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3 years ago

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=16...

Mathematics

2 answers:

olchik [2.2K]3 years ago

6 0

Step-by-step explanation:

y = kx, where k is a real constant.

When x = 2, y = 7.

=> (7) = k(2), 2k = 7, k = 3.5.

Therefore when x = 16,

y = (3.5)(16) = 56.

The value of y is 56 when x is 16.

bija089 [108]3 years ago

5 0

The formula for direct variation is y = kx

Using the known x and y solve for k:

7 = k2

Divide both sides by 2:

k =7/2 = 3.5

Now solve for y when x = 16:

y = 3.5(16)

y = 56

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nordsb [41]

Answer:

1) 2x+7

2) -3x+11

3) 0.75x-2

4) -2x+0

5) -1.5x+2

6) -4x+16

Step-by-step explanation:

1) y = mx + c

m = 2 when x=1 , y=9

9 = 2(1)+c

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When x=4, y= -1

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c = -1+12 = 11

y = -3x + 11

3) m = 0.75

When x= -4, y= -5

-5 = 0.75(-4) + c

-5 = -3 + c

c = -2

y = 0.75x - 2

4) m = (y2-y1)/(x2-x1)

m = (2-(-6))/(-1-3) = 8/-4 = -2

y = -2x + c

When x= -1, y= 2

2 = -2(-1) + c

2 = 2 + c

c = 0

y = -2x + 0

5) m = (-10-(-4))/(8-4)

m = (-10+4)/4 = -6/4 = -1.5

y = -1.5x + c

When x= 4, y= -4

-4 = -1.5(4) + c

-4 = -6 + c

c = 2

y = -1.5x + 2

6) m = (-4-4)/(5-3) = -8/2 = -4

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4 = -4(3) + c

4 = -12 + c

c = 16

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3 years ago

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Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

mars1129 [50]

Answer:

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If m∠E = m∠Y and m∠F = m∠X

then

Triangles EFG and YXZ are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

FE and XY

EG and YZ

GF and ZX

so therefore

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.

From the figure in the attachment , we can conclude that:

m∠E = m∠Y

m∠F= m∠X

m∠G = m∠Z

∴ ΔEFG ~ ΔYXZ ( ΔEFG is similar to ΔYXZ )

Because of the similarity , then:

FE : XY = EG : YZ = GF : ZX

Conclusion:

ΔFG is similar to ΔYXZ.

Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

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