It is ten units, as the two sides are of 6 and 8 so you must square them both, add them together (which gives you 100) and then square root that, which gives you 10

8 0

4 years ago

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The sales tax for an item was $24.50 and it cost $350 before tax. Find the sales tax rate.

Karo-lina-s [1.5K]

Find the number that when multiplied with 350 will give you 24.5. This number happens to be .07 or in terms of sales tax, 7%.

3 0

3 years ago

The value of w varies directly with z. If z = 4, then w = 12. What is the value

IrinaVladis [17]

Answer:

Step-by-step explanation:

w varies directly with z, let k be the constant of proportionality, hence this can be represented by the equation:

w = kz

When z = 4, w = 12, hence we need to find the value of the constant of proportionality, substituting:

12 = 4k

Dividing both sides by 4:

12/4 = 4k/4

k = 3

Therefore the equation becomes:

w = 3z

The value of w when z = 6 is given as:

w = 3(6)

w = 18

7 0

3 years ago

Which of these choices show a pair of equivalent expressions? Check all that apply.

AleksAgata [21]

The main rule we use in this exercise is

$( \sqrt{a} ) ^{m} =( a^{ \frac{1}{2}} )^{m} = a^{ \frac{1}{2}*m}=a^{ \frac{m}{2}}$

and the more general case:

$( \sqrt[n]{a} ) ^{m} =( a^{ \frac{1}{n}} )^{m} = a^{ \frac{1}{n}*m}=a^{ \frac{m}{n}}$
Using these rules, we make all the indices, or exponents, look like $a^{ \frac{m}{n}}$ , and compare them to each other.

A. $( \sqrt{8} )^{9} = ( 8^{ \frac{1}{2}} )^{9} = 8^{ \frac{1}{2}*9}= 8^{ \frac{9}{2}}$

B. $( \sqrt{4} ) ^{5} =( 4^{ \frac{1}{2}} )^{5} = 4^{ \frac{1}{2}*5}=4^{ \frac{5}{2}}$

C. $( \sqrt[3]{125} ) ^{7} =( 125^{ \frac{1}{3}} )^{7} = 125^{ \frac{1}{3}*7}= 125^{ \frac{7}{3}}$

D. $( \sqrt{12} ) ^{7} =( 12^{ \frac{1}{2}} )^{7} = 12^{ \frac{1}{2}*7}=12^{ \frac{7}{2}}$

4 0

3 years ago

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