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Rudiy27
3 years ago
11

The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?

Mathematics
1 answer:
frosja888 [35]3 years ago
8 0
Y=(kx)/z


15=(k10)/4
15=(5k/2)
15=k(5/2)
ties both sides by 2/5 to clear fraction
6=k

y=(6x)/z

x=20
z=6
y=(6*20)/6
y=20
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Plot point C(2,7). If M is the midpoint of CD , what are the coordinates of D?
Y_Kistochka [10]

Answer:

The coordinates of D is (-4,-9)

Step-by-step explanation:

Given

C = (2,7)

<em>M=(-1,-1)  ----- Missing part of question</em>

Required

Determine the coordinates of D

<em>Let the coordinates of D be (x₂,y₂)</em>

<em>We'll solve this question using mid point formula;</em>

<em></em>M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})<em></em>

<em>Where</em>

C(x_1,y_1) = (2,7)    and     M(x,y) = (-1,-1)

Put these values in the formula

(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})

By comparison;

-1 = \frac{2+x_2}{2}  and -1 = \frac{7+y_2}{2}

-1 = \frac{2+x_2}{2}

Multiply both sides by 2

-2 = 2 + x_2

Subtract 2 from both sides

-2 -2 = x_2

x_2 = -4

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Multiply both sides by 2

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<em>Hence, the coordinates of D is (-4,-9)</em>

4 0
3 years ago
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Tpy6a [65]

Answer:

a = 3, b = -1, c = 10

Step-by-step explanation:

Let the three numbers be a, b and c.

Equation 1: a + b + c = 12

Equation 2: a + 2b + 3c = 31

Equation 3: 9b + c = 1

Equation 2 - Equation 1:

Equation 4: b + 2c = 19

Equation 3 times by the number 2

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Equation 5 - Equation 4

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8 0
3 years ago
Read 2 more answers
an art teacher has 1 1/2 pounds of red clay and 3/4 pound of yellow clay.The teacher mixes the red clay and yellow clay together
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3 years ago
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