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stira [4]
3 years ago
10

The area rug in your living room is 5 feet longer than it is wide. If the rug is

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
4 0

Answer:

length = 17 ft and width = 12 ft

Step-by-step explanation:

The rug is rectangular .

Let

width = a

length = a + 5

Area of the rug = a × (a + 5) = a² + 5a

The rug is always placed 2 ft from the wall. The illustration describes a rectangle place into another. The space between the rug and the wall is 100 ft².  

The living room

length = a + 5 + 2 + 2= a + 9

width  = a + 2 + 2 = a + 4

area = (a + 9)(a + 4) = a² + 4a + 9a + 36 = a² + 13a + 36

a² + 13a + 36 - (a² + 5a) = 100

a² + 13a + 36 - a² - 5a = 100

8a + 36 = 100

8a = 100 - 36

8a = 64

a = 64/8

a = 8

Dimension of the living room

length = a + 9

length = 8 + 9 = 17 ft

width  = a + 4

width = 8 + 4 = 12 ft

length = 17 ft and width = 12 ft

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2 years ago
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6 0
3 years ago
What equation best represents the circumference of a circle with a radius of 6 feet? A y = 2π B y = 6π C y = 12π D y = 16π
professor190 [17]

Answer:

12π

Step-by-step explanation:

The circumference is the distance you need to walk to do 1 full rotation of a shape. The formula to calculate the circumference of a circle will be

circumference =2πr

where π is a constant that equal to 3.14 or 22/7 and r is the radius of the circle (radius = 6 feet).

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4 0
3 years ago
Need help! :(
snow_tiger [21]
Given:
2x² + 8x - 12 = 0

Solution:
The first term 2x² can't be changed to a complete square form. If we want to change it to the complete square form, we need to change 2x² to 4x². So, multiply both sides of the equation by 2
2x² + 8x - 12 = 0
------------------------- multiplied by 2
4x² + 16x - 24 = 0

then change it to complete quadratic form by adding 16 to both sides
4x² + 16x - 24 = 0
4x² + 16x + 16 - 24 = 16
4x² + 16x + 16 = 16 + 24
4x² + 16x + 16 = 40
(2x + 4)(2x + 4) = 40
(2x + 4)² = 40
This is the complete quadratic form of the equation.

Because there is no option of the solution, we can modify the equation by multiplying the two sides by a square number. I multiply the equation by 4.
(2x + 4)² = 40
4 (2x + 4)² = 4 × 40
4 (2x + 4)² = 160
4 (2x + 4)(2x + 4) = 160
2(2x + 4) 2(2x + 4) = 160
(4x + 8)(4x + 8) = 160
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5 0
3 years ago
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When she checked the answer by estimating, it did not make sense. What error did Janice make?
Leokris [45]
<h2>Answer</h2>

Janice convert a mixed number to the wrong improper fraction

<h2>Explanation</h2>

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the result to the numerator of the fraction; while keeping the denominator of the fraction as the denominator of the improper fraction.

Let's convert our mixed numbers to improper fractions:

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Now let's convert 1\frac{2}{3}:

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Notice that Janice converted 1\frac{2}{3} as \frac{5}{2}, which is incorrect.

Since 1\frac{2}{3} =\frac{5}{3}, we can conclude that Janice convert a mixed number to the wrong improper fraction.

8 0
4 years ago
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