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Allushta [10]
3 years ago
6

isabella collected a bunch of dimes and quarters for her school fundraiser she collected a total of 211 coins and a total of 37.

30 how many dimes and how many quarters did she collect
Mathematics
1 answer:
weqwewe [10]3 years ago
6 0

Answer:

103 dimes and 108 quarters

Step-by-step explanation:

Given

Value = \$37.30

Amount = 211

Required

Determine the number of each coin collected

Represent dimes with D and quarters with Q.

1\ D= \$0.10

1\ Q= \$0.25

So:

0.10D + 0.25Q = 37.30 --- Value

D + Q = 211 --- Amount

Make D the subject in D + Q = 211

D = 211 - Q

Substitute 211 - Q for D in 0.10D + 0.25Q = 37.30

0.10(211 - Q) + 0.25Q = 37.30

Open brackets

21.1 - 0.10Q + 0.25Q = 37.30

Collect Like Terms

- 0.10Q + 0.25Q = 37.30 - 21.1

0.15Q = 16.2

Make Q the subject

Q = 16.2/0.15

Q = 108

Substitute 108 for Q in D = 211 - Q

D = 211 - 108

D = 103

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Determine the number of terms, n, given the geometric series 1 3 9 27 ... and sn=3280.
lina2011 [118]

The number of terms, 'n' is 8

<h3 /><h3>How to determine the number of terms</h3>

Let's determine the common ratio;

common ratio, r = 3/1 = 3

The formula for sum of geometric series with 'r' greater than 1 is given as;  Sn = a( r^n - 1) / (r - 1)

n is unknown

Sn = 3280

Substitute the value

3280 = 1 ( 3^n - 1) / 3- 1

3280 = 3^n -1 /2

Cross multiply

3280 × 2 = 3^n - 1

6560 + 1 = 3^n

6561 = 3^n

This could be represented as;

3^8 = 3^n

like coefficient cancels out

n = 8

Thus, the number of terms, 'n' is 8

Learn more about geometric series here:

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5 0
1 year ago
Solve, then write, each equation in slope intercept form. ​
djyliett [7]

Answer:

1) (3,5)

2) (4,-7)

3)  (6,4)

4) (-4,-3)

Step-by-step explanation:

1)

Subtract  y  from both sides of the equation.

x  =  8  −  y

x  −  y  =  −2

Replace all occurrences of x  in x  −  y  =  −2  with  8  −  y.

x  =  8  −  y

(8  −  y)  −  y  =  −2

Subtract y from  −y.

x  =  8  − y

8  −  2y  =  −2

Solve for  y  in the second equation.

x  =  8  −  y  

y  = 5

Replace all occurrences of  y  in  x  =  8  −  y  with  5.

x  =  8  −(5)

y  =  5

Simplify  8  −(5).

x  =  3

y  =  5

Slope = (3,5)

2)

Multiply each term by  2  and simplify.

2x+y=12

y+6=−x−4

Move all terms containing variables to the left side of the equation.

2x+y=1x+2

y+6=−4

Move all terms not containing a variable to the right side of the equation.

2x+y=1x+2

y=−10

Multiply each equation by the value that makes the coefficients of  x  opposite.

2x+y=1(−2)⋅

(x+2y)=(−2)(−10)

Simplify.

2x+y=1−2x−4

y=20

Add the two equations together to eliminate  x  from the system.

2x+y=1+−2x−4

y=20−3

y=21

Divide each term by  −3  and simplify.

y  = −7

Substitute the value found for  y  into one of the original equations, then solve for  x.

x  =  4

slope (4,-7)

3)

Subtract  y  from both sides of the equation.

2x−y=8x−y=2

Multiply each equation by the value that makes the coefficients of  y  opposite

2x−y=8(−1)⋅

(x−y)=(−1)(2)

Simplify. 2x−y=8

−x+y=−2

Add the two equations together to eliminate  y  from the system.

2x−y=8  +  −x+y=−2x=6

Substitute the value found for  x  into one of the original equations, then solve for  y.

y=4

slope (6,4)

4)

Simplify 2(x+1).

y−3=2x+2

y=−3(x+5)

Simplify  −3(x+5)

y−3=2x+2

y=−3x−15

Move all terms containing variables to the left side of the equation.

−2x+y−3=2

y=−3x−15

Add  3x  to both sides of the equation.

−2x+y−3=2

y+3x=−15

Move all terms not containing a variable to the right side of the equation.

−2x+y=5

y+3x=−15

Reorder the polynomial.

−2x+y=5

3x  +  y=−15

Multiply each equation by the value that makes the coefficients of  y  opposite.

−2x+y=5(−1)⋅

(3x+y)=(−1)(−15)

Simplify.

−2x+y=5

−3x−y=15

Add the two equations together to eliminate  y  from the system.

−2x+y=5  +  −3x−y=15−5x=20

Divide each term by  −5  and simplify.

x=−4

Substitute the value found for  x  into one of the original equations, then solve for y.

y=−3

slope (-4,-3)

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3 years ago
Simply the radical expression 189
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Step-by-step explanation:

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D

Step-by-step explanation:

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A rectangular floor measures 10 1/8 feet by 13 3/4 feet. If Emily buys 150 square feet of carpet, will she have enough carpet to
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Yes she will have enough. Here is why.

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