Bob and James are finishing the roof of a house =. Working alone, Bob can shingle the roof in 10 hours. James can shingle the roof in 16 hours. How long will it take them working together to shingle the roof? Round your answer to the nearest hundredth if necessary.A) 13 hours
B) 26.67 hours
C) 6.15 hours
D) 0.04 hours

Answers

Answer 1

Answer: Bob can do a tenth of the roof in an hour
James can do a sixteenth in an hour

Bob can do 16/160 of the roof in an hour
James can do 10/160 of the roof in an hour

Together they do 26/160 of the roof in an hour
160/26 = 6.15 (to 2 d.p.)

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Select the correct answer.What is the factored form of 1,458x3 − 2?

A.
2(9x − 1)(81x2 + 9x + 1)
B.
2(9x + 1)(81x2 − 9x + 1)
C.
(9x − 2)(81x2 + 18x + 4)
D.
(9x + 2)(81x2 − 18x + 4)

Answers

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

What is the factored form of 1,458x³ − 2?

A. 2(9x − 1)(81x² + 9x + 1)

B. 2(9x + 1)(81x² − 9x + 1)

C. (9x − 2)(81x² + 18x + 4)

D. (9x + 2)(81x² − 18x + 4)

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\sf \: 1458 x ^ { 3 } - 2$

Factor out 2 (common factor).

$\sf \: 2\left(729x^(3)-1\right)$

Consider $729x^(3)-1$ . Rewrite $729x^(3)-1$ as $\left(9x\right)^(3)-1^(3)$ . The difference of cubes can be factored using the rule: $a^(3)-b^(3)=\left(a-b\right)\left(a^(2)+ab+b^(2)\right)$ .

$\sf\left(9x-1\right)\left(81x^(2)+9x+1\right)$

Rewrite the complete factored expression. Polynomial 81x²+9x+1 is not factored as it does not have any rational roots.

$\boxed{ \boxed{ \bf A) \: \: 2\left(9x-1\right)\left(81x^(2)+9x+1\right) }}$

If you make an annual salary of $18,920, what is the maximum monthly rent you can afford?$529.76

$441.47

$882.94

$536.22

Answers

If you make an annual salary of $18,920, Find the maximum monthly rent you can afford:
=> 18 920 dollars / 12 months = 1576.67 dollars is your monthly payment.
Base on the given choices, you can afford all prices but practicality wise, 441.47 dollars is the most recommended rentals.

Answer with explanation:

We will use , $(28)/(36)$ rule here, which states that , 28 % of your monthly income should be used for housing finances and 36 % of your total gross income should be used for debt purposes.

Total Annual Salary = $ 18,920

Monthly salary $=(18920)/(12)$

→→28% of 18,920

$=(28)/(100)* (18920)/(12)\n\n=(529760)/(100* 12)=441.4666\n\n=441.47$

Option B: $ 441.47

After six weeks the tomato plant that was given extra food and water was 26 cm tall . The tomato plant that was not given any extra food was only 74.5% as tall . How tall was the tomato plant that was no given extra plant food?

Answers

The answer is 19.37 cm. The problem is only asking what's 74.5% of 26 cm, 0.745 • 26 = 19.37 cm.

A professional quarterback passed for 4,384 yards in 16 games in one football season. If he passed for the same number of yards each game, how many yards did he pass for in each game? Enter your answer in the box.

Answers

274 yards per game
hope this helps

Simplify the polynomial.

1. 4a²b + 5 - 6a³b - 3a²b + 2a³b

Answers

$1.\n \n 4a^2b + 5 - 6a^3b - 3a^2b + 2a^3b = \n \n = - 6a^3b + 2a^3b +4a^2b - 3a^2b+ 5=\n \n= - 4a^3b + a^2b + 5$

4a²b + 5 - 6a³b - 3a²b + 2a³b

We first simplify similar expressions,

4a²b - 3a²b + 5 -6a³b + 2a³b

= a²b + 5 - 4a³b

Which are all the solutions of 5sinθ-4=2sinθ-4, where 0≤θ≤2π

Answers

5sinx-4 =2sinx-4
5sinx-2sinx= 4-4
3sinx=0
sinx=(0÷3)
sinx = 0
x = sin^-1 (0)
x= 0 degrees

And also x = (180- 0 ) = 180 degrees

so x; has 2 answers within the above given interval.

They are;
x= 0 degrees and x=180 degrees

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