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Blababa [14]
3 years ago
12

Solve with a system of equations: Two angles are supplementary if the sum of their measures are 180 degrees. If one is 90 degree

s more than twice the measure of the other angle, what are the measures of the angles?
Mathematics
1 answer:
julsineya [31]3 years ago
6 0

Answer:

  The measures of the angles are 150° and 30°.

Step-by-step explanation:

Let x and y represent the measures of the angles, with x representing the larger angle.

  x + y = 180 . . . . . . the two angles are supplementary

  x = 90 + 2y . . . . . one is 90° more than twice the other

___

Substituting the expression given by the second equation into the first, we have ...

  (90 +2y) +y = 180

  3y = 90 . . . . . . . . . . collect terms, subtract 90

  y = 30 . . . . . . . . . . . divide by the coefficient of y

  x = 180 -y = 150

The measures of the angles are 150° and 30°.

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timama [110]
Since they are congruent, cpctc,
just set the congruent parts equal to each other. 
so 2x-20=30
and
15=3y-9
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Convert the decimal 0.92 to a fraction
yan [13]

Answer:

0.92 as a fraction is 23/25

Good luck, hope this helped!

5 0
3 years ago
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Lucie drank 3/4 of a pint of bottled water. One serving of the water is 7/8 of a pint. How much of a serving did she drink.
attashe74 [19]
7/8
3/4
I'm order for them to have the same denominator you need to multiply so:
¾×2=6/8
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3 years ago
Read 2 more answers
On rainy days, Izzy goes from his house to the school by running 1.2 miles on West St, then makes a 90º turn and runs 0.5 miles
OlgaM077 [116]

Answer:

a) It will take Izzy 0.226 hours = 13.6 minutes = 13 minutes 36 seconds to run to school on dashed days.

b) Izzy runs 1.30 miles on dry days.

c) Izzy saves 3 minutes and 12 seconds cutting through the woods.

Step-by-step explanation:

This problem can be solved by a simpe rule of three problem.

a) On rainy days, she runs 1.2 + 0.5 = 1.7 miles.

The problem states that for rainy days, she runs 7.5 miles per hour. We know that in a hour, Izzy will run 7.5 miles. We want to know how long it takes for her to run 1.7 miles. So

1 hour - 7.5 miles

x hours - 1.7 miles

7.5x = 1.7

x = \frac{1.7}{7.5}

x = 0.226 hours

It will take Izzy 0.226 hours = 13.6 minutes = 13 minutes 36 seconds to run to school on dashed days.

b) Now we have a right triangle, where the sides are the 1.2 miles and the 0.5miles, and the path through the woods x is the hypotenuse.

So, we apply the pythagorean theorem.

x^{2} = (1.2)^{2} + (0.5)^{2}

x^{2} = 1.44 + 0.25

x^{2} = 1.69

x = 1.30

So, Izzy runs 1.30 miles on dry days.

c) The first step for this question is knowing how long it takes for Izzy to run 1.30 miles at 7.50 miles a hour. So:

1 hour - 7.50 miles

x hours = 1.30 miles

7.50x = 1.30

x = \frac{1.3}{7.5}

x = 0.173 hours

So, it takes Izzy 0.173 hours = 10.4 minutes = 10 minutes 24 seconds to run through the woods.

13' 36''

-10' 24''

3' 12''

Izzy saves 3 minutes and 12 seconds cutting through the woods.

5 0
3 years ago
Mary bought 4 gallons of milk for $10.00. Jill bought 2.5 gallons for $6.00.
RoseWind [281]

Step-by-step explanation:  

In order to find the better buy, we must find the cheaper unit price or price per gallon.  To find the price per gallon, divide the cost by the number of gallons.

Mary

Mary bought 4 gallons for $11.

The price is $11 and the gallons are 4.

Jill

Jill bought 2.5 gallons for $7.25

The price is $7.25 and the gallons are 2.5

Better buy

Mary paid $2.75 per gallon and Jill paid $2.90 per gallon. 2.75 is less than 2.90, so Mary had the better buy.

3 0
2 years ago
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