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3 years ago

6(8-3)+3(7-4) evaluat the expression

Mathematics

2 answers:

Ksju [112]3 years ago

7 0

Answer: 39

Step-by-step explanation:

6(8-3)+3(7-4) 1. Make sure to multiply what's in the parentheses first.

6(5)+3(3) 2. Multiply before you add the coefficients

30+9 3. Add

Answer is 39

Tems11 [23]3 years ago

6 0

You do it like this
30+9
39

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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

Which describes the difference between the two sequences?

mrs_skeptik [129]

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6 0

3 years ago

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What is the interquartile range of the data set?

AveGali [126]

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6 0

3 years ago

What is the minimum number of clients the travel agent should survey? Note that z=1.96 for a 95% confidence interval.

slega [8]

Answer:

121

Step-by-step explanation:

Given data as per the question

Standard deviation = $\sigma$ = 840

Margin of error = E = 150

Confidence level = c = 95%

For 95% confidence, z = 1.96

based on the above information, the minimum number of clients surveyed by the travel agent is

$n = (\frac{z\times \sigma}{E})^2$

$= (\frac{1.96\times 840}{150})^2$

= 120.47

= 121

hence, the 121 number of clients to be surveyed

Therefore we applied the above formula to determine the minimum number of clients

4 0

3 years ago

Lol please help find the value of x thank you

bagirrra123 [75]

Answer:

x=30

Step-by-step explanation:

that's a 90º angle so 90÷3=30

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3 years ago