Mathematics, 18.09.2019 00:20 hihihi129473838

1. ac = 95, ab = 15x - 10, bc = 5x + 5
2. ac = 8x - 16, ab = 3x - 8, bc = 4x
3. ac = x - 0.4, ab = x - 4.9, bc = 0.5x
4. ac = 383, ab = 6x, bc = 8x + 1

Answers: 1

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Answers

Answer from: barattah

Part 1) x=5, AB=65 units, BC=30 units

Part 2) x=8, AB=16 units, BC=32 units

Part 3) x=9, AB=4.1 units, BC=4.5 units

Part 4) x=2 3/4, AB=16 1/2 units, BC=22 1/4 units

Step-by-step explanation:

The complete question in the attached figure

we have that

Point B is between A and C on segment AC

we know that

AC=AB+BC -----> equation A (by addition segment postulate)

Part 1) we have

AC = 95, AB = 15x - 10, BC = 5x + 5

substitute the given values in equation A and solve for x

95=(15x-10)+(5x+5)

Combine like terms in the right side

95=(20x-5)

Adds 5 both sides

95+5=20x-5+5

100=20x

Divide by 20 both sides

100/20=20x/20

5=x

Rewrite

x=5

Find the value of AB

AB=(15x-10)

substitute the value of x

$AB=(15(5)-10)=65\ units$

Find the value of BC

BC=(5x+5)

substitute the value of x

$BC=(5(5)+5)=30\ units$

Part 2) we have

AC = 8x - 16, AB = 3x - 8, BC = 4x

substitute the given values in equation A and solve for x

8x-16=(3x-8)+(4x)

Combine like terms in the right side

8x-16=(7x-8)

Adds 16 both sides

8x-16+16=7x-8+16

8x=7x+8

Subtract 7x both sides

8x-7x=7x+8-7x

x=8

Find the value of AB

AB=(3x-8)

substitute the value of x

$AB=(3(8)-8)=16\ units$

Find the value of BC

BC=(4x)

substitute the value of x

$BC=4(8)=32\ units$

Part 3) we have

AC = x - 0.4, AB = x - 4.9, BC = 0.5x

substitute the given values in equation A and solve for x

x-0.4=(x-4.9)+(0.5x)

Combine like terms in the right side

x-0.4=(1.5x-4.9)

Adds 4.9 both sides

x-0.4+4.9=1.5x-4.9+4.9

x+4.5=1.5x

Subtract x both sides

x+4.5-x=1.5x-x

4.5=0.5x

Divide by 0.5 both sides

4.5/0.5=0.5x/0.5

9=x

Rewrite

x=9

Find the value of AB

AB=(x-4.9)

substitute the value of x

$AB=(9-4.9)=4.1\ units$

Find the value of BC

BC=(0.5x)

substitute the value of x

$BC=0.5(9)=4.5\ units$

Part 4) we have

AC = 38 3/4, AB = 6x, BC = 8x + 1/4

substitute the given values in equation A and solve for x

$38\frac{3}{4}=(6x)+(8x+\frac{1}{4})$

Convert mixed number to an improper fraction

$38\frac{3}{4}=38+\frac{3}{4}=\frac{38*4+3}{4}=\frac{155}{4}$

substitute

$\frac{155}{4}=(6x)+(8x+\frac{1}{4})$

Multiply by 4 both sides to remove the fraction

155=(24x)+(32x+1)

Combine like terms in the right side

155=56x+1

Subtract 1 both sides

155-1=56x+1-1

154=56x

Divide by 56 both sides

154/56=56x/56

154/56=x

Rewrite

$x=\frac{154}{56}$

Simplify

$x=\frac{11}{4}$

Rewrite x as mixed number

$x=\frac{11}{4}=\frac{8}{4} +\frac{3}{4}=2\frac{3}{4}$

Find the value of AB

AB=(6x)

substitute the value of x

$AB=6(\frac{11}{4})=16.5\ units$

Rewrite AB as mixed number

$AB=16.5\ units=16+0.5=16+\frac{1}{2}=16\frac{1}{2}\ units$

Find the value of BC

$BC=(8x+\frac{1}{4})$

substitute the value of x

$BC=8(\frac{11}{4})+\frac{1}{4}$

$BC=22+\frac{1}{4}=22\frac{1}{4}\ units$

1. ac = 95, ab = 15x - 10, bc = 5x + 5 2. ac = 8x - 16, ab = 3x - 8, bc = 4x 3. ac = x - 0.4, ab = x

Answer from: Quest

answer: $34.31

step-by-step explanation:

$11.99 x 3 = $35.97

$35.97 - 10% = $32.37

$32.37 + 6% = $34.31

Answer from: Quest

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.

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1. ac = 95, ab = 15x - 10, bc = 5x + 5
2. ac = 8x - 16, ab = 3x - 8, bc = 4x
3. ac = x -...