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2 years ago

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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2 years ago

Read 2 more answers

Help asap thank you .

frosja888 [35]

Answer:

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2 years ago

What is the perimeter of the triangle (4,1) (2,5) (1,-1)

Naya [18.7K]

the perimeter of the triangle=14.38

The coordinates of the triangle (4,1),(2,5),(1,-1);

In geometry, the perimeter of a shape is defined as the total length of its boundary.

The perimeter of the triangle is the sum of all the sides of the triangle =a+b+c (assuming a,b, and c are the sides of the triangle)

By using the distances formula find the length of the sides of the triangle:√[(x₂ - x₁)² + (y₂ - y₁)²],

where (x₁,y₁),(x₂,y₂) are the coordinates ,

a=√[(4 - 2)² + (1- 5)²] = $\sqrt 20$ =4.7

b=√[(2 -1)² + (5 -(-1))²]= $\sqrt37$ =6.08

c=√[(1 -4)² + ((-1)-1)²]= $\sqrt13$ =3.60

the perimeter of the triangle=a+b+c=4.7+6.08+3.60=14.38

hence ,perimeter of the triangle=14.38

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11 months ago

Calvin had 30 minutes in time-out. For the first 23 1/3 minutes, Calvin counted spots on the ceiling. For the rest of the time,

scoundrel [369]

Answer: $\frac{20}{3}\ minutes$ or $6 \frac{2}{3}\ minutes$

Step-by-step explanation:

For this exercise you can convert the mixed number to an improper fraction:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained and the numerator of the fraction (This will be the new numerator).

3. The denominator does not change.

Then:

$23\frac{1}{3}= \frac{(23*3)+1}{3}= \frac{70}{3}\ minutes$

You know that he had 30 minutes in time-out, he counted spots on the ceiling for $\frac{70}{3}$ minutes and the rest of the time he made faces at his stuffed tiger.