Question 2 options: A. y=5x+5 B. y=15x+5 D. Y=1/5x+5 C. Y=10x+5

What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = -6?

Dmitrij [34]

Answer:

y = $\frac{3}{2}$ x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x - 2y = - 6 into this form

Subtract 3x from both sides

- 2y = - 3x - 6 ( divide all terms by - 2 )

y = $\frac{3}{2}$ x + 3 ← in slope- intercept form

with slope m = $\frac{3}{2}$

• Parallel lines have equal slopes, hence

y = $\frac{3}{2}$ x + c ← partial equation of parallel line

To find c substitute (4, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = $\frac{3}{2}$ x - 4 ← equation of parallel line

3 0

3 years ago

A figure is composed of a semicircle and a right triangle. Determine the area of the shaded region. Use 3.14 for π and round to

Aliun [14]

Answer:

$A=9.5\ ft^2$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of triangle plus the area of semicircle

so

$A=\frac{1}{2}bh+\frac{1}{2}\pi r^{2}$

we have

$b=4\ ft$

Find the height of the right triangle applying the Pythagorean Theorem

$5^2=h^2+4^2$

$h^2=9\\h=3\ ft$

The radius of the semicircle is half the height of triangle

$r=3/2=1.5\ ft$

substitute in the formula

$A=\frac{1}{2}(4)(3)+\frac{1}{2}(3.14)(1.5)^{2}$

$A=6+3.5=9.5\ ft^2$

5 0

3 years ago

Read 2 more answers

Writing and Solving an Equation to Find Negative Integers Two negative integers are 5 units apart on the number line, and their

Shtirlitz [24]

Answer:

-23

Step-by-step explanation:

Let first negative integer = x

The second = x +5

Their product = 126, hence,

x * (x +5) = 126

x^2 + 5x = 126

x^2 + 5x - 126 = 0

Two numbers whose product gives - 126 and sun gives 5

x(x + 14) - 9(x+14) =0

(x - 9) = 0 or (x + 14) = 0

x = 9 or x = - 14

Since x is said to be a negative integer,, the our x = - 14

First integer = - 14

Second integer = (x + 5) = (-14 + 5) = - 9

Sum of both integers :

-14 + - 9 = - 23

3 0

3 years ago

Lin sold 4 more shirts than Greg. Fran sold 3 times as many shirts as Lin. In total the three sold 51 shirts. Which represents t

Alex17521 [72]

Your Answer: D

Why....

You can make equations out of the information
Let L be Lin, G be Greg, and F be Fran

L = 4 + G ---"Lin sold 4 more shirts than Greg"
F = 3L ---"Fran sold 3 times as many shirts as Lin"
F + G + L = 51 ---"In total the three sold 51 shirts"

Use F + G + L = 51
Substitute the equations in for F and L (because you need to know the G) like this....

(3L) + G + (4+G) = 51

You still have a variable besides G in there... you can use the L= 4+G and substitute again so that there are only G's

( 3(4+G) ) + G + (4+G) = 51 ---- SIMPLIFY :D
( 12 + 3G ) + G + 4 + G = 51
12 + 3G + G + 4 + G = 51 ---Combine like terms
16 + 5G = 51

6 0

3 years ago

How many integers from 1 through 100 are neither multiples of 2 nor multiples of 3 ?

julia-pushkina [17]

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Find total number of integers
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Number of integers from 1 to 100 = 100
There are 100 numbers altogether

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Find total numbers that can be divided by 2
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Number that are multiples of 2 = 100 ÷ 2 = 50
50 of the number are multiples of 2

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Find total numbers that are multiples of 3
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Numbers that are multiples of 3 = 100 ÷ 3 = 33 R 1
33 of the numbers are multiples of 3

Of the 33 numbers that are multiples of 3, half of the numbers are even and had been included in multiples of 2.
33 ÷ 2 = 16 R 1

33 - 16 = 17
17 of the numbers are multiples of 3

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Total numbers that can be multiples of 2 or 3
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50 + 17 = 67

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Total number that are neither multiples of 2 nor 3
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100 - 67 = 33

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Ans: 33 integers are neither multiples of 2 nor multiples 3
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8 0

3 years ago