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DerKrebs [107]
3 years ago
15

Mary has a collection of nickels and quarters for a total of $4.90. If she has 42 coins in total, how many of each kind are ther

e?
Mathematics
1 answer:
damaskus [11]3 years ago
5 0

Answer:

14 quarters and 28 nickels

Step-by-step explanation:

System of Equations where x = number of quarters and y = number of nickels

(1) equation with value of each coin

    0.25(x)+0.05(y) = 4.90

(2) total number of coins

    x + y = 42

Solve system of equations using either substitution or elimination

(elimination multiplying equation 2 by -0.5)

.25(x) + 0.05(y) = 4.90

-0.05(x) - 0.05(y) = 42 * (-0.05)

(3) Resulting equation

.20(x) = 2.8

x = 14

plug x into equation 2

14 + y = 42

y = 28

There are 14 quarters and 28 nickels in Mary's collection.

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What is the solution to this equation 5x -8(x + 5)= 6-3x
Solnce55 [7]

Answer:

no solution

Step-by-step explanation:

5x - 8(x + 5) = 6 - 3x

Remember to follow PEMDAS. Note the equal sign, what you do to one side, you do to the other.

First, distribute -8 to all terms within the parenthesis

-8(x + 5) = (-8)(x) + (-8)(5) = -8x - 40

5x - 8x - 40 = 6 - 3x

Isolate the variable (x). Add 3x & 40 to both sides

5x - 8x (+3x) - 40 (+40) = 6 (+40) - 3x (+3x)

5x - 8x + 3x = 6 + 40

Simplify. Combine like terms

(5x - 8x + 3x) = (6 + 40)

0 = 46 ; False 0 ≠ 46 ∴ no solution is your answer

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3 years ago
Area of a octagon with radii of 13.07 in. and perimeter of 80 in.
Brilliant_brown [7]

<em><u>Answer:</u></em>

<em>A≈482.84in²</em>

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<u><em>Step(s) of Explanation:</em></u>

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3 years ago
Estimate the perimeter of the figure to the nearest whole number.
Paha777 [63]

Answer:

The perimeter (to the nearest integer) is 9.

Step-by-step explanation:

The upper half of this figure is a triangle with height 3 and base 6.  If we divide this vertically we get two congruent triangles of height 3 and base 3.  Using the Pythagorean Theorem we find the length of the diagonal of one of these small triangles:  (diagonal)^2 = 3^2 + 3^2, or (diagonal)^2 = 2*3^2.

Therefore the diagonal length is (diagonal) = 3√2, and thus the total length of the uppermost two sides of this figure is 6√2.

The lower half of the figure has the shape of a trapezoid.  Its base is 4.  Both to the left and to the right of the vertical centerline of this trapezoid is a triangle of base 1 and height 3; we need to find the length of the diagonal of one such triangle.  Using the Pythagorean Theorem, we get

(diagonal)^2 = 1^2 + 3^2, or 1 + 9, or 10.  Thus, the length of each diagonal is √10, and so two diagonals comes to 2√10.

Then the perimeter consists of the sum 2√10 + 4 + 6√2.

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