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butalik [34]
2 years ago
13

Explain how you could estimate 16% of $118.56 to check if your answer is reasonable.

Mathematics
1 answer:
denis23 [38]2 years ago
6 0
You could multiply 118.56 by .16 which is 19 dollars rounded and subtract 19 from 117.56 to get your answer
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Problem 8) In the diagram, RQ ⊥ PQ, m∠QPS = 32°, m∠RPS = 24°, and PQ = 14.Find RS to the nearest tenth of a unit. Image is provi
Sav [38]

Since S is a point on the segment QR, then:

QS+SR=QR

Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.

In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:

\tan\left(32º\right)=\frac{QS}{PQ}

Isolate QS and replace PQ=14:

\begin{gathered} \Rightarrow QS=PQ\cdot\tan\mleft(32º\mright) \\ \operatorname{\Rightarrow}QS=14\tan\mleft(32º\mright) \end{gathered}

On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.

Then, by a similar reasoning, we can use again the tangent function to find QR:

\begin{gathered} \tan\mleft(56º\mright)=\frac{QR}{PQ} \\ \Rightarrow QR=PQ\cdot\tan\mleft(56º\mright) \\ \Rightarrow QR=14\cdot\tan\mleft(56º\mright) \end{gathered}

We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR:

\begin{gathered} QS+SR=QR \\ \Rightarrow SR=QR-QS \end{gathered}

Replace the expressions for QR and QS:

SR=14\tan\mleft(56º\mright)-14\tan\mleft(32º\mright)

Use a calculator to find decimal expressions for tan(56º) and tan(32º). Then, find SR:

\begin{gathered} SR=14\times1.482560969...-14\times0.6248693519... \\ \Rightarrow SR=12.00768263... \end{gathered}

Therefore, to the nearest tenth, the length of the side SR (or RS, which is the same) is 12.0.

3 0
1 year ago
Write two equivalent ratios 6/5
Mekhanik [1.2K]
Two equivalent ratios to 6/5

12/10, 18/15

hope this helps


6 0
2 years ago
Read 2 more answers
Find the surface area of a cylinder the has a base radius of 2 feet and the height of 14 feet
Mashutka [201]

Answer: If I am correct the answer is 201.06ft²

please do correct me if i am wrong.

Step-by-step explanation:

A=2πrh+2πr2=2·π·2·14+2·π·22≈201.06193ft²

5 0
2 years ago
Marsha uses 8.5 pints of white paint and blue paint to paint her bedroom walls. 2/5
Serjik [45]

Answer:

5.1 pints

Step-by-step explanation:

Theres 2 ways

First way:

We can do 2/5 of 8.5 which is 3.4. Then, we can subtract 3.4 from 8.5 and get 5.1 pints.

Second way:

We can simply do 3/5 of 8.5 because the remaining 3/5 of the paint is blue. 3/5 of 8.5 is 5.1 pints

Hope this helped! I would appreciate a Brainliest if this helped you!

6 0
1 year ago
The captain of a submarine orders the crew
Molodets [167]

Answer:

-200 ft., -380 ft., -600 ft., -922 ft.

Step-by-step explanation:

the lowest number in negative form is considered the highest...hoped this helped!

7 0
3 years ago
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