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4 years ago

3. An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed?

Mathematics

2 answers:

ella [17]4 years ago

6 0

Answer:

105 at 30 min.

<em>x</em> at 75 min.

105 mph x 2 = 210 mph at one hour

There is still 15 min to go soooo...

210/4 = 52.5

210 + 52.5 = 262.5 mph for 75 min

Check by dividing

262.5/75=3.5

raketka [301]4 years ago

5 0

262.5 miles
explanation 1/4 is half of 1/2 so 52.5 is half of 105 and then 210 for an hour of travel

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The area of the rectangle shown is 2x^2-x-15 square units. What is the width of the rectangle?

yuradex [85]

Answer:

<h2>The width is (2x + 5) or (x - 3)</h2>

Step-by-step explanation:

The formula of an area of a rectangle:

$A=lw$

l - length

w - width

We have

$A=2x^2-x-15$

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4 years ago

Please help<br> x2 + 14x + 37 = 0

tatiyna

Answer:

x = −37/16

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3 years ago

which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

$\frac{\sqrt[3]{(2y)}^{4}}{x^2}$

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

3 years ago

ASAP<br> Can someone help me with this pleaseeee

Rashid [163]

It’s option D.) I did a quiz on this !

4 0

3 years ago

Stephen earns $11 per hour at his job. Last month, Stephen worked for 112 hours. On his paycheck, Stephen noticed that he paid $

Pachacha [2.7K]

Answer: Stephen's net income is $921.71

Step-by-step explanation:

Hi, to answer this question, first, we have to multiply the amount of hours worked (112) by 11 (because he earns $11 per hour)

Mathematically speaking:

112 x 11 = $1,232

Now we have to sum the federal income tax ($216.05),Social Security ($76.38), and Medicare ($17.86) to obtain the total expenditures:

Total expenditures: $216.05 +$76.38 +$17.86 = $310.29

Finally we subtract the total expenditures ($310.29) to Stephen's revenue ($1,232) to obtain Stephen's net income.

Net income = 1,232 - 310.29 =921.71

Stephen's net income is $921.71

4 0

3 years ago