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kenny6666 [7]
3 years ago
14

20. A rectangle has an area of 45 cm². The length is one cm less than twice the width. Find the dimensions of

Mathematics
1 answer:
prohojiy [21]3 years ago
7 0
Width = 5, length = 9

Area = length * width

length = (2 * width) - 1

sub equation for length

45 = (2w - 1) * w
45 = 2w^2 - w
2w^2 - w - 45 = 0
(2w - 9)(w - 5)
2w - 9 = 0
w = 9/2, l = 8 no

w -5 = 0
w = 5, l = 9 yes
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How many positive integers can be expressed ad a product of two or more of the prime numbers 5,7,11,and 13 if no one product is
sertanlavr [38]

Answer:

11 positive integers can be expressed.

Step-by-step explanation:

Consider the provided information.

The number of possible prime numbers are 5,7,11,and 13.

There are 4 possible prime numbers.

How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.

The formula to calculate combinations is: ^nC_r=\frac{n!}{r!(n-r)!}

The number of ways are:

^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}

^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1

^4C_2+^4C_3+^4C_4=6+4+1

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Hence, 11 positive integers can be expressed.

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The larger of two number is 12 more than the smaller number.if the sum of the two numbers is 74, find the two numbers
Mars2501 [29]
<h3><u>The value of the smaller number is 31.</u></h3><h3><u>The value of the larger number is 43.</u></h3>

y = 12 + x

y + x = 74

Since we have a value for y, we can plug it into the second equation

12 + x + x = 74

Subtract 12 from both sides.

x + x = 62

Combine like terms.

2x = 62

Divide both sides by 2.

x = 31


Now that we have a value of x, we can plug it into the original equation to get a value for y.

y = 12 + 31

y = 43

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3 years ago
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34kurt

Answer: D 2/3

Step-by-step explanation:

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