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3 years ago

Factor completely 25x2 − 36.

Mathematics

2 answers:

Ivenika [448]3 years ago

6 0

25x² - 36
25x² + 30x - 30x - 36
5x(5x) + 5x(6) - 6(5x) - 6(6)
5x(5x + 6) - 6(5x + 6)
(5x - 6)(5x + 6)

The answer is C.

kondaur [170]3 years ago

5 0

Answer:

Option (3) is correct.

The factored form of given equation $25x^2-36$ is $(5x+6)(5x-6)$

Step-by-step explanation:

Given : equation $25x^2-36$

We have to factorize the given equation completely.

Consider the given equation $25x^2-36$

Using algebraic identity $a^2-b^2=(a+b)(a-b)$

We have ,

$25x^2-36$ can be written as $(5x)^2-(6)^2$

Applying above idenity, we have,

$(5x)^2-(6)^2=(5x+6)(5x-6)$

Thus, the factored form of given equation $25x^2-36$ is $(5x+6)(5x-6)$

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3 years ago

Prove that sin3a-cos3a/sina+cosa=2sin2a-1

Sloan [31]

Answer:

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

Step-by-step explanation:

we are given

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

we can simplify left side and make it equal to right side

we can use trig identity

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now, we can plug values

$\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}$

now, we can simplify

$\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}$

$\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}$

$\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}$

now, we can factor it

$\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}$

$\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can use trig identity

$sin^2(a)+cos^2(a)=1$

$\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can cancel terms

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now, we can simplify it further

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now, we can use trig identity

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7 0

3 years ago

Read 2 more answers

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deff fn [24]

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7 0

3 years ago

Read 2 more answers

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ikadub [295]

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5 0

3 years ago

Find the measures of two angles, one positive and one negative, that are coterminal with <img src="https://tex.z-dn.net/?f=%5Cfr

aleksandrvk [35]

Answer:

a. 11/5 pi; -9/5 pi

Step-by-step explanation:

Coterminal angles are those which have a common terminal side. For example 30° is coterminal with −330° and 390° (see figure).

From the example we can see that the following expressions must be fulfilled:

positive angle - reference angle = 360°

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where positive angle is 390°, reference angle is 30° and negative angle is -330°. In this problem reference angle is pi/5. Also, we have to change 360° for its equivalent in radians, i. e., 2 pi. So,

positive angle - pi/5 = 2 pi

positive angle = 2 pi + pi/5

positive angle = 11/5 pi

pi/5 - negative angle = 2 pi

negative angle = pi/5 - 2 pi

negative angle = -9/5 pi

5 0

3 years ago