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3 years ago

Which law would you use to simplify the expression 3^10/3^4

Mathematics

2 answers:

ZanzabumX [31]3 years ago

6 0

Answer:

Step-by-step explanation:

3^10/3^4 = 3 ^(10 - 4) = 3^6

anygoal [31]3 years ago

6 0

Answer:

Quotient rule of exponent is used to simplify the given expression.

Step-by-step explanation:

The given expression is

$\frac{3^{10}}{3^{4}}$

In this expression the power of 3 is difference but the base of numerator and denominator are same.

Quotient rule of exponent: To divide the power of same base, we subtract the exponents.

$\frac{a^x}{a^y}=a^{x-y}$

Using quotient rule of exponent, we get

$\frac{3^{10}}{3^{4}}=3^{10-4}=3^6$

Therefore, quotient rule of exponent is used to simplify the given expression.

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Solve the system of linear equations by adding or subtracting -6x+y=5 7x-y=-4

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A jeweler wants to make 14 grams of an alloy that is precisely 75% gold.. The jeweler has alloys that are 25% gold, 50% gold, &a

Goryan [66]

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\$

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)$ [as x+y=14]

$\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\$

$\Rightarrow x =(25 \times 14)/32=10.9375$ grams

and $y = 14-x= 14-10.9375=3.0625$ grams.

Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\$

$\Rightarrow x =(50 \times 14)/57=12.28$ grams

and $y = 14-x= 14-12.28=1.72$ grams.

Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.

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3 years ago

SAT Help

posledela

Well, their speeds are ( $V_1$ is Jack's speed, and $V_2$ is Richard's.
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They, together, can paint 12 houses in 35 days. To get a single house, we only have to calculate $\frac{35}{12}$ which is very close to 3 (a bit below)

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3 years ago

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4+7x=-24 how do you solve this algebraic expression

Lady_Fox [76]

Answer:

In order to solve this algebraic expression, you need to get the variable x by itself

Step 1: subtract 4 from each side

4-4+7x=-24-4 (4-4=0, those cancel out) (-24-4=-28)

7x=-28

Step 2: divide both sides by 7

7x/7=-28/7 (7x/7=x) -28/7=-4)

Your final answer would be x=-4

Hope this helps ;)

Step-by-step explanation:

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A car that cost 700,000.00 depreciates 15% in the value each year for the first five years. What is the cost after 5 years?

Setler79 [48]

Answer:

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