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3 years ago

Solve the inequality: -1+4y < 31

2 answers:

6 0

Let's solve your inequality step-by-step.−1+4y<31Step 1: Simplify both sides of the inequality.4y−1<31Step 2: Add 1 to both sides.4y−1+1<31+14y<32Step 3: Divide both sides by 4.4y4<324y<8

Andrews [41]3 years ago

3 0

-1 +4y < 31

add 1 to each side:

4y < 32

divide both sides by 4

y<32/4

y<8

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Prove the divisibility: 45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(9*5)^{45}=9^{45}*5^{45}$

$15^{15}=(3*5)^{15}=3^{15}*5^{15}$

$75^{30}=(15*5)^{30}=15^{30}*5^{30}$

Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}$

$\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}$

$\frac{3^{105}*5^{60}}{3^{30}*5^{60}}$

$\frac{3^{105}}{3^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

7 0

3 years ago

A cyclist rides his bike at a rate of 15 miles per hour. what is this rate in miles per minute? how many miles will the cyclist

ryzh [129]

Answer:

15 miles/hour = 0.25 miles/minute

The cyclist would have traveled 5 miles in 20 minutes.

Step-by-step explanation:

15 miles per hour is written as

15 miles/hour

To convert 15 miles/hour to miles/minute

From 1 hour = 60 minutes

∴ 15 miles/hour = 15 miles/ 60 minutes

= (15/60) miles/minute

= 0.25 miles/minute

To calculate how many miles the cyclist will travel in 20 minutes

That is, Time, t = 20 minutes

Velocity, v = 15 miles/hour = 0.25 miles/minute

Distance, s = ??

From,

$Velocity = \frac{Distance}{Time}\\$

∴ $Distance = Velocity$ × $Time$

$Distance = 0.25 miles/minute$ × $20 minutes$

$Distance = 5 miles$

Hence, The cyclist would have traveled 5 miles in 20 minutes.

7 0

3 years ago

A pair of designer sunglasses was marked up 10% and is now selling for $165.00. What was the original price of the sunglasses?

grandymaker [24]

They were originally $150.00.

4 0

3 years ago

Read 2 more answers

What is the product of the rational expression?? CORRECT ANSWER'S ONLY

padilas [110]

The answer is B.

Breaking down the operation:

NUmerators: x × x = x² and +3 × -3 = -9

Denumerators: x × x = x² and +2 × -2 = -4

Answer:

$\frac{x+3}{x+2}$ × $\frac{x-3}{x-2}$

Hope it helped,

Happy homework/ study/ exam!

7 0

3 years ago

63 12/60 simplified

Andreas93 [3]

Your question is not clear, if you are asking: what is $63 \frac{12}{60}$ simplified? Then the answer is $63 \frac{1}{5}$ or $63.2$ .

If 63 is just the question number and you are asking, what is $\frac{12}{60}$ simplified. Then the answer is $\frac{1}{5}$ or $0.2$

You get this answer by finding the highest number that both the numerator and denominator are divisible by, and diving both numbers by that:

$\frac{12}{60} \div \frac{12}{12} = \frac{12 \div 12}{ 60 \div 12} = \frac{1}{5} = 0.2$

7 0

3 years ago

Read 2 more answers