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Anna35 [415]
2 years ago
7

For what value of k are the lines 2x + 3y = 4k and x - 2ky = 7 parallel?

Mathematics
1 answer:
natulia [17]2 years ago
5 0

Answer:

k = -3/4

Step-by-step explanation:

The lines will be parallel if their slopes are equal.  To find the slope of each line, write its equation in slope-intercept form (y = mx + b).  In other words, solve each equation for y and look at the coefficient of x.

2x + 3y = 4k

3y = -2x + 4k

y = (-2/3)x + 4k/3

The slope of the first line is -2/3.

x - 2ky = 7

-2ky = -x + 7

y = [1/(2k)]x - 7/(2k)

The slope of the second line is 1/(2k).

If the slopes are equal, then

1/(2k) = -2/3

Multiply by 2k.

1 = (-2/3)(2k) = (-4/3)k

1 = (-4/3)k

k = -3/4

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Answer:

He saves $14.50

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58* .25  = 14.50

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A 34-foot pole casts a 30-foot shadow. At the same time, a nearby tree casts a 24-foot shadow. How tall is the tree?
artcher [175]

Answer:

27.2 ft

Step-by-step explanation:

Let's set up a ratio that represents the problem:

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Substitute with the dimensions of the 34 foot pole and its 30 foot shadow.

34 : 30

Find the unit rate:

The unit rate is when one number in a ratio is 1.

Let's make the Shadow equal to one by dividing by 30 on both sides.

Object's Height (ft) : Shadow (ft)

34 : 30

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1.13 : 1

Now, let's multiply by 24 on both sides to find the height of the tree.

Multiply:

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A rocket was launched and its height, h, in metres, above the ground after time,
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The ABC Toy Company is creating two similar pieces for board game, as shown below. Find the value of y that makes the two pieces
Ira Lisetskai [31]
A shape that is similar to another shape will be enlarged by a scale factor. 
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3 years ago
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