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3 years ago

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Dimitri rode his bike 32 miles yesterday. He rode 12 4/5 miles before lunch and the rest of the distance after lunch. How far di

d he ride after lunch?

1 answer:

Karo-lina-s [1.5K]3 years ago

7 0

The answer is 19.2 miles.

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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

Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink ha

ICE Princess25 [194]

Answer:

Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

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Step-by-step explanation:

Sugar concentration of first drink = 20%

Volume of first soda = 250 ml

Sugar in first soda = 20% of 250 ...... (1)

Sugar concentration of second drink = 45%

Volume of second soda = 250 ml

Sugar in second soda = 45% of 250 ...... (2)

Let $x\%$ be the sugar concentration in resultant mixture.

Volume of mixture = 250 + 250 = 500 ml

Sugar in mixture = $x\%$ of 500 ml ...... (3)

Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):

20% of 250 + 45% of 250 = $x\%$ of 500

$\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%$

Hence, Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

8 0

2 years ago

Use factoring to solve <br> x^2-2x-35=0

mrs_skeptik [129]

Answer:

I'm sorry I don't have an answer but for all future math work you should download photomath on your phone it's rly good

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3 years ago

Read 2 more answers

Are the triangles named below congruent? Justify your answer.<br> AABC<br> AAED

Anni [7]

Yes, sides AC and AD are congruent and lines BC and DE are also congruent. They also share angle A and bc of the SSA congruence Theorem that means they are congruent.

4 0

2 years ago

Read 2 more answers

Identify the corresponding word problem given the equation: x = 10.20 × 9

crimeas [40]

B) At a restaurant, William and eight friends divided the bill evenly. If each person paid $10.20, what was the total bill?

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3 years ago