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meriva
3 years ago
5

M is the midpoint of jk. find the y coordinate of k if j(-8,4) and m(-3,2)

Mathematics
1 answer:
zalisa [80]3 years ago
4 0

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ j(\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad  k(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 +  x_1}{2}~~~ ,~~~ \cfrac{ y_2 +  y_1}{2} \right) \\\\\\ \left( \cfrac{x-8}{2}~~,~~\cfrac{y+4}{2} \right)~~=~~\stackrel{m}{(-3,2)}\implies  \begin{cases} \cfrac{x-8}{2}=-3\\[0.8em] x-8=-6\\ \boxed{x=2}\\[-0.5em] \hrulefill\\ \cfrac{y+4}{2}=2\\[0.8em] y+4=4\\ \boxed{y=0} \end{cases}

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Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa
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Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

  • Samuel traveled 3 km/h faster than Heather
  • After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
  • Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

   distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

   and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

#LearnwithBrainly

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3 years ago
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Wait if he worked 1 hour this question still makes no since

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Help please!! Stuck on this question!! ∠ABC is adjacent to ∠CBD. If the m∠ABC=4x+23, m∠CBD=6x+7, and m∠ABD=130°, what is the mea
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Answer:

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3 years ago
A cylinder has a radius of 40 ft and a height of 17 ft. What is the exact surface area of the cylinder?
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we know that

surface area of the cylinder=2*{area of the base}+perimeter of base*height

area of the base=pi*r²

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Area of base=pi*40²

Area of the base=1600*pi ft²


Perimeter of the base=2*pi*r

Perimeter of the base=2*pi*40

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surface area=4560*pi ft²


therefore

the answer is the option

4560π ft2

8 0
3 years ago
Read 2 more answers
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