A parallelogram has an interior angle measuring 81°. Which MUST also be the measure of an interior angle of the parallelogram?

John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What i

Inga [223]

Answer:

Skiing costs $30 per hour and Boating costs $51 per hour.

Step-by-step explanation:

Let cost per hour of skiing be x and cost per hour of boating be y. Let's dissect the problem into 2 simultaneous equations.

"John paid $222 for four hours of skiing and two hours boating":

$4x+2y=222$

"He paid $213 for two hours skiing and three hours boating":

$2x+3y=213$

Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y. Work shown below.

$2x+3y=213\\2x=213-3y\\x=\frac{213-3y}{2}\\Equation 1: 4x+2y=222\\Substituting :\\4(\frac{213-3y}{2})+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=\frac{204}{4}=51$

Hence, y = 51

Now, substituting this y value into the 1st equation and solving for x will give us the value of x.

$First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30$

Hence, skiing costs $30 per hour and boating costs $51 per hour.

4 0

3 years ago

Use properties to find the sum or product 8x51

SCORPION-xisa [38]

$8\times51=8\times(50+1)=8\times50+8\times1=400+8=408$

3 0

3 years ago

Rewrite the following fractions as division problems. a. 7⁄11 b. 5⁄2 c. 9⁄10 d. 7⁄15

larisa [96]

A. 7/11= 7 ÷ 11
B. 5/2= 5 ÷ 2
C. 9/10= 9 ÷ 10
D. 7/15= 7 ÷ 15

A fraction is just a division problem. 7/11 would be considered 7 ÷ 11 (or just 7/11) just do the same for the rest of the fractions.

3 0

3 years ago

What’s the gcf of 18k and 15k cubed?

Contact [7]

Answer:

The GCF for the variable part is

k

Step-by-step explanation:

Since

18

k

,

15

k

3

contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.

Steps to find the GCF for

18

k

,

15

k

3

:

1. Find the GCF for the numerical part

18

,

15

2. Find the GCF for the variable part

k

1

,

k

3

3. Multiply the values together

Find the common factors for the numerical part:

18

,

15

The factors for

18

are

1

,

2

,

3

,

6

,

9

,

18

.

Tap for more steps...

1

,

2

,

3

,

6

,

9

,

18

The factors for

15

are

1

,

3

,

5

,

15

.

Tap for more steps...

1

,

3

,

5

,

15

List all the factors for

18

,

15

to find the common factors.

18

:

1

,

2

,

3

,

6

,

9

,

18

15

:

1

,

3

,

5

,

15

The common factors for

18

,

15

are

1

,

3

.

1

,

3

The GCF for the numerical part is

3

.

GCF

Numerical

=

3

Next, find the common factors for the variable part:

k

,

k

3

The factor for

k

1

is

k

itself.

k

The factors for

k

3

are

k

⋅

k

⋅

k

.

k

⋅

k

⋅

k

List all the factors for

k

1

,

k

3

to find the common factors.

k

1

=

k

3

=

k

⋅

k

⋅

k

The common factor for the variables

k

1

,

k

3

is

k

.

k

The GCF for the variable part is

k

.

GCF

Variable

=

k

Multiply the GCF of the numerical part

3

and the GCF of the variable part

k

.

3

k

3 0

3 years ago

Write words to match expression 24 divided by 6

miv72 [106K]

twenty four divisible by six, if that what u meant . or 24÷6

3 0

3 years ago