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3 years ago

Completely factor 40^4 - 324.

Mathematics

1 answer:

Setler [38]3 years ago

3 0

Answer:

40^4 - 324 = 2,559,676

Step-by-step explanation:

First we need to factor the left side of the equation, which is 40 to the 4th power. 40*40*40*40 is 2,560,000, now we need to subtract 324 from it which is 2,559,676.

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Convert standard to slope-intercept forms. 1. Standard form: 10x − 7y = −8

garri49 [273]

Answer:

Step-by-step explanation:

-7y = -10x - 8

y = 10/7x + 8/7

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3 years ago

If the sales tax in your city is 5.6% and an item costs$76 before tax, how much tax would you pay on that item? Round to the nea

bagirrra123 [75]

To find the amount of money you pay for tax, you have to multiply the price of the product by the percentage of the tax, then divide it by 100. in this case, 76x5.6=425.6/100=4.256 which is $4.26 (to the nearest cent)

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4 years ago

Read 2 more answers

Suppose it takes 45 hours for robot A to construct a new robot. Working together with robot B, it takes 25 hours for both robots

Len [333]

Answer:

56 hours 25 minutes

Step-by-step explanation:

Given:

Suppose it takes 45 hours for robot A to construct a new robot

It takes 25 hours for both robots to construct a new robot.

Question asked:

How long would it take robot B to construct a new robot, working alone ?

Solution:

Let the time taken by robot B to construct new robot = $x$

By robot A

It takes 45 hours to construct = 1 new robot

It takes 1 hour to construct = $\frac{1}{45} \ new\ robot$

By robot B

It takes $x$ hours to construct = 1 new robot

It takes 1 hour to construct = $\frac{1}{x}$ new robot

By working together

It takes 25 hours to construct = 1 new robot

It takes 1 hour to construct = $\frac{1}{25} \ new\ robot$

$\frac{1}{25}$ new robot is constructed in = 1 hour

New robot is constructed by both working together in 1 hour = New robot is constructed by robot A in 1 hour + New robot is constructed by robot B in 1 hour

$\frac{1}{25} =\frac{1}{45} +\frac{1}{x} \\$

Subtracting both sides by $\frac{1}{45}$

$\frac{1}{25}-\frac{1}{45} =\frac{1}{45} -\frac{1}{45}+\frac{1}{x} \\\\\frac{1}{25}-\frac{1}{45} =\frac{1}{x}\\\\ Taking\ LCM \ of \ 25\ and\ 45,\ we\ got\ 225$

$\frac{9-5}{225} =\frac{1}{x} \\ \\ \frac{4}{225} =\frac{1}{x}\\\\ By\ cross \ multiplication\\4\times x=225\\Dividing\ both\ sides\ by\ 4\\x=56.25\ hours$

Thus, robot B would take 56 hours 25 minutes to construct a new robot, working alone.

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3 years ago

Read 2 more answers

Darnelle drew this figure and the accompanying equations.

kondor19780726 [428]

Answer:

Option D. w + x = z

Step-by-step explanation:

see the attached figure to better understand the problem

we have

$w+x+y=180$ ----> equation A

$y+z=180$ ----> equation B

equate equation A and equation B

$w+x+y=y+z$

Subtract y both sides

$w+x=z$

This equation satisfy the Triangle Exterior Angle Theorem (An exterior angle of a triangle is equal to the sum of the opposite interior angles)

4 0

3 years ago

Sebastian swam laps every day in the community swimming pool. He swam 45 minutes each day, 5 days each week, for 12 weeks. In th

lord [1]

Answer:

$\text{Average rate}=\frac{\text{40 laps}}{\text{ hour}}$

Step-by-step explanation:

Please consider the complete question.

Sebastian swan laps every day in the community swimming pool. He swam 45 minutes each day, 5 days each week, for 12 weeks. In that time, he swam 1800 laps. What was his average rate in laps per hour?

Let us convert time taken into hours as:

$\text{Days}=5\times 12=60$