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3 years ago

Help me help me help me help me

Mathematics

1 answer:

madreJ [45]3 years ago

8 0

Answer:

12.56%

Step-by-step explanation:

Total Area = bh = 10*10 = 100 square units.

Area of the red circle = $\pi r^2=3.14\cdot 2^2=12.56\:$ square units.

$\frac{12.56}{100}\cdot 100\%=12.56\%$

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Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago

Jen had 60 fossils. If she put 6 fossils in each box, how many boxes were there?

Monica [59]

Answer:

10 boxes

Step-by-step explanation:

Take the number of fossils and divide by the number per box to determine the number of boxes

60/6 = 10

She needs 10 boxes

5 0

3 years ago

Read 2 more answers

20 POINTS

noname [10]

Answer:

EXAMPLE

Pete bought a shirt on sale for $

18, which is one-half the original price. What was the original price of the shirt?

Solution:

Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

Let

p= the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Write the equation.

18=12p

Multiply both sides by 2.

⋅

2⋅18=2⋅1

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

Let

p= the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Write the equation.

18=12p

Multiply both sides by 2.

⋅

2⋅18=2⋅12p

Simplify.

36=pStep 6. Check the answer in the problem and make sure it makes sense.

We found that

p=36, which means the original price was

$36

$36. Does

$36

$36 make sense in the problem? Yes, because

18 is one-half of

36, and the shirt was on sale at half the original price.Step 7. Answer the question with a complete sentence.

The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was

$36

$36.”

If this were a homework exercise, our work might look like this:

The top reads,

TRY IT

Step-by-step explanation:

<em>#CarryOnLearning</em>

4 0

3 years ago

Calculate the average rate of change for the given graph from x = 0 to x = 3 and select the correct answer below. (0,6) (3,0)

algol13

Answer:

(3,0)

Step-by-step explanation:

The number on the x axis is the only number that changes not the number on the y axis.

5 0

3 years ago

Write an inequality for the given graph.

Aliun [14]

Y=MX+B

M = slope

B = y intercept (number that intersects with the line in the y axis)

y=-3/4x+2

It starts on the y intercept (2) then we travel to the next point (4 on the x axis)

So we travel 3 spaces down (-3) landing on the origin (0,0) then four spaces to the right (4). Getting the slope of -3/4 (rise over run)

Then just plug in these into the equation

y = -3/4 + 2

5 0

3 years ago