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2 years ago

If ray NP bisects <MNQ, m<MNQ=(8x+12)°, m<PNQ=78°, and m<RNM=(3y-9)°, find the value of x and y

Mathematics

1 answer:

aksik [14]2 years ago

7 0

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

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sertanlavr [38]

Answer:

Yes. Juan will break even because 16 and -16 are a zero pair. -16 is the additive inverse of 16. So the sum will be 0.

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2 years ago

Read 2 more answers

What values of b satisfy 3(2b + 3)2 = 36?

meriva

What values of b satisfy 3(2b+3)^2 = 36

we have
3(2b+3)^2 = 36
Divide both sides by 3
(2b+3)^2 = 12
take the square root of both sides
( 2b+3)} =(+ /-) \sqrt{12} \\ 2b=(+ /-) \sqrt{12}-3

b1=\frac{\sqrt{12}}{2} -\frac{3}{2}
b1=\sqrt{3} -\frac{3}{2}

b2=\frac{-\sqrt{12}}{2} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}
therefore

the answer is
the values of b are
b1=\sqrt{3} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}

9 0

1 year ago

The ratio of money in Brian's wallet to Colin's wallet one day was 5:1. Brian spent £27 that day. Brian now had £3 less than Col

myrzilka [38]

Answer:

Brian had $30 initially.Brian had $30 initially.

Step-by-step explanation:

WE are given the following in the question:

Let Brian have x dollars and Colin have y dollars.

Ration of Brian's money to Colin's money is 5:1. This, we can write the equation:

$\dfrac{x}{y} = \dfrac{5}{1}\\\\x = 5y$

"Brian spent £27 that day. Brian now had £3 less than Colin."

Thus, we can write the equation:

$x-27 = y-3\\x-y = 24$

Solving the two equation by substitution, we get,

$x - y - 24\\5y - y = 24\\4y = 24\\y=6\\x = 5y =30$

Thus, Brian had $30 initially.

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1 year ago

A rectangular floor tile is shown it dimensions are given to the nearest 0.1 metres the tile is only able to sustain maximum pre

egoroff_w [7]

Answer:

736 N

Step-by-step explanation:

The dimensions of the rectangular tile are:

Length = 2.3m

Width = 1.6m

The pressure exerted on a surface is given by the formula

$p=\frac{F}{A}$

where

p is the pressure

F is the force exerted

A is the area on which the force is exerted

In this problem, we have:

$p=200 N/m^2$ is the maximum pressure that the tile is able to sustain

A is the area of the tile, which can be calculated as the product between length and width, so:

$A=L\cdot w =(2.3)(1.6)=3.68 m^2$

Re-arranging the formula for F, we can find the maximum force that can be safely applied to the tile:

$F=pA=(200)(3.68)=736 N$

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1 year ago

Theresa has hired Chuck and Diana to paint a fence. Diana can paint 150 fence posts in the same time it takes Chuck to paint 130

Alenkasestr [34]

Answer: Chuck can paint 65 posts per hour.

Step-by-step explanation:

The data we have here is:

Diana can paint 150 fence posts in a time T

Chuck can pint 130 fence posts in a time T.

In one hour, Diana can paint 10 more fence posts than Chuck.

If D is the hourly rate of Daian, and C is the hourly rate for Chuck, we have:

D = 150/T

C = 130/T

D = C + 10

we can replace the last equation in the first one and geT:

C + 10 =150/T

C = 130/T

Now we can replace the bottom equation in the above one:

130/T + 10 = 150/T

10 = 150/T - 130/T = 20/T

T*10 = 20

T = 20/10 = 2

So T is 2 hours, then whe have:

D = 150post/2hours = 75 posts per hour.

C = 130 posts/2hours = 65 posts per hour.

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1 year ago