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Novay_Z [31]
3 years ago
10

Find the value of w to make the statement true.-w = -10 + 4w

Mathematics
1 answer:
Alinara [238K]3 years ago
8 0
Move variable to the left. -w= -10+ 4W
-w-4W =-10
Collect like terms
-5w=-10 divide both sides by 5
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Nicole has 16 nickels and dimes. If the value of her coins is 1.05, how many of each coin does she have?
earnstyle [38]

Answer:

  • 11 nickels
  • 5 dimes

Step-by-step explanation:

If all were dimes, she would have $1.60, which is $0.55 more than she actually has. Replacing a dime with a nickel reduces the total by .05, so there must be .55/.05 = 11 such replacements. This is the number of nickels. The number of dimes makes up the rest of the 16 coins.

Nicole has 11 nickels and 5 dimes.

_____

You can write equations for this several ways. My personal favorite is to use a single variable to represent the number of highest-value coin: d = number of dimes. Then the number of nickels is 16-d and the total value is ...

  0.10d + 0.05(16 -d) = 1.05

  0.05d + 0.80 = 1.05 . . . eliminate parentheses, collect terms

  0.05d = 0.25 . . . . . . . . . subtract 0.80

  d = 0.25/0.05 = 5 . . . . . number of dimes

  16-d = 16-5 = 11 . . . . . . . .number of nickels

__

If you let the variable match the number of nickels, the solution looks a lot like the one described in words, above.

  0.05n + 0.10(16 -n) = 1.05

  -0.05n +1.60 = 1.05

  -0.05n = -0.55 . . . . . . . subtract 1.60

  n = -0.55/-0.05 = 11 . . . number of nickels

  16-n = 16-11 = 5 . . . . . . . number of dimes

__

Comparing these two solutions, you see that we work with negative numbers in the second solution. The reason for choosing the variable to represent the higher-value coin is to keep the numbers positive, as they are in the first solution. (It's no big deal, if you're not bothered by negative number arithmetic.)

3 0
3 years ago
I’m slow so what’s the answer to these?
umka2103 [35]

Answer:

0, -8, 2

Step-by-step explanation:

Opposite of 0 is still 0.

Opposite of 8 = -8

Opposite of the opposite of 2: -2 is the opposite, then the opposite of opposite is -(-2) = 2

7 0
2 years ago
A plastic alphabet cube is 7 cm on each side. What is the surface area of the cube?
MrRa [10]

Answer:

In a cube, the length and width are the same, so both sides will be 7 cm, yielding an area of 49 square centimeters.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Merry Soy, married, earns a weekly salary of $830 and claims one withholding allowance. By the percentage method, how much incom
xxMikexx [17]
You need to find the amount subject to withholding, subtracting from the weekly salary the amount for one withholding allowance for weekly salaries, which is 77.90$:

830 - 77.90 = 752.1 $.

Then, look in the Fed Tax tables (
http://www.opers.ok.gov/Websites/opers/images/pdfs/2016-Fed-Tax-Tables.pdf ) for a married person with a weekly payroll.

You previously found an amount of  752.1 which is greater than 521 but less than 1613$: therefore the income tax to withhold is 35.70$ + 15% of excess over $521.

Therefore, calculate the income tax due: 35.70 + (752.1 - 521) × 15 ÷ 100 = 70.37$

The total amount of income tax that will be withheld is 70.37$
4 0
2 years ago
A number x plus 10 is more than 2
makvit [3.9K]
X+10>2. The simplified answer is x>-8
4 0
3 years ago
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