What is the tangent of angle M? A. 12/35 B. 37/35 C. 12/37 D. 35/12

Solve for n. n - 26 = -13 n =

JulsSmile [24]

N = 13, 13 - 26 = -13

3 0

3 years ago

Which expressions show how to calculate the volume of this prism? Check all that apply. 1 + 7(4) 1(4)(7) 4(4)(4) 4 + 1 + 7 4(7)(

lyudmila [28]

Answer:

1(4)(7)

4(7)(1)

7(4)(1)

Step-by-step explanation:

5 0

3 years ago

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In ΔSTU, the measure of ∠U=90°, TU = 6.6 feet, and US = 2.3 feet. Find the measure of ∠S to the nearest tenth of a degree.

zimovet [89]

Answer:

70.8°

Step-by-step explanation:

The sides and angles are related in a right triangle such that ...

Tan = Opposite/Adjacent

tan(S) = UT/US = 6.6/2.3

The inverse tangent function is used to find the angle from its value:

∠S = arctan(6.6/23)

∠S ≈ 70.8°

8 0

3 years ago

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Fiona needs to chose a five-character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8. If she

Yanka [14]

For the five characters of the five-character password, the first three slots are already taken for the initial F, J, S, the password would become,
FJS_ _
The last two slots could be any of the even digits. In the fourth slot, Fiona can have any of the 5 values. On the fifth slot, she can have only 4 choices as the other digit was already used. Multiplying 5 and 4, the answer would be 20.

8 0

3 years ago

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Part 1: Identify the vertex, focus, and directrix of each. Then sketch the graph.

Lina20 [59]

Answer: $\bold{1.\quad \text{Vertex}:(4,-1)\qquad \text{Focus}:\bigg(4,-\dfrac{9}{8}\bigg)\qquad \text{Directrix}:y=-\dfrac{7}{8}}$

$\bold{2.\quad \text{Vertex}:(2,1)\qquad \text{Focus}:\bigg(\dfrac{9}{4},1\bigg)\qquad \text{Directrix}:y=\dfrac{7}{4}}$

Step-by-step explanation:

The vertex form of a parabola is y = a(x - h)² + k or x = a(y - k)² + h

(h, k) is the vertex

p is the distance from the vertex to the focus

-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = -2(x - 4)² - 1 → a = -2 (h, k) = (4, -1)

$a=\dfrac{1}{4p}\quad \rightarrow \quad -2=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{8}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{-8}{8}+\dfrac{-1}{8}\\\\.\qquad =-\dfrac{9}{8}\qquad \rightarrow \qquad \text{Focus}=\bigg(4,-\dfrac{9}{8}\bigg)\\\\\\\text{Directrix: y=Vertex - p}\\\\.\qquad \qquad y=\dfrac{-8}{8}-\dfrac{-1}{8}\\\\.\qquad \qquad y=-\dfrac{7}{8}$

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2) x = (y - 1)² + 2 → a = 1 (h, k) = (2, 1)

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{4}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{8}{4}+\dfrac{1}{4}\\\\.\qquad =\dfrac{9}{4}\qquad \rightarrow \qquad \text{Focus}=\bigg(\dfrac{9}{4},1\bigg)\\\\\\\text{Directrix: x=Vertex - p}\\\\.\qquad \qquad x=\dfrac{8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=\dfrac{7}{4}$

6 0

3 years ago