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4 years ago

suppose y varies directly with x and y=5 when x=20. Write a direct variation equation then find the value of x when y=3/2

Mathematics

1 answer:

jek_recluse [69]4 years ago

6 0

X=k*Y
K*Y=X
K=X/Y
K=20/5
K=4

For Y=3/2
X=k*3/2
X=4*3/2
X=6

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The longer leg of a right triangle is 7 ft longer than the shorter leg. The hypotenuse is 9ft longer than the shorter leg. Find

julia-pushkina [17]

Answer:

8, 15 and 17 feet respectively

Step-by-step explanation:

Let the shorter leg=l feet

The longer leg of a right triangle is 7 ft longer than the shorter leg, therefore Length of the longer leg=(l+7) feet

The hypotenuse is 9ft longer than the shorter leg. Therefore Length of the hypotenuse=(l+9) feet

Using Pythagoras Theorem

$Hyp^2=Opp^2+Adj^2\\(l+9)^2=l^2+(l+7)^2\\(l+9)(l+9)=l^2+(l+7)(l+7)\\l^2+9l+9l+81=l^2+l^2+7l+7l+49\\l^2+18l+81=2l^2+14l+49$

This results into:

$2l^2-l^2+14l-18l-81+49=0$

$l^2-4l-32=0\\l^2-8l+4l-32=0\\l(l-8)+4(l-8)=0\\(l-8)(l+4)=0$

l-8=0 or l+4=0

l=8 or -4

Since length cannot be negative, The length l=8 feet

The sides of the rectangle are therefore: 8, 15 and 17 feet respectively

5 0

3 years ago

There are 15 marbles in a jar: 4 red, 5 green, and 6 yellow. You select one marble and do not replace it. Then, you select anoth

Marina86 [1]

That events are independent

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3 years ago

60 in the ratio of 5:7

dusya [7]

5+7 = 12
60/12 = 5

5 x 5 = 25
5 x 7 = 35

<span>60 in the ratio of 5:7 = 25:35
hope it helps</span>

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3 years ago

Read 2 more answers

HELP

cestrela7 [59]

Answer:

9/4

Step-by-step explanation:

2(x - 10) + 4 = -6x + 2

2x - 20 + 4 = -6x + 2

2x - 16 = -6x + 2

8x - 16 = 2

8x = 18

x = 18/8 or 9/4

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3 years ago

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Sladkaya [172]

Answer:

a=(2/5), b = (-2,6)

Step-by-step explanation:

well slope formula is rise/run. So for the first one you start at the point rise 2 run 5 and you reach the endpoint. That is how you know you got the correct slope. (2/5)

For the second one you start at the first point and you cannot go up because it is a negative slope you run 6 till you hit the other point go down 2. Since you go down 2 that would make it -2. (-2,6)

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3 years ago