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2 years ago

Please help me solve this

Mathematics

1 answer:

Nataly_w [17]2 years ago

8 0

Answer:

x = 24

Step-by-step explanation:

using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m +n)}$

consider left side

$5^{\frac{x}{6} }$ × $5^{\frac{x}{2} }$

= $5^{\frac{x}{6} }$ × $5^{\frac{3x}{6} }$

= $5^{\frac{4x}{6} }$

then

$5^{\frac{4x}{6} }$ = $5^{16}$

since the bases on both sides are equal, both 5 then equate exponents

$\frac{4x}{6}$ = 16 ( multiply both sides by 6 )

4x = 96 ( divide both sides by 4 )

x = 24

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Justin wants to fence in his yard for his dog. He lives on a rectangular lot 48 feet long and 62 feet wide. How much fencing doe

Alenkasestr [34]

48 X 2 = 96
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You could also do it this way:
P = 2(W + L)
P = 2(48 + 62) 
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Jeremy swims 5 3··5 kilometers in a 7-day period. He swims the same distance each day. What distance does he swim in a day?

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Answer:

Jeremy swims 4/5 of a kilometer each day.

Step-by-step explanation:

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2 years ago

Louie Foster invested $4,500 at 3% interest compounded semiannually for 2 years

viktelen [127]

Answer:

$\huge\boxed{5064.79 (2d.p)}$

Useful Information:

The formula for compound interest is: $\sf{amount*decimal^{{No. calculations}}$

Step-by-step explanation:

This is an example of compound percentage increase.

To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 3% by 100, this gives you 0.03. This is because percentages are out of 100 and so dividing the value by 100 gives you the percentage as a part of 1.

The next step is to add 1 to 0.03, this gives you 1.03. This is because you are working out the percentage increase.

The penultimate step is to work out the number of times that the new amount would need to be calculated. This can be done by multiplying 2 by 2, which gives you 4. This is because it will be compounded semiannually, which is twice a year.

The fnal step is to work out the total amount you would need to multiply the amount of 4,500 by 1.03 to the power of 4, this gives you 5064.79 (2 D.P). This is because you are working out 3% of the amount, and then adding it to the new amount and then finding 3% of that amount, and so on.

1) Divide 3% by 100.

$\frac{3}{100}=0.03$