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3241004551 [841]
3 years ago
9

Weekly math review 3:3

Mathematics
1 answer:
rusak2 [61]3 years ago
6 0
What’s the question?
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Algebra isn’t my best subject, please help
kogti [31]

The Distributive property states that when we have the statement a(b + c), we can "distribute" the a by multiplying a times both terms that are inside the parenthses.

So in this problem, 2(5 + 7) can be simplified by distributing the

2 through both terms that are inside the set of parenthses.

So we have (2 · 5) + (2 · 7).

8 0
3 years ago
find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu
topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}

Now, differentiate P with respect to x, and we get,

\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}

Solving the above equation to zero, we get,

\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\begin{aligned}y&=108-36\\y&=72\end{aligned}

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0
1 year ago
What is the surface of a cube with the side lenght of 9cm
marissa [1.9K]
<span>The total surface area is SA = 6 </span>× a^{2};
SA = 6 × 9^{2} = 6 × 81 = 486 cm^{2};
5 0
3 years ago
Bernadette works at a Car Lot in Buffalo selling used cars. Each month Bernadette receives $2000 plus she receives a 5% commissi
natta225 [31]

Answer:

The total amount of money Bernadette earned in April was $6200

Step-by-step explanation:

Let us solve the question

∵ Each month Bernadette receives $2000

∵ She also receives a 5% commission for all of her sales

∴ She earns each month = 2000 + 5% of her sales

∵ In April, Bernadette sold $84,000 worth of used cars

→ Multiply it by 5% to find her commission

∴ Her commission = 5% × 84,000

→ Change 5% to decimal by divide it by 100

∵ 5% = 5 ÷ 100 = 0.05

∴ Her commission = 0.05 × 84,000

∴ Her commission = $4200

→ Add her commission to her fixed amount to find her salary in April

∵ She earned in April = 2000 + 4200

∴ She earned in April = 6200

∴ The total amount of money Bernadette earned in April was $6200

3 0
3 years ago
Read 2 more answers
When rolling a number cube with sides labeled 1 through 6, what is the probability of rolling a number greater than 2?
vlabodo [156]
That would be 4/6, or 2/3 simplified. As a percent, that would be 66%.

I hope this answer helped you! If you have any further questions or concerns, feel free to ask! :)
4 0
3 years ago
Read 2 more answers
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