What would the answer to -|-24| be?

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

grandymaker [24]

Answer:

Lines a and b are parallel

Lines a and c are perpendicular

Lines d and c are perpendicular

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Part 1) Find the slope of Line a

we have the points

(-3,4) and (3,6)

substitute in the formula

$m=\frac{6-4}{3+3}$

$m=\frac{2}{6}$

simplify

$m_a=\frac{1}{3}$

Part 2) Find the slope of Line b

we have the points

(-10,-3) and (-8,3)

substitute in the formula

$m=\frac{3+3}{-8+10}$

$m=\frac{6}{2}$

$m_b=3$

Part 3) Find the slope of Line c

we have the points

(0,5) and (3,-4)

substitute in the formula

$m=\frac{-4-5}{3-0}$

$m=\frac{-9}{3}$

$m_c=-3$

Part 4) Find the slope of Line d

we have the points

(4,-7) and (13,-4)

substitute in the formula

$m=\frac{-4+7}{13-4}$

$m=\frac{3}{9}$

simplify

$m_d=\frac{1}{3}$

Part 5) Compare the slopes

Remember that

If two lines are parallel then their slopes are the same

If two lines are perpendicular then their slopes are opposite reciprocal

we have

$m_a=\frac{1}{3}$

$m_b=3$

$m_c=-3$

$m_d=\frac{1}{3}$

therefore

Lines a and b are parallel (slopes are equal)

Lines a and c are perpendicular (slopes are opposite reciprocal)

Lines d and c are perpendicular (slopes are opposite reciprocal)

6 0

3 years ago

The perimeter of a rectangle is 54 feet. The area of the rectangle is 176 square feet. Find the dimensions of the rectangle.

Murrr4er [49]

11 by 16

Explanation:

Set up two equations

2

x

+

2

y

=

54

x

×

y

=

176

Solving the first equation for x

2

x

+

2

y

−

2

y

=

54

−

2

y

this gives

2

x

=

54

−

2

y

Divide both sides by 2

(

2

x

2

)

=

54

−

2

y

2

This gives.

x

=

27

−

y

putting this value into the second equation gives.

(

27

−

y

)

×

y

=

176

multiplying across the parenthesis gives

27

y

−

y

2

=

176

subtracting 176 from both sides gives

is

27

y

−

y

2

−

176

=

0

multiplying by negative one gives

−

27

y

+

y

2

+

176

=

0

factoring this into y gives

(

y

−

11

)

×

(

y

−

16

)

=

0

Solving for both y's gives

y

=

11

,

y

=

16

6 0

2 years ago

Rupert buys a bicycle with a marked price of £ 12500.He gets a rebate of 10% on it. After getting

yarga [219]

Answer:

£ 12,150

Step-by-step explanation:

Marked price of bicycle = £ 12500

Rebate = 10%

Amount of rebate = 12500*10/100 = £1250

Rebated price = 12500 - 1250 = £ 11,250

Tax = 8%

Amount of tax = 11250*8/100 = £ 900

Total amount paid for bicycle = Rebated price + amount of tax

= £ 11,250 + £ 900

= £ 12,150

4 0

4 years ago

3. Determine the Area and Perimeter of the<br> shape below.<br> 13<br> 5<br> 12

BigorU [14]

Perimeter: 30units
Area: 30units^2

Explanation: Checked with calc!

3 0

3 years ago

Read 2 more answers

Rita is designing a building shaped like a pyramid that's cut off in a plane parallel to its base (this is called a truncated py

Maru [420]

Answer:

48128m^3

Step-by-step explanation:

Given data

For the building

L=64m

W= 6m

H= 36m

The volume is

V= LWH/3

V=64*64*36/3

V=147456/3

V=49152m^3

For the off-Cut

L=16m

W= 16m

H= 12m

The volume is

V= LWH/3

V=16*16*12/3

V=3072/3

V=1024m^3

Hence the volume of the truncated part/Building

= Volume of building-volume of off-cut

=49152-1024

=48128m^3

7 0

3 years ago

Read 2 more answers