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3 years ago

What is the surface area of the rectangular prism below?

Mathematics

1 answer:

pychu [463]3 years ago

8 0

Answer:

C) 490 units²

Step-by-step explanation:

$SA=2(7*7)+2(14*7)+2(14*7)$

$SA=2(49)+2(98)+2(98)$

$SA=98+196+196$

$SA=490$

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Guys please help me with this question

diamong [38]

Answer: Can I get brainliest and 5 stars? thank you.

a) $\frac{65}{99}$

b) $\frac{59}{90}$

c) $\frac{13}{20}$

Step-by-step explanation:

a) $0.65$ I can't put line above it, but the line expresses that 6 and 5 and repeating infinitely. Let X equal the decimal number.

$x=0.65$

First multiply by 1 followed by as many zeros as repeating numbers there are. In this case since 6 and 5 are the repeating numbers, we have to add 2 zeros which is basically multiplying by 100

0.65*100=65.65 (another 65 remains on the right because they're infinite.)

Now substract from the original number. Now we have a new equation that says: $100x=65.65$ .

Substract equation 1 from equation 2.

$100x=65.65\\-x=0.65$

---------------------------------

$99x=65$

Solve just like any other equation. Divide by 99 to isolate x.

$\frac{99x}{99}=\frac{65}{99}$

$x=\frac{65}{99}$ This is the fraction.

------------------------------------------------------------------------------------------------

b) $0.65^-$ This one is a little bit different because we only have 1 repeating number.

In this case we have to multiply by 10.

$0.65^-*10=6.55^-$

Equation 1: $x=0.65^-$

Equation 2: $10x=6.55^-$

Substract.

$10x=6.55^-\\-x=0.65^-$

-----------------------

$9x=5.9$

divide by 9 to isolate x

$\frac{9x}{9}=\frac{5.9}{9}$

$x=\frac{5.9}{9}$

To get rid of the decimal in the numerator, multiply both numerator and denominator by 10 so that we don't change the fraction.

$x=(\frac{5.9*10}{9*10} )$

$x=\frac{59}{90}$ and this is your fraction.

------------------------------------------------------------------------------------------------------

c) 0.65 this one has no repeating number. It's a finite decimal number.

I assume you already know that; $a=\frac{a}{1}$ , so, we can do the same here to have a fraction.

$0.65=\frac{0.65}{1}$

Now, in order to get rid of the decimal, multiply by 1 followed by as many zeros as decimal numbers are. In this case 2 zeros because there are 2 decimal numbers, so it's 100. Remember that if you do it in the numerator, you have to do it in the denominator as well to not change the fraction.

$\frac{0.65*100}{1*100} =\frac{65}{100}$

Simplify if possible.

$\frac{65/5}{100/5} =\frac{13}{20}$ This is your fraction.

6 0

3 years ago

What fraction represents the sum of 1/5 + 1/5 + 1/5

Drupady [299]

Answer:

0.6=6/10=3/5

Step-by-step explanation:

0.2+0.2+0.2

0.6

The tenth place wich means 6/10

Simplify by which gives you 3/5

6 0

3 years ago

What is a solution to the equation 3 / m + 3 - M / 3 - M equals m^2 + 9 / m^2-9?

Mnenie [13.5K]

Answer: Last option.

Step-by-step explanation:

Given the equation:

$\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}$

Follow these steps to solve it:

- Subtract the fractions on the left side of the equation:

$\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}$

- Using the Difference of squares formula ( $a^2-b^2=(a+b)(a-b)$ ) we can simplify the denominator of the right side of the equation:

$\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}$

- Multiply both sides of the equation by $(m+3)(3-m)$ and simplify:

$\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}$

- Multiply both sides by $m-3$ :

$(-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)$

- Apply Distributive property and simplify:

$(-m^2-6m+9)(m-3)=(m^2+9)(3-m)\\\\-m^3-6m^2+9m+3m^2+18m-27=3m^2+27-m^3-9m\\\\-m^3-3m^2+27m-27+m^3-3m^2+9m-27=0\\\\-6m^2+36m-54=0$

- Divide both sides of the equation by -6:

$\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0$

- Factor the equation and solve for "m":

$(m-3)^2=0\\\\m=3$

In order to verify it, you must substitute $m=3$ into the equation and solve it:

$\frac{3}{3+3}-\frac{3}{3-3}=\frac{3^2+9}{3^2-9}\\\\\frac{3}{6}-\frac{3}{0}=\frac{18}{0}$

<em>NO SOLUTION</em>

7 0

3 years ago

Miranda earns $72,000 annually. She contributes $300 a month to a savings bond. What percent of her salary does she contribute t

Vitek1552 [10]

Answer: 5%

Step-by-step explanation:

First notice that she contributes $300 a month and annually means yearly, so find the amount that she contributes yearly by multiplying 300 by 12 because there are 12 months in a year.

300 * 12 = 3600

Now to find the percentage, divide the amount she contributes in year by her annual salary.

3600/ 72000 = 0.05

Convert 0.05 into a percent by multiplying 0.05 by one hundred.

0.05 * 100 = 5%

4 0

3 years ago

The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 120 feet, what is the length of the

ipn [44]

Answer:

a = length

b = height(width)

a=3b

2(a+b)=120

2(b+3b)=2(4b)=8b

8b=120

b=15

a=45

length is 45 feet

width is 15 feet

4 0

3 years ago