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nikitadnepr [17]
3 years ago
7

A 7 by 10 inch mirror was put in a frame and hung on the wall. The mirror and frame together cover an area of 130 inches squared

. How wide is the frame?
Mathematics
1 answer:
xxTIMURxx [149]3 years ago
7 0

Answer: the width of the frame is 3 inches.

Step-by-step explanation:

Let x represent the width of the frame.

If the length of the mirror is 10 inches, the length of the mirror and the frame would be (x + 10) inches

If the width of the mirror is 7 inches, the width of the mirror and the frame would be (x + 7) inches

The mirror and frame together cover an area of 130 inches squared. This means that

(x + 10)(x + 7) = 130

x² + 7x + 10x + 70 = 130

x² + 17x + 70 - 130 = 0

x² + 17x - 60 = 0

x² + 20x - 3x - 60 = 0

x(x + 20) - 3(x + 20) = 0

x - 3 = 0 or x + 20 = 0

x = 3 or x = - 20

Since the width cannot be negative, then x = 3

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A company mixes two kinds of cleansers to get a blend they sell for 59 cents a liter. One of the cleansers costs 50 cents per li
Lilit [14]

Answer:

Cleanser that costs 50 cents is 1400 liters, Cleanser that costs 80 cents is 600 liters.

Step-by-step explanation:

We can solve this by using <em>simultaneous equations</em>:

  1. Let us express the question in terms of equations

Let a be cleanser at 50 cents and let b be the cleanser at 80 cents.

Equation 1: 0.5a + 0.8b = 0.59(a+b)

Equation 2: a + b = 2000

From equation 2, a = 2000 - b (Let's call this equation 3)

    2. Substituting equations 2 and 3 in Equation 1:

0.5a + 0.8b = 0.59(a+b)

0.5(2000 - b) + 0.8b = 0.59(2000)

1000 - 0.5b + 0.8b = 1180

0.3b = 180

b = 600

Substitute in equation 3:

a = 2000 - 600

a = 1400

As a note, I formed equation 1 because I know for a fact the cost per liter of a and b. I also know it is sold at 0.59 cents per liter. We are selling 2000 liters in this instance, therefore 0.59(2000) = 1180, which in this case is the selling price.

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3 years ago
What is the area of the figure
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Step-by-step explanation: area of the square= 36cm²

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The formula for the ares of the circle is πr²

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