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kirill [66]
3 years ago
12

The width of a rectangle is (x-5) and the length is (x+2). What is the length and width of the rectangle if the area is 18 squar

e feet?
Mathematics
2 answers:
Murrr4er [49]3 years ago
3 0

Answer:

Length: 9

Width: 2

Step-by-step explanation:

Area = length × width

18 = (x - 5)(x + 2)

18 = x² - 5x + 2x - 10

x² - 3x - 28 = 0

x² - 7x + 4x - 28 = 0

x(x - 7) + 4(x - 7) = 0

(x - 7)(x + 4) = 0

x = 7, -4(not possible)

Length: 7+2 = 9

Width: 7-5 = 2

aleksklad [387]3 years ago
3 0

(x-5)(x+2)= 60

x^2 + 2x - 5x -10 = 60

x^2 -3x -10 = 60

x^2 -3x -70

(x-10)(x+7)

x= 7

Proof:

x + 2

x - 5

Plug in 7.

7 + 2 = 9

7 - 5 = 2

9 x 2 = 18

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Answer:

Part (A): The number of ways to select 12 jurors are 86493225.

Part (B): The number of ways to select 2 alternates are 306.

Part (C): Part (a) is an example of combination  and Part (a) is an example of permutation

Step-by-step explanation:

Consider the provided information.

A band director wants to form a committee of 4 parents from a list of 45 band parents.

Part (A):  How many different groups of 4 parents can the band director select?

Since order doesn't matter so we will use combination.

Use the formula for combination ^{n}C_{r}=\frac{n!}{r!(n-r)!}

Substitute n=45 and r=4 in above formula.

^{45}C_{4}=\frac{45!}{4!(45-4)!}

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^{45}C_{4}=148995

Hence, the number of ways are 148995.

Part (B) How many different ways can the band director select 4 parents to serve in the band parents’ association as president, vice president, treasurer, and secretary?

Since the order matter so we will use permutation:

The formula for permutation is:  ^{n}P_{r}=\frac{n!}{(n-r)!}

Substitute n=45 and r=4 in above formula.

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^{45}P_{4}=3575880

Hence, the number of ways are 3575880.

Part (C) . Explain the difference between parts (a) and (b) in terms of how you decided to solve each part.

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Part (B) is an example of permutation where order matter.

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