:\\\\\bigg(\dfrac{1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)}\bigg)\\\\\\\bigg(\dfrac{1}{sin(x)}\bigg)\times cot(x)}\qquad \rightarrow \qquad \dfrac{cot(x)}{sin(x)}

6 0
3 years ago
Do anybody know geometry?
choli [55]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
4. Determine whether the statement is true or false. Prove the statement directly from the definition if it is true, and give a
natta225 [31]

Answer:

The statement is false.

Step-by-step explanation:

Let a and b represent two odd integers.

The average (A) is defined by:

A=\frac{a+b}{2}

In order to prove the statement, you have to show that it's true for all odd integers. But, to disprove it, you just have to find a counterexample where the statement is false.

Notice that it is easier to try to find a counterexample.

For example, a=3 and b=5

A= \frac{3+5}{2} = \frac{8}{2} = 4

The result of the average is even, therefore the statement is false.

The previous calculation is a counterexample.

3 0
3 years ago
Name the multiplication property shown the equation 12 • m = m • 12.
Levart [38]

Answer:

a. commutative

Step-by-step explanation:

rearranging of elements in an equation

5 0
3 years ago
A kite flying in the air has an 11 - ft line attached to it. Its line is pulled taut and casts an 8 - ft shadow. Find the height
Fofino [41]
The line, shadow and the height form a right angled triangle so we can apply the Pythagoras theorem here:-

11^2 = h^2 + 8^2       where h = height of the kite
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h^2 = 57
h = 7.55 ft to the nearest foot   Answer
5 0
3 years ago
Read 2 more answers
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