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3 years ago

The length of a rectangle is 3 feet more than twice the width. The perimeter is 128 feet. Find the length and width in feet.

Mathematics

2 answers:

Tcecarenko [31]3 years ago

8 0

Answer:

w = 20 1/3 ft.

l = 43 2/3 ft.

Step-by-step explanation:

w=width l = length

l = 3 + 2w

128 = 2l + 2w

128 = 2(3 + 2w) + 2w

128 = 6 + 4w +2w

122 = 6w

20 1/3 = w

Helga [31]3 years ago

4 0

Answer:

Step-by-step explanation:

<h3>The first part of finding the length and width of this rectangle is defining each of the lengths as <em>variables</em>. We usually do this by writing, "let" for each statement. Let's try!</h3><h2>Let x = the width</h2><h2> 2x + 3 = the length</h2>

Now, let's define the perimeter in terms of x. So, we understand that the perimeter consists of the width times 2 and the length times 2. It's simply how rectangles work, right? Let's do this, then! Let's find the perimeter in terms of x!

Considering the width of the rectangle is x and the length is 2x + 3, the perimeter of the rectangle is 6x + 6. But hey, we already know what the actual perimeter of the rectangle is! Let's make a system of equations! (We're getting a little advanced here but it's alright, ask me questions if you need to!)

<h2>Let P = total perimeter of the rectangle</h2><h2>P = 6x + 6</h2><h2>P = 128 feet</h2><h3>We can solve this system of equations by using the equal values method. If you need more help, you can search the equal values method on the internet. If you need more explanation, please ask!</h3><h2>Now we know that both 6x + 6 and 128 are both equal to P. This means that 6x + 6 and 128 are equal, too! We can now make an equation to find x, the width!</h2><h2>6x + 6 = 128</h2><h2> - 6 - 6</h2><h2>6x = 122</h2><h2>x = 122/6 = 20 ¹/₃ feet</h2><h3>Since we have already defined x as 20 1/3 feet. Now we can find the length, 2x + 3. We can plug x into the equation.</h3><h2>2 ( 20 ¹/₃ ) + 3 = length</h2><h2>40 ²/₃ + 3 = length</h2><h2>length = 43 ²/₃.</h2><h2><em>Now we can check our work!</em></h2><h2>6x + 6 = 128</h2><h2>6(20 ¹/₃) + 6 = 128</h2><h2>6(20 ¹/₃) = 122</h2><h3>If we multiply 6 and 20 ¹/₃, we find the product as 122. This means that x is true in the situation and that it is correct.</h3><h2>If you need help, please tell me in the comments! I'm happy to help! <3</h2><h2><em></em></h2>

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ohaa [14]

The least common denominator is
20 = 2 * 2 * 5
25 = 5 * 5

The least common denominator has two 5s and two 2s.
LCD = 2*2*5*5 = 100

17/20 = 17 * 5/ 20*5 = 85 / 100
21/25 = 21* 4/25*4 = 84 / 100

Talk about close
17/20 > 21/25 <<<< answer

But I hate to have predicted that before hand.

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3 years ago

A) |9+x|=2x<br> b) |x+6|=2x+9

levacccp [35]

Answer:

a) 9

b) -3

Step-by-step explanation:

|9+x|=2x

9 + x = 2x

- x -x

---------------

9 = x

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x +6 = 2x +9

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6 = x + 9

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3 years ago

You just graduated college (age 23) and now have your dream job of a computer animator. Your gross salary is 43,000 a year. Answ

Kipish [7]

Answer:

$93.72

Step-by-step explanation:

To be able to find how much is deducted from our paycheck monthly, we have to compute for the total amount left to pay for the health insurance.

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Total amount left = $4500- $4500x0.75

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Now that we know the total amount left, we simply divide the total by 12 to find the monthly payments.

Monthly Payment = $1125/12

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So a total of $93.72 will be deducted from our monthly paycheck for the health insurance.

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3 years ago

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Write a situation that can be represented by the expression 3a+6 where a=age in years

mars1129 [50]

This equation can be used when comparing ages.

An example to illustrate this:
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3 years ago

Problem 9

lapo4ka [179]

Answer:

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at $\frac{1}{4}$ capacity, we can use the equation:

$\frac{1}{4} * 12 = \boxed{3}$

This shows $\frac{1}{4}$ of his tank's capacity ( $12$ ) is equal to $3$ gallons. This means he will stop for gas when $3$ gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

$\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}$

This is a simple proportion, and now we know he uses $2.5$ gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has $7$ gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

$\frac{7-3}{2.5} = 1.6$

The $7-3$ is because Leon doesn't stop when his tank is empty, he stops $3$ gallons earlier. We are dividing by $2.5$ because that is how much gas he uses per hour, meaning the result of this division ( $1.6$ ) is how many hours he has left.

Now we can solve for what time Leon will stop to get gas.

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( $1.6$ hours is equal to 1 hour and 36 minutes)

Therefore, Leon will stop for gas at 3:36PM

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