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3 years ago

What is 12/24, 3/30, 10/8, 34/20, and 14/8 in lowest term and in percent form

1 answer:

3 0

To find a fraction's lowest term, just simplify them and divide to find the decimal form.
12/24 = 1/2, 0.5
3/30 = 1/10, 0.1
10/8 = 5/4, 1.25
34/20 = 17/10, 1.7
14/8 = 7/4, 1.75

Finished!

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The smiths have two children. The sum of their ages is 23. The produce of their ages is 132. How old are the children?

kolezko [41]

For this case we propose a system of equations:

x: Let the variable representing the age of the first child of the Smiths

y: Let the variable representing the age of the second child of the Smiths

According to the data of the statement we have to:

$x + y = 23\\x * y = 132$

From the first equation we have to:

$x = 23-y$

We substitute in the second equation:

$(23-y) * y = 132\\23y-y ^ 2 = 132\\y ^ 2-23y + 132 = 0$

We find the solutions by factoring:

We look for two numbers that, when multiplied, result in 132 and when added, result in 23. These numbers are 11 and 12.

Thus, we have that the factorized equation is:

$(y-11) (y-12) = 0$

Thus, the solutions are: $y_ {1} = 11\\y_ {2} = 12$

So, we can take any of the solutions:

With $y = 11$

Then $x = 23-11 = 12$

Therefore, the ages of the children are 11 and 12 respectively.

Answer:

The ages of the children are 11 and 12 respectively.

6 0

3 years ago

Put a digit in the gap, such that the answer is a whole number:<br> 9x–42=5... I will give brainiest

cestrela7 [59]

9x–42=5 is x = 11.

<u>Step-by-step explanation:</u>

9x- 42 = 5...

When we put x = 9

then we will get 81 - 42 =39

put x = 10 then

9(10) - 42 = 90 - 42 - 48

put x = 11

then 9(11) - 42 = 99-42 = 57

So x = 11 is the answer.

7 0

3 years ago

Pinto is planning to paint the walls of a bedroom that is 20 feet long, 15 feet wide, and 8 feet high. Is he too has 1 gallon of

eimsori [14]

Answer:

0.4 gallons

Step-by-step explanation:

Length of a bedroom= 20 feet

Breadth of a bedroom= 15 feet

Height of a bedroom= 8 feet

Area of walls of a bedroom= 2(l+b)×h

Area of walls of a bedroom=2(20+15)×8 $ft^{2}$

Area of walls of a bedroom= 2× 35×8 $ft^{2}$

Area of walls of a bedroom=560 $ft^{2}$

Amount of paint in 1 gallon = 400 $ft^{2}$

Number of gallons required= $\frac{560}{400}$

Number of gallons required= 1.4 gallons

Hence, 0.4 extra gallons required

5 0

3 years ago

Does anyone know the answer to number 37?

kotegsom [21]

Answer: 37) 170

Step-by-step explanation:

85 - (-85) = 85 + 85 = 170

$\textit{\textbf{Spymore}}$

7 0

3 years ago

Find the indefinite integral using the substitution provided.

Nady [450]

Answer: $7\text{Ln}\left(e^{2x}+10\right)+C$

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation $u = e^{2x}+10$

Apply the derivative and multiply both sides by 7 like so

$u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\$

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

$\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\$

Integrating leads to

$\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\$

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of $\frac{14e^{2x}}{e^{2x}+10}$

4 0

2 years ago