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tangare [24]
1 year ago
13

1. Mitch needs to do his laundry. It takes him 75 minutes to do each load when he washes and dries the load. It takes him 43 les

s minutes if he hangs up his laundry to dry. He decides to hang up one load of laundry to dry.
Mitch writes the equation 75x - 43= 332 where x is the number loads of laundry he needs to do in order to determine how long it is going to take him.

the next step Mitch wrote to solve the equation is shown here: 75x = 375

Which property did he use to get to this step?

Hint: Mitch has to do the opposite of subtract 43 to both sides.

A. addition property of equality

B. subtraction property of equality

C. combining like-terms

2. Lacey has $20 to spend at the movie theater. She spends $10.25 on the movie ticket, and $2.25 each on boxes of candy. The inequality 10.25 + 2.25c <_ can be used to determine c, the number of boxes of candy she can buy.

Which statements about the number of boxes of candy Lacey can buy are true?

Hint: Move the constant term to the right. Divide by the coefficient of the variable.

Select TWO that apply.

A. Lacey can buy 2 boxes of candy, but this number is neither the maximum or minimum number of boxes of candy she can buy.

B. The minimum boxes of candy Lacey can buy is 12.

C. Lacey can buy 5 boxes of candy.

D. Lacey can buy 4 boxes of candy.

3. Josephine is going on a run around the lake. She knows the distance around the lake. but she would like to complete her run in a certain amount of time. Josephine knows she can used the formula d=n

Which equation correctly rearranges the formula to find the time it will take her to run around the lake?

Hint: Isolate the t. In other words, move the r to the other side, do the opposite.

A. t = d - r
B. t = d/r
C. t = r/d
Mathematics
1 answer:
NARA [144]1 year ago
5 0

not sure if this is correct but 1. A ( reasoning: "Hint: Mitch has to do the opposite of subtract 43 to both sides." which means he had to add. 2. She can get no more than 4

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6ft

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An engineer measures the peak current (in microamps) when a solution containing an amount of nickel (in parts per 106 ) is added
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B. decrease the intercept, increase the slope

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Nikki had a $50 gift card for her favorite store. She used the gift card to buy 4 DVDs and still had money available on the card
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c

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5(0.04y-0.08) &gt;3(0.2y-0.05-0.4y)
MAXImum [283]

0.08(y + -1) + 0.12y = 0.14 + -0.05(10)

Reorder the terms:

0.08(-1 + y) + 0.12y = 0.14 + -0.05(10)

(-1 * 0.08 + y * 0.08) + 0.12y = 0.14 + -0.05(10)

(-0.08 + 0.08y) + 0.12y = 0.14 + -0.05(10)

Combine like terms: 0.08y + 0.12y = 0.2y

-0.08 + 0.2y = 0.14 + -0.05(10)

Multiply -0.05 * 10

-0.08 + 0.2y = 0.14 + -0.5

Combine like terms: 0.14 + -0.5 = -0.36

-0.08 + 0.2y = -0.36

Solving

-0.08 + 0.2y = -0.36

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '0.08' to each side of the equation.

-0.08 + 0.08 + 0.2y = -0.36 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00

0.00 + 0.2y = -0.36 + 0.08

0.2y = -0.36 + 0.08

Combine like terms: -0.36 + 0.08 = -0.28

0.2y = -0.28

Divide each side by '0.2'.

y = -1.4

Simplifying

y = -1.4

3 0
2 years ago
The first term of a finite geometric series is 6 and the last term is 4374. The sum of all the term os 6558. find the common rat
Oliga [24]

A geometric series is written as ar^n, where a is the first term of the series and r is the common ratio.

In other words, to compute the next term in the series you have to multiply the previous one by r.

Since we know that the first time is 6 (but we don't know the common ratio), the first terms are

6, 6r, 6r^2, 6r^3, 6r^4, 6r^5, \ldots.

Let's use the other information, since the last term is 4374 > 6, we know that r>1, otherwise the terms would be bigger and bigger.

The information about the sum tells us that

\displaystyle \sum_{i=0}^n 6r^i = 6\sum_{i=0}^n r^i = 6558

We have a formula to compute the sum of the powers of a certain variable, namely

\displaystyle \sum_{i=0}^n r^i = \cfrac{r^{n+1}-1}{r-1}

So, the equation becomes

6\cfrac{r^{n+1}-1}{r-1} = 6558

The only integer solution to this expression is n=6, r=3.

If you want to check the result, we have

6+6*3+6*3^2+6*3^3+6*3^4+6*3^5+6*3^6 = 6558

and the last term is

6*3^6 = 4374

7 0
1 year ago
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