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lyudmila [28]
2 years ago
15

If m PQS=16, M SQR=(9x+17),and m PQR=(12x-6) find m PQR Please answer with work

Mathematics
1 answer:
docker41 [41]2 years ago
4 0

Answer:

\angle PQR=30^{\circ}

Step-by-step explanation:

It is given that,

\angle PQS=16^{\circ}\\\\\angle SQR=(9x+17)^{\circ}\\\\\angle PQR=(12x-6)^{\circ}

We need to find the measure of \angle PQR.

From the given figure, \angle PQR=\angle  PQS+\angle SQR

Putting all the values, we get :

12x-6=16+9x+17\\\\12x-9x=16+17+6\\\\3x=39\\\\x=13

\angle PQR=12x-6\\\\=12(3)-6\\\\=30^{\circ}

So, the measure of \angle PQR is 30 degrees.

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Given: ∠AOC, ∠BOC - complementary angles
34kurt

Answer:

  • 30
  • COB . . . . or . . . . BOC

Step-by-step explanation:

The reason given on the line of interest is "substitution," so the problem boils down to determining what was substituted for what. The previous statement says ...

  AOC + COB = 90

and the first part of the statement we're to complete has BOC + ___.

We see from the given statements that m∠AOC = m∠BOC + 30°, so it appears that is the substitution that has been made: AOC has been replaced by BOC + 30.

This means the first blank is filled with 30.

__

The second part of the previous statement is ...

  AOC + COB = 90

so we believe this (COB) should go in the second blank.

__

Then the line of interest would read ...

  BOC + 30 + COB = 90

_____

<em>Comment on the problem</em>

There is a curious mix of notations here. Usually, (as in the beginning of this problem) we refer to the measure of an angle using "m∠" in front of the angle designator, and we use a degree symbol to indicate the units of that measure. Part-way through the problem statement written here, those notations were dropped, and we're to assume they are intended. IMO, this is a poor way to demonstrate careful problem solving.

The substitution given for AOC is BOC+30, but the line into which that is substituted has AOC +COB = 90. This means the equation after substitution is ...

  BOC +30 +COB = 90

Since BOC and COB are the same angle, we can sort of fudge the "algebra" to get to  BOC=30, but if the problem were more carefully written, the angle would be referred to by consistent nomenclature:

  m∠AOC + m∠BOC = 90° . . . . . . . . . preferred angle designations

  (m∠BOC + 30°) + m∠BOC = 90° . . . . substitution for m∠AOC

  2(m∠BOC) = 60° . . . . . . algebra (subtract 30°, collect terms)

  m∠BOC = 30° . . . . . . . . algebra (divide by 2)

3 0
2 years ago
An initial deposit of $7,000 earns 6.5% interest, compounded monthly. How
zavuch27 [327]

Answer:

$34,300

Step-by-step explanation:

First, we need to find how much interest is earned in one month : 7,000 * 6.5% = 455

455 is how much you gain monthly, multiply that by 12 to find the annual interest so 455 * 12 = 5,460

You then multiply that number by 5 to find the interest of the span of the 5 years

5,460 * 5 = 27,300

You add the original number to the interest with 27,300 + 7,000 = 34,300 in the account

6 0
2 years ago
What is the midpoint for the points (2, 4) and (8, 10)?
expeople1 [14]

Answer:

(5,7)

Step-by-step explanation:

5 0
3 years ago
Solve the expression: 45x+-3(4-6)
joja [24]
45x+6 is the answer

Simply
Subtract the numbers
45x-3(4-6)
45x-3(-2)
Multiply the numbers
Solution
45x+6
5 0
3 years ago
Read 2 more answers
P(A) = .6, P(B) = .3, P(Β | A) = .5
Reika [66]

Answer:

A

Step-by-step explanation:

P(B|A)=\frac{A ~and~B}{P(A)} \\0.5=\frac{P(A and B)}{0.6} \\P(A~and~B)=0.5 \times 0.6=0.30

8 0
2 years ago
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