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Sidana [21]
3 years ago
11

In the above figure, m∠P = 105° and m∠Q = 5x. If angles P and Q are supplementary angles, what is the value of x and the measure

of angle Q? A. x = 15, m∠Q = 20° B. x = 15, m∠Q = 75° C. x = 57, m∠Q = 75° D. x = 39, m∠Q = 195°
Mathematics
1 answer:
Igoryamba3 years ago
4 0

Answer:

B. x = 15, m∠Q = 75°

Step-by-step explanation:

Given:

m∠P = 105°

m∠Q = 5x

Angles P and Q are supplementary angles

To find value of x and m∠Q.

Solution:

m\angle P+m\angle Q =180\°     [Sum of supplementary angles =180°]

105+5x =180   [Substitution ∵ m∠P = 105° and m∠Q = 5x ]

Subtracting both sides by 105°.

105+5x-105 =180-105

5x =75

Dividing both sides by 5.

\frac{5x}{5} =\frac{75}{5}

∴ x=15

∴ m\angle Q=5x=5\times 15=75\°

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Answer:

altitude = 15 cm

Step-by-step explanation:

you can use the Pythagorean Theorem where you have a right triangle with a base of 8 (half of 16), a hypotenue of 17, and the altitude is 'a'

a² + 8² = 17²

a² + 64 = 289

a² = 225

a = \sqrt{225}

a = 15

4 0
3 years ago
Officials project that between 2010 and 2050, the population of a certain city will drastically change. The model below gives th
MaRussiya [10]

Answer:

In the year 2010, the population of the city was 175,000

Step-by-step explanation:

If we rewrote this as a linear expression in standard form (it is linear, btw), it would look like this:

P(t)=\frac{11}{2}t+175

The rate of change, the slope of this line, is 11/2.  If the year 2010 is our time zero (in other words, we start the clock at that year), then 0 time has gone by in the year 2010.  In the year 2011, t = 1 (one year goes by from 2010 to 2011); in the year 2012, t = 2 (two years have gone by from 2010 to 2012), etc.  If we plug in a 0 for t we get that y = 175,000.  That is our y-intercept, which also serves to give us the starting amount of something time-related when NO time has gone by.

3 0
3 years ago
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Vlada [557]
14 + 2x = 62 14 - 14 + 2x = 62 - 14. subtract 14 from both sides 2x = 48 48 ÷ 2 = 24. x = 24

Did this help?
8 0
3 years ago
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MB=xB-AC solve for B!!!!<br> I don't understand this so can you also explain it step by step
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Answer:

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Step-by-step explanation:

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3 years ago
You are asked to recommend whether a firm should make or purchase product A. The following are data concerning the two options.
MArishka [77]

Answer:

a. 6000 units

b. The firm should make the product

2. $ 184200

3. $ 197500

Step-by-step explanation:

a. When is someone indifferent towards buying something? In this case when the cost in dollars is the same. The Break Even Point <u><em>(BEP)</em></u>  makes sense when the firm is indifferent between purchasing it or manufacturing it because the cost of either one or the other is the same. We know the cost of purchasing it ($25 per unit), now we would have to know the cost of producing it with the given data.

Cost of production = Fixed cost + Variable cost

Fixed cost = Rental + labor

Fixed cost = 39200 + ( 5 Operator * 5 days * 8 hours * $14 per hour)

Fixed cost = 39200 + 2800

Fixed cost = 42000

Variable cost =  $18 u                u (units)

Cost of production = 42000 + 18u

When does this cost of production is equal to the cost of purchase?

when

Cost of production = Cost of purchase

42000- 18u = 25u

42000 = 25u - 18 u

42000 = 7u

u = 42000/7

u= 6000

b. The firm should make the product because the cost would be cheaper than purchasing it. It costs 184200 dollars to produce 7900 units vs 197500 dollars when buying them.

2. The cost of production is

Cost of production = 42000 + 18u

Cost of production = 42000 + 18(7900)

Cost of production = 42000 + 142200

Cost of production = 184200

3. The cost of purchase is

Cost of purchase = 25u

Cost of purchase = 25(7900)

Cost of purchase = 197500

 

3 0
3 years ago
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