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3 years ago

Tim and Jim are working on a school project together. If he had to work by himself, it would take

Mathematics

1 answer:

Vladimir [108]3 years ago

4 0

Answer: 6 hours

Step-by-step explanation:

Given, Tim and Jim are working on a school project together.

Tim takes 10 hours to complete the school project.

If Jim worked alone, it would take him 15 hours

Let t be the time they both take if they work together.

Then, $\dfrac{1}{t}=\dfrac{1}{\text{Time taken by Tim}}+\dfrac{1}{\text{Time taken by jim}}$

$\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3+2}{30}=\dfrac{5}{30}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow t=6$

So, it will take<u> 6 hours</u> to complete the school project together .

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10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x

ddd [48]

Rationalizing the denominator, simply means "getting rid of that pesky root at the bottom", and we do so by simply multiplying it by something to take it out, of course, we multiply the bottom, we have to also multiply the top,

$\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}$

$\bf \cfrac{4\sqrt{28350x}}{189x}\qquad 
\begin{cases}
28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\
\qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\
\qquad 2\cdot (45)^2\cdot 7\\
\qquad 14\cdot 45^2
\end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x}
\\\\\\
\cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}$

4 0

4 years ago

The council rates are set to rise by 15%. If Teresa pays $950 per year now, what will she pay next year after the rise?

Eddi Din [679]

Answer:

She will pay $1092.50 because .15x950 is 142.50 and if you add that to 950. you get $1092.50

7 0

3 years ago

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

Bad White [126]

Answer:

The final answers are x = 1 OR x = -3.

Step-by-step explanation:

Given the equation is x^2 -3 = -2x

Rewriting it in quadratic form as:- x^2 +2x -3 = 0.

a = 1, b = 2, c = -3.

Using Quadratic formula as follows:- x = ( -b ± √(b² -4ac) ) / (2a)

x = ( -2 ± √(4 -4*1*-3) ) / (2*1)

x = ( -2 ± √(4 +12) ) / (2)

x = ( -2 ± √(16) ) / (2)

x = ( -2 ± 4 ) / (2)

x = (-2+4) / (2) OR x = (-2-4) / (2)

x = 2/2 OR x = -6/2

x = 1 OR x = -3

Hence, final answers are x = 1 OR x = -3.

8 0

3 years ago

Read 2 more answers

At the amusement park, it is important for restrooms to be located in close proximity to the major attractions. The average dist

aksik [14]

Answer:

700

Step-by-step explanation:

to find the range, you subtract the smaller number of the two numbers from the larger one. If there is more than two numbers, you subtract the smallest one of the group from the largest one in the group. In this situation, you do 750-50, which is 700.

5 0

3 years ago

Which number line represents the solution of x + 3 > 2?

Ghella [55]

Answer:

x > -1

(-1, infinity)

Step-by-step explanation:

6 0

3 years ago