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3 years ago

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X+4/4=x/x-2 A:{-4,2} B:{-2,4} C:{}

1 answer:

Andreyy893 years ago

3 0

Answer:

<u>The correct answer is B. {-2,4}</u>

Step-by-step explanation:

Let's solve for x, this way:

x + 4/4 = x /x -2

(x + 4) * ((x - 2) = 4 * x

x² - 2x + 4x -8 = 4x

x² - 2x + 4x -8 - 4x = 0

x² - 2x -8 = 0

(x - 4) * (x +2) = 0

x - 4 = 0

x + 2 = 0

x₁ = 4

x₂ = - 2

<u>The correct answer is B. {-2,4}</u>

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Hello,

Part A:

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f(1)=4*2^1=8
2-1=1
(f(2)-f(1))/(2-1)=(16-8)/1=8 ; r_1=8

f(3)=4*2^3=32
f(4)=4*2^4=64
(f(4)-f(3))/(4-3)=(64-32)/1=32 ; r_2=32

Part B:
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Explainations:

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1.) What is the value of cosθ given that (−5, −4) is a point on the terminal side of θ?

jeka57 [31]

Answer:

1) C

2) D

Step-by-step explanation:

1)

We want to find the value of cos(θ) given that (-5, -4) is a point on the terminal side of θ.

This is represented by the diagram below.

Recall that cosine is the ratio of the adjacent side to the hypotenuse.

Find the hypotenuse:

$\displaystlye \begin{aligned} a^2 + b^2 &= c^2 \\ c &= \sqrt{a^2 + b^2} \\ &= \sqrt{(4)^2 + (5)^2} \\ &= \sqrt{41}\end{aligned}$

The adjacent side with respect to θ is -5 and the hypotenuse is √41. Hence:

$\displaystyle \begin{aligned}\cos \theta &= \frac{(-5)}{(\sqrt{41})} \\ \\ &= - \frac{5\sqrt{41}}{41} \end{aligned}$

Our answer is C.

2)

We want to find the value of sin(θ) given that (-6, -8) is a point on the terminal side of θ.

This is represented in the diagram below.

Likewise, find the hypotenuse:

$\displaystyle c = \sqrt{(-6)^2 + (-8)^2} = 10$

Sine is given by the ratio of the opposite side to the hypotenuse.

The opposite side with respect to θ is -8 and the hypotenuse is 10. Hence:

$\displaystyle \begin{aligned}\sin \theta &= \frac{(-8)}{(10)} \\ \\ &= -\frac{4}{5} \end{aligned}$

Our answer is D.

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3 years ago