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ale4655 [162]
3 years ago
11

Solve for x and justify your answer ​

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0
The answer is 51°.

The top two lines are parallel to each other. Therefore alternate interior angles theorem applies. The bottom right corner that is underneath the line (for lack of a better description) is also 58°.

We also know that a triangle equals 180°. So 58+71= 129°.

So to find that missing angle we subtract 129 from 180 to get the 51°.
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Four small cakes are shared equally among 5 children what part does each child receive?
erastova [34]

Answer:

0.8 of a cake

Step-by-step explanation:

all you do is divide 4 by 5

4 0
3 years ago
1+3x=x+9 solve for x.. Help?
anzhelika [568]

Answer: <em>x=4</em>

Step-by-step explanation:

<em>1+3x=x+9</em>

<em>   -x  -x</em>

<em>1+2x=9</em>

<em>-1      -1</em>

<em>2x=8</em>

<em>Divide by 2 on each side</em>

<em>Final result</em>

<em>x=4</em>

7 0
3 years ago
A bank loaned out 16,000 ​$​, part of it at the rate of 6% per year and the rest at 14% per year. If the interest received in on
MakcuM [25]

Answer:

This question requires a comparison between two different variables 6% and 16% values.  If we let x=$ loaned on 6% loans and y=$ loaned on 16% loans, then we can relate two equations.

0.06x + 0.16y = $1500  --> referencing the interest earned from each percentage loaned.

x + y = $16000  --> referencing the total amount of money loaned out.

Rearrange either equation and substitute for a value in the other equation or use elimination to determine each individual variable.

Step-by-step explanation:

6 0
3 years ago
Help with this please i have a few minutes left!!!!
lara [203]
Answer: 5.44449

step-by-step explanation:
5 0
3 years ago
A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio
guapka [62]
Answer: 4.5 miles

Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b)  distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x  (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.
5 0
3 years ago
Read 2 more answers
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