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Elza [17]
2 years ago
7

after saving 2/7 of his paycheck for the month, mr. donovan has $1,335 left to spend. Mrs. spencer saves 3/8 of her paycheck. bo

th of them save the same amount of money. how much is mrs. spencers paycheck?
Mathematics
1 answer:
faltersainse [42]2 years ago
3 0
Given:
Mr. Donovan
2/7 = savings
5/7 = $1,335

Mrs. Spencer
3/8 = savings

Both saved the same amount of money. How much is Mrs. Spencer's paycheck?

Mr. Donovan's paycheck.
1,335 ÷ 5/7 = 1,335 * 7/5 = 9345/5 = 1869

Mr.Donovan's savings
1869 * 2/7 = (1869*2)/7 = 3738/7 = 534

Mr. Donovan's savings = Mrs. Spencer's savings

Mrs. Spencer's pay check
534 ÷ 3/8 = 534 * 8/3 = 4272/3 = 1424

Mrs. Spencer's paycheck is $1,424
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marta [7]

<u>Given</u>:

The given expression is 16 x^{8}-1

We need to determine the factor of the given expression.

<u>Factor</u>:

Let us rewrite the given expression.

Thus, we have;

\left(4 x^{4}\right)^{2}-1^{2}

Since, the above expression is of the form a^2-b^2, let us apply the identity a^2-b^2=(a+b)(a-b)

Thus, we have;

\left(4 x^{4}+1\right)\left(4 x^{4}-1\right) ------ (1)

Now, we shall factor the term 4x^4-1

4x^4-1=(2x^2)^2-1^2

           =(2x^2+1)(2x^2-1)

Substituting the above expression in equation (1), we have;

\left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)

Therefore, the factor of the given expression is \left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)

Hence, Option B is the correct answer.

5 0
2 years ago
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It takes 12 minutes to fill an entire bathtub using both the cold and hot water. If just the cold water is used, it takes 18 min
Kipish [7]

Answer:

<h2>It takes 36 minutes to fill the bathtub using just hot water.</h2>

Step-by-step explanation:

We are gonna name V the complete volume of the bathtub, which is filled a certain amount of minutes. Each filling rate or speed is gonna be expressed as: \frac{V}{t}.

So, if we apply this consideration to each case we have:

Using cold and hot water: \frac{V}{12}

Using only cold water: \frac{V}{18}

Using only hot water: \frac{V}{x}; because we don't knot the time it takes to fill the bathtub with hot water.

Now, as you can see, Cold and Hot water is a sum of cold water only and hot water only:

\frac{V}{12}=\frac{V}{18}+\frac{V}{x}

Solving the equation for <em>x: </em>

\frac{V}{12}=\frac{xV+18V}{18x} \\\frac{V}{12}=\frac{(x+18)V}{18x}\\\\\frac{18xV}{V}=12(x+18)\\18x=12x+216\\18x-12x=216\\6x=216\\x=\frac{216}{6}=36

Therefore, it takes 36 minutes to fill the bathtub using just hot water.

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2 years ago
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Novosadov [1.4K]
The 300th customer would be the first to recieve both. They would have given away 5 of the 20$ gift cards and 12 of the 10$ ones for a total of 17 gift cards.
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For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7
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Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

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Answer:

The correct answer is diagonals are equal and bisect each other.

Step-by-step explanation:

A rectangle is a quadrilateral with opposites sides equal in length and all interior angles equal to 90°. Opposite sides are parallel and adjacent sides are perpendicular. Diagonals in a rectangle are equal in length and they bisect each other. If we want to draw a circumcircle, then the point of intersection of these diagonals give the circumcenter.

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