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Tom [10]
3 years ago
14

The rectangle shown has a perimeter of 44 cm and the given area. Its length is 7 more than twice its width. Write and solve a sy

stem of equations to find the dimensions of the rectangle.
The length of the rectangle is __ cm and the width of the rectangle is __ cm
Mathematics
1 answer:
Paha777 [63]3 years ago
3 0

Answer:

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm.

Step-by-step explanation:

Given the measurements in the question, you can set up two different equations to find the length and width of the rectangle.  First, the formula for the perimeter of a rectangle is:  P = 2W + 2L, where W = width and L=length.  In this problem the L is '7 more than twice its width', this means our first equation is:

L = 2W + 7

Next, we can use this expression in our formula for perimeter to get our second equation:

P = 2W + 2(2W + 7)  or 44 = 2W + 2(2W + 7)

Distribute:  44 = 2W + 4W + 14

Combine like terms:  44 = 6W + 14

Subtract 14 from both sides:  44 - 14 = 6W + 14 - 14 or 30 = 6W

Divide 6 from both sides:  30/6 = 6W/6 or W = 5

Now, solve for L:  L = 2(5) + 7 or L = 10 + 7 = 17

So, the width is 5cm and the length is 17 cm.

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You have drawn a simple random sample of 36 college students, asking each student how much rent they pay per month. You obtain a
Karo-lina-s [1.5K]

Answer:

573-1.690\frac{22}{\sqrt{36}}=566.8033    

573+1.690\frac{22}{\sqrt{36}}=579.1967      

And the 90% confidence interval would be between [566.80 and 579.20]

Step-by-step explanation:

Information given

\bar X=573 represent the sample mean

\mu population mean (variable of interest)

s=22 represent the sample standard deviation

n=36 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The degrees of freedom are given by:

df=n-1=36-1=35

The Confidence level is 0.90 or 90%, the significance would be \alpha=0.1 and \alpha/2 =0.05, and the critical value for this case would be t_{\alpha/2}=1.690

And replacing we got:

573-1.690\frac{22}{\sqrt{36}}=566.8033    

573+1.690\frac{22}{\sqrt{36}}=579.1967    

And the 90% confidence interval would be between [566.8033 and 579.1967]

6 0
3 years ago
debt payments of $800 due now and $1400 due in 5 months are to be repaid by a payment of $1000 in 3 months and a final payment i
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Answer:

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Step-by-step explanation:

If interest 6% annually, monthly is 0.5%.

The debt in 5 months will be 800 plus compounded interest for 5 months plus new due debt

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In 3 more months the debt will be 2220.201 plus compounded interest for 3 months minus payment

2220.201(1.005)^3-1000=1253.67

After 8 months the debt would be 1253.67 plus compounded interest for 8 months

2220.201(1.005)^3=1304.70

Then the size of the final payment would be $1,304.70

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Answer:

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Step-by-step explanation:

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Answer:

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Explanation:

A diameter is twice the radius. Here, we can use the formula d=2r (d=diameter r=radius)

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