What are some ways to describe the relationship between sets of numbers?

faust18 [17]

$6.\\\text{We know}\ 9=3^2.\ \text{Therefore}\\\\9^2=(3^2)^2\\\\\text{use}\ (a^n)^m=a^{nm}\\\\9^2=(3^2)^2=3^{2\cdot2}=3^4\\\\\boxed{3^4=9^2}\\=================$

$7.\\METHOD\ 1:\\\\\sqrt{7^4}=\sqrt{7^{2\cdot2}}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(7^2)^2}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\boxed{7^2}\\\\METHOD\ 2:\\\\\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\\sqrt{7^4}=7^\frac{4}{2}=\boxed{7^2}\\=================$

$8.\\5^a\times5^b=5^{11}\\\\a)\\\text{use}\ a^n\times a^m=a^{n+m}\\\\5^a\times5^b=5^{a+b}\\\\5^{a+b}=5^{11}\Rightarrow a+b=11\\\\11\ \text{is odd. The sum of even and odd is odd. Therefore}\ a\ \text{and}\ b\ \text{can't be even.}\\--------------------\\\\b)\\5\ \text{solutions}\\\\11=5+6\\11=4+7\\11=3+8\\11=2+9\\11=1+10$

3 0

2 years ago

A chemist is using 381 milliliters of a solution of acid and water. If 17.4% of the solution is acid, how many milliliters of ac

Romashka-Z-Leto [24]

Answer:

66.3 mL

Step-by-step explanation:

17.4% of 381 mL is ...

0.174 × 381 mL = 66.3 mL

7 0

3 years ago

Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall

miskamm [114]

Answer:

4 inches.

Step-by-step explanation:

The height of a rectangle is reduced by Shawna to a size of 2 inches.

The original width of the rectangle was 24 inches and the height was 12 inches.

If the ratio of width to height remains the same, then we can find the new width.

If the new width is x inches then, we can write

$\frac{x}{2} = \frac{24}{12}$

⇒ x = 4 inches. (Answer)

7 0

2 years ago

Read 2 more answers

What about this one ??

V125BC [204]

The first expression is equivalent to B

The second expression is equivalent to A

The third expression is equivalent to C

You are basically adding like terms. For example for the first expression, it is 7x^2 + 2x^2, which equals 9x^2. Remember since you're adding, do not add the exponents.

4 0

3 years ago

Last week salazar played 13 more tennis games than perry. if they played a combined total of 53 games. How many games did salaza

d1i1m1o1n [39]

If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒ x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

Learn more on total here:

brainly.com/question/14306809

#SPJ1

6 0

2 years ago