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4 years ago

Find the GCF of 21, 30

Mathematics

2 answers:

sweet-ann [11.9K]4 years ago

5 0

Answer:

The GCF of 21 and 30 is 3.

Step-by-step explanation:

Find the prime factorization of 21

21 = 3 × 7

Find the prime factorization of 30

30 = 2 × 3 × 5

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 3

Evgesh-ka [11]4 years ago

3 0

Answer:

Step-by-step explanation:

Factors of 21: 1, 3, 7, 21

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

The GCF is the largest factor they both have.

GCF = 3

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Using the distributive property simplify the expression<br> -2(5y + 6) + 3 - 5y

vivado [14]

Answer:

$\Huge \boxed{-15y-9}$

Step-by-step explanation:

To solve this problem, first you have to use the distributive property of $\displaystyle a(b+c)=ab+ac$ .

First, expand.

$\displaystyle -2(5y+6)$

$-2*5=-10$

$\displaystyle -2*6=-12$

$\displaystyle -10y-12$

$\displaystyle -10y-12+3-5y$

Next, solve.

$\displaystyle -10-12+3-5=\boxed{-15y-9}$

In conclusion, the correct answer is -15y-9.

5 0

4 years ago

You travel 3 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 4 miles upstream at a speed

shtirl [24]

<h3>Write a model in simplified form for the total time t (in hours) of the trip:</h3>

$Total\ time\ taken = \frac{3}{r} + \frac{4}{0.5r} + \frac{1}{r+1}\\$

<h3>It takes 2.95 hours when r is 4 miles per hour</h3>

<em><u>Solution</u></em>:

Given that,

<h3>You travel 3 miles downstream in a kayak at a speed of r miles per hour</h3>

Downstream:

Speed = r miles per hour

Distance = 3 miles

Time taken is given as:

$Downstream\ time = \frac{distance}{speed}\\\\Downstream\ time = \frac{3}{r} ------- eqn\ 1$

<h3>You turn around and travel 4 miles upstream at a speed of 0.5r miles per hour</h3>

Upstream:

Speed = 0.5r miles per hour

Distance = 4 miles

Therefore,

$Upstream\ time = \frac{4}{0.5r} -------- eqn 2$

<h3>Finally, you turn around and return to your original starting point at a speed of r + 1 miles per hour</h3>

Therefore,

$time = \frac{1}{r+1} ----------- eqn\ 3$

<em><u>a)Write a model in simplified form for the total time t (in hours) of the trip</u></em>

The total time taken is:

eqn 1 + eqn 2 + eqn 3

$Total\ time\ taken = \frac{3}{r} + \frac{4}{0.5r} + \frac{1}{r+1}\\$

<em><u>b)How long does your trip take when r is 4 miles per hour?</u></em>

Substitute r = 4

$Total\ time\ taken = \frac{3}{4} + \frac{4}{0.5 \times 4} + \frac{1}{4+1}\\\\Total\ time\ taken = 0.75 + 2 + 0.2\\\\Total\ time\ taken = 2.95$

Thus it takes 2.95 hours when r is 4 miles per hour

8 0

3 years ago

The Statue of Liberty is in New York, and the Golden Gate Bridge is in California.

slega [8]

If you';re asking if this is True or False, then the answer would be True.

3 0

3 years ago

Read 2 more answers

Rebecca drove 44 1/3 miles in 1 1/3 hours. What is the unit rate for miles per hour?

saul85 [17]

$unit\ rate=\frac{distance}{time}\\\\
distance=44\frac{1}{3} miles\\
time=1\frac{1}{3}hour\\\\
unit\ rate=\frac{44\frac{1}{3}}{1\frac{1}{3}}=\ \ \ | make\ improper\ fractions\\
\frac{\frac{133}{3}}{\frac{4}{3}}=\frac{133}{3}*\frac{3}{4}=\frac{133}{4}=33\frac{1}{4}\\\\
unit\ rate= 33\frac{1}{4}\frac{miles}{hour}
$

5 0

4 years ago

A number squared divided by 2 and added to 16

nadya68 [22]

Answer:

Suppose the number is 4

Square of this number (4 x 4 ) = 16

Divided by 2 = 16/2 = 8

Added to 16 = 8+16 = 24

Step-by-step explanation:

4 0

4 years ago