Aaron is 15 centimeters taller than Peter, and five times Aaron's height exceeds two times Peter's height by 525 centimeters.The system of linear equations that relates Aaron's height (x) and Peter's height (y) is given by . Aaron's height is centimeters, and Peter's height is centimeters.
Answers
5x = 3y + 525
Answer with Step-by-step explanation:
Let Aaron's height be represented by x
and Peter's height be represented by y
Aaron is 15 centimeters taller than Peter.
i.e. x=y+15
Five times Aaron's height exceeds two times Peter's height by 525 centimeters.
i.e. 5x=2y+525
Putting x=y+15 in 5x=2y+525
5(y+15)=2y+525
5y+75=2y+525
5y-2y=525-75
3y=450
Dividing both sides by 3,we get
y=150
Putting the value of y in x=y+15,we get
x=150+15
x=165
Hence, system of linear equations that relates Aaron's height (x) and Peter's height (y) is:
x=y+15
5x=2y+525
Aaron's height is 165 centimeters
and Peter's height is 150 centimeters
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Answer: 9 boys remained in the choir.
Step-by-step explanation:
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In a school choir, 1/2(half) of the members were girls.
i.e (1)
At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4.
Put y= x from (1), we get
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Answers
1. isolate variable
2. divide by coeficient of variable
3. celebrate because you found the answer
remember you can do anything to an equation as long as you do it to both sides
distributive propoerty
a(b+c)=ab+ac
2(x+4)-10=12
distribute the 2 to (x+4)
2(x+4)=2x+8
now we have
2x+8-10=12
add
2x-2=12
add 2 to both sides
2x+2-2=12+2
2x+0=14
2x=14
divide both sides by 2
2/2x=14/2
1x=7
x=7
Hi there!
To solve, let's rewrite this equation.
Step 1) Simplify both sides of the equation.
(Distribute)
(Combine Like Terms)
Step 2) Add 2 to both sides.
Step 3) Divide both sides by 2.
Final Answer -
Hope this helps!
Message me if you need anything else, I'd be happy to help you! :D
Answers
Question
Find x and y of this triangle.
Answer:
x = 52°
y = 23°
Step-by-step explanation:
the sum of the interior angles of a triangle is 180°
from the picture you have 90°, 67° and y in one triangle
and 90°, 38° and x in the other.
triangle with y:
180 - 90 - 67 = 23°
triangle with x
180 - 90 - 38 = 52°
Answers
Answer: The maximum number of people they could have at the party is 18.
Step-by-step explanation:
$250 - $75 = $175
$175 - $47 = $128
$128 / $7 = 18.28
Hope this helps:)
Answers
A) To convert 7.000 cubic centimeters to kiloliters:
7.000 cm^3 * (1 kL / 1,000,000 cm^3) = 0.000007 kL
B) To convert 80. cm^2 to square inches:
80. cm^2 * (1 in^2 / 6.4516 cm^2) ≈ 12.44 in^2
other endpoint?
A (3,5.5)
B (9, 12)
C (12,5)
D (9, 13)
Answers
Answer:
the answer is the letter D
Final answer:
By rearranging the midpoint formula, it can be determined that the other endpoint of the line segment is (9, 13) (option D) when one endpoint is (1,3) and the midpoint is (5,8).
Explanation:
This question relates to coordinate geometry, a branch of mathematics. In coordinate geometry, the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is determined by the mean of the x-coordinates and y-coordinates, meaning the midpoint (xm, ym) is given by ((x1+x2)/2, (y1+y2)/2). If you have one endpoint ((x1, y1) which is (1,3) in this case) and the midpoint (xm, ym which is (5,8) in this question), you can solve for the unknown endpoint (x2, y2) by rearranging the midpoint formula to x2 = 2*xm - x1 and y2 = 2*ym - y1. Substituting the given coordinates into the formulas, we find that x2 = 2*5 - 1 = 9 and y2 = 2*8 - 3 = 13. Therefore, the other endpoint of the line segment is (9,13), hence option D is the correct answer.
Learn more about Midpoint Formula here:
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