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Mathematics

2 answers:

Anastaziya [24]2 years ago

4 0

Answer:

23 degrees

Step-by-step explanation:

We can use basic trigonometric equations to solve for the angle x because we are given a right triangle.

I will use the sin x = opposite / hypotenuse

sin x = 5 / 13

x = sin^-1 (5 / 13)

x = 22.61986 degrees

The question requires us to round to the nearest degree which is 23.

Other alternative methods you can use include the tangent and cosine functions or the law of cosines.

KatRina [158]2 years ago

3 0

Answer:

x = 23°

Step-by-step explanation:

I will use

$tanx=opposite/adjacent$

$tanx=\frac{5}{12}$

$x=tan^{-1} (\frac{5}{12} )=tan^{-1} (0.417)=22.62^{o}$

rounded to the nearest degree : 23°

Hope this helps

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A feasible region has vertices at (-1,3), (3,5), (4,-1), and (-1,-2) find the maximum and minimum values of each function

Molodets [167]

Answer: Choice D.
Max: f (-1,-2)=4; min:f(3,5)=-11

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Work Shown:

Plug in (x,y) = (-1,3)
f(x,y) = -2x-y
f(-1,3) = -2*(-1)-3
f(-1,3) = 2-3
f(-1,3) = -1
------------------
Plug in (x,y) = (3,5)
f(x,y) = -2x-y
f(3,5) = -2*3-5
f(3,5) = -6-5
f(3,5) = -11
------------------
Plug in (x,y) = (4,-1)
f(x,y) = -2x-y
f(4,-1) = -2*4-(-1)
f(4,-1) = -8+1
f(4,-1) = -7
------------------
Plug in (x,y) = (-1,-2)
f(x,y) = -2x-y
f(-1,-2) = -2*(-1)-(-2)
f(-1,-2) = 2+2
f(-1,-2) = 4
------------------
The four outputs are: -1, -11, -7, and 4

The largest output is 4 and that happens when (x,y) = (-1,-2)
So the max is f(x,y) = 4

The smallest output is -11 and that happens when (x,y) = (3,5)
So the min is f(x,y) = -11

This all points to choice D being the answer.

6 0

3 years ago

The trailer ramp is shaped like a triangle prism . The height of the ramp is 14 inches and the volume of the ramp is 4704 inches

Hatshy [7]

Answer:

A = 2167.73 cm²

Step-by-step explanation:

Given that,

A trailer ramp is in the shape of a triangular prism.

the height of the ramp, h = 14 inches

The volume of the ramp, V = 4704 inches²

We need to find the area of the base of the trailer ramp.