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3 years ago

What is an equation of the line that passes through the points (-3, 7) and (3, 3)?

Mathematics

1 answer:

Margarita [4]3 years ago

3 0

Answer:

$y = -\frac{2}{3}x + 5$

Step-by-step explanation:

First you have to find the slope

$m = \frac{7 - 3}{-3 - 3} = \frac{4}{-6} = -\frac{2}{3}$

Now use the point-slope form by using one of the points and the slope. Let's use the point (3, 3)

$y - 3 = -\frac{2}{3} (x - 3)$

Multiply thru the equation by 3 to remove the fraction

3y - 9 = -2(x - 3) =

3y - 9 = -2x +6

3y = -2x + 15

$y = -\frac{2}{3}x + 5$ is the equation in slope-intercept form

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Which figure shows a reflection of pre-image QRS over the line t?

Igoryamba

Answer:

A, because its reflecting off of the y axis

Step-by-step explanation:

I have proof links, and I took the test

4 0

3 years ago

Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less

Sergio039 [100]

Answer:

The shortest side of the triangle is 18

Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.

4 0

3 years ago

Which of the following definitions is the best way to describe popular culture?

marin [14]

Answer:

A-cultural patterns that can change quickly and are accepted by the majority of people.

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3 years ago

An equivalent expression to a2/3

scoundrel [369]

Answer:

4/6 6/9 8/12 10/15 and so on, just multiply both the numerator and denominator by the same number and get your answer.

Step-by-step explanation:

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3 years ago

pam deposited $6,900 in a savings account with simple interest. Four months later she had earned $23 in interest. What was the i

3241004551 [841]

Answer:

Step-by-step explanation:

We use the simple interest equation of A=P(1+rt).

A-the total amount with interest earned

P-the initial amount or principal

r-rate

t-time in years

We substitute the values P=6900, A=6923, and t=0.33 since 4 months divided by 12 months is 0.333 years. We then solve for r.

$6923=6900(1+r(0.33))\\6923=6900(1+0.33r)\\\frac{6923}{6900} =\frac{6900(1+0.33r)}{6900} \\1.0033=1+0.33r\\1.0033-1=1-1+0.33r\\0.0033=0.33r$

Our final step is to divide both sides by 0.33.

$\frac{0.0033}{0.33} =\frac{0.33r}{0.33} \\0.01=r$

This is the decimal of the rate. We convert to a percentage by multiplying by 100. 0.01(100)=1%.

5 0

3 years ago