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3 years ago

Angles A and B are congruent. Find the value of x. Show all work to receive credit.

Mathematics

1 answer:

kolezko [41]3 years ago

8 0

Answer:

x = 15

Step-by-step explanation:

Sides opposite congruent angles are congruent:

x + 10 = 2x - 5

15 = x . . . . . . . . . add 5-x

The value of x is 15.

_____

I suppose you could show the intermediate step:

x +10 +(5 -x) = 2x -5 +(5 -x)

15 = x . . . . . simplified

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A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four re

ddd [48]

Answer:

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which $\theta$ is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = $2\pi$ radians

So, the change in angle with respect to t ( time ),

$\frac{d\theta}{dt}=8\pi\text{ radians per min}$

Let x be the distance of beam from P,

$\implies \tan \theta = \frac{x}{2}$

Differentiating with respect to x,

$\sec^2 \theta \frac{d\theta}{dt}=\frac{1}{2}\frac{dx}{dt}$

$(1+\tan^2 \theta) (8\pi) = \frac{1}{2}\frac{dx}{dt}$

$(1+\frac{x^2}{2^2})(8\pi) = \frac{1}{2}\frac{dx}{dt}$

If x = 1 km,

$(1+\frac{1}{4})8\pi =\frac{1}{2}\frac{dx}{dt}$

$\frac{5}{4}8\pi = \frac{1}{2}\frac{dx}{dt}$

$\implies \frac{dx}{dt}=\frac{80\pi}{4}= 20\pi\approx 62.8\text{ km per min}$

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

7 0

4 years ago

It costs the quality company $.14 per mile to run its van. On Monday the van traveled 87.6 miles. How much did it cost to run th

aksik [14]

We can find this answer by multiplying .14 by 87.6 to represent 14 cents for every mile.

87.6
<u> .14
</u>12.264

Since we are rounding to the nearest cent, that being the hundredths place, we know that it cost $12.26 to run the van that day.

8 0

4 years ago

Read 2 more answers

Which expression shows 20 + 24 with 2 as a factor of each term?

stira [4]

Answer:

2(10 + 12)

Step-by-step explanation:

20 + 24

=> 2(10 + 12)

Therefore, 2(10 + 12) is our expression with 2 as a factor for each term.

Hoped this helped.

8 0

2 years ago

All these answers I need help

kkurt [141]

I’m afraid I only had time to answer 1-4

5 0

3 years ago

2. There are two common paths to earning a bachelor's degree:

fomenos

Answer:

Whenever i enroll into a college, i don't want to transfer my credits out of somewhere else. I want to get there, get my work done, and graduate. Cost will be reduced due to financial aid and staying in state. I will live on-post so campus life and living arrangements wont be an issue either.

Step-by-step explanation:

8 0

3 years ago