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3 years ago

The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is

Mathematics

2 answers:

SCORPION-xisa [38]3 years ago

6 0

The width of the mat around the photo is 3 inches

The combined area of the of the photo and math = 224 square inches

The combined area is represented as:

(2w +8)(2w + 10) = 224

Expand the equation using the distributive rule

$4w^2+20w+16w+80=224\\\\4w^2+36w+80-224=0\\\\4w^2+36w-144=0$

Divide through by 4

$w^2+9w-36=0$

Factorize the resulting quadratic equation to solve for w

$w^2-3w+12w-36=0\\\\w(w-3)+12(w-3)=0\\\\(w-3)(w+12)=0$

w - 3 = 0

w = 3

w + 12 = 0

w = -12

The width of the mat around the photo is 3 inches

Learn more on area here: brainly.com/question/20968176

vitfil [10]3 years ago

4 0

The width of the mat around the photo is 3 inches

Combined area:

2w +8)(2w + 10) = 224

where,

w = width of the mat around the photo

(2w +8)(2w + 10) = 224

open parenthesis

4w² + 20w + 16w + 80 = 224

4w² + 36w + 80 - 224 = 0

4w² + 36w - 144 = 0

divide through by 4

w² + 9w - 36 = 0

solve quadratic equation using factorization method

w² + 12w - 3w - 36 = 0

w(w + 12) - 3(w + 12) = 0

(w + 12) (w - 3) = 0

w + 12 = 0 or w - 3 = 0

w = -12 or w = 3

The width of the mat around the photo cannot be a negative value.

Therefore, the width of the mat around the photo is 3 inches

Learn more about quadratic equation:

brainly.com/question/1214333

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Solution:

Given , a television sells for $ 900

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3 years ago

The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are ask

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If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then C. the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease.

Step-by-step explanation:

The margin of error helps in mentioning the amount of random sampling error that occurred in a survey. Increase in the margin of error, makes the result less confidence. So the margin of error of the survey should be less.

The margin of error can be calculated in two different ways:

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What is the difference in 2/8 and 1/2

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an urn contains twenty chips, numbered 1 through 20. two are drawn at random simultaneously (without replacement). what is the p

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The probability of the numbers on the two chips differing by more than two are 0.805.

<h3>What is probability? </h3>

The study of numerical representations of the possibility of an event occurring or a proposition being true is known as probability. A probability is a number between 0 and 1, where 0 denotes impossibility and 1 denotes certainty.

Given that,

Urn is composed of twenty chips, numbered one through twenty.

Two are drawn at random simultaneously.

The probability that the numbers on the two chips deviate by greater than two.

Probability = 20 x 20 - 20

Probability = 400 – 20

Probability = 380 total possible outcomes for 20 outcomes.

In the first and last rows, we can also observe that there are 20-3 = 17 choices with a difference greater than 2.

In the second and next-to-last rows, there are 20-4 =16 possibilities for a difference greater than 2.

As a result, the total is 2(17) + 2(16) + 2(15) = 306

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1 year ago