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4 years ago

10

What is the difference between rate and unit rate

1 answer:

dalvyx [7]4 years ago

4 0

Unit rate is in the quantity of one.
2/1 is a unit rate
6/3 is a rate
4/1 is a unit rate

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Prove the divisibility:<br><br>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

U - 5 = -4(w - 1)<br> What does u=

Andru [333]

Answer:

u = -4(w - 1) + 5

Step-by-step explanation:

u - 5 = -4(w - 1)

add 5 to both sides

u = -4(w - 1) + 5

3 0

3 years ago

X + 3 = 6<br> Im dumb so help me!

Lynna [10]

Answer:

$x=3$

Step-by-step explanation:

$x+3=6$

Subtract 3 from both sides:

$x+3-3=6-3\\x=3$

Hope this helps!

TestedHyperr

6 0

3 years ago

10 POINTS (t−2)(t2−5t+1)

padilas [110]

Answer:

$t^3-7t^2+11t-2$

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A recipe for banana pudding calls for 2/3 cups of sugar for the flour and 1/4 cups of sugar for the meringue topping, how many c

Brrunno [24]

Answer: 11/12 cups sugar

1 1/4 lbs candy

Step-by-step explanation:

2/3 + 1/4=8/3 + 3/4=11/12

6 1/4 / 5=25/4 x 1/5=25/20=1 5/20= 1 1/4

6 0

3 years ago