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3 years ago

Analyze the diagram below and complete the instructions that follow?

Mathematics

1 answer:

yan [13]3 years ago

6 0

Answer:

The exact value of tan(M) is 5/12 ⇒ answer (C)

Step-by-step explanation:

* Lets revise the trigonometry functions

- In ΔABC

# m∠B = 90°

# Length of AB = a , length of BC = b and length of AC = c

# The trigonometry functions of angle C are

- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse

- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse

- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C

* Now lets solve the problem

- In ΔONM

∵ m∠N = 90°

∵ MN = 12

∵ ON = 5

∵ tan(M) = ON/NM ⇒ opposite side of ∠(M) ÷ adjacent side of ∠(M)

∴ tan(M) = 5/12

* The exact value of tan(M) is 5/12

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2 years ago

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Step-by-step explanation:

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5 0

2 years ago

Determine the intercepts of the line. -5x-4y=10

storchak [24]

Answer:

$x-intercept:(-2,0)\\\\y-intercept:(0,-\frac{5}{2})$

Step-by-step explanation:

The y-intercept is where x is 0 (0,y)

The x-intercept is where y is 0 (x,0)

Insert 0 as the value for x to find the corresponding y value:

$-5(0)-4y=10$

Simplify multiplication:

$0-4y=10\\\\-4y=10$

Isolate the variable. Divide both sides by 4:

$\frac{-4y}{4}=\frac{10}{4} \\\\-y=\frac{10}{4} \\\\-y=\frac{5}{2}$

Make the variable positive. Multiply both sides by -1:

$-1(-y)=-1(\frac{5}{2})\\\\y=-\frac{5}{2}$

The y-intercept is at $(0,-\frac{5}{2})$ .

Insert 0 as the value for y to determine the value of x:

$-5x-4(0)=10$

Simplify multiplication:

$-5x-0=10\\\\-5x=10$

Isolate x. Divide both sides by 5:

$\frac{-5x}{5} =\frac{10}{5} \\\\-x=2$

Multiply both sides by -1:

$-1(-x)=-1(2)\\\\x=-2$

The x-intercept is at $(-2,0)$ .

:Done

8 0

2 years ago

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Rashid [163]

Answer:

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3 years ago