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2 years ago

The length of a rectangle is twice its width. Find its area, if its perimeter is 7 and 1/3 cm.

Mathematics

1 answer:

laila [671]2 years ago

7 0

Answer:

2.99 cm²

Step-by-step explanation:

<em>(The "..." at the end of the decimal means that number is repeating)</em>

The perimeter of a rectangle is the length around the shape. The equation for a rectangle's perimeter is L + W × 2, with L and W representing length and width, respectively (You multiply the length and width by two because the shape is four-sided, so it has two length sides and two width sides). To find the area of the rectangle, you need to know the individual length and width, so you'll solve for that first.

Since you're only given the perimeter and you know the length is double the width, you'll need to work backwards with this equation. To do this, first divide the perimeter (7 $\frac{1}{3}$ , also written as 7.33...) by 2; this equals 3 $\frac{2}{3\\}$ , also written as 3.66...

Next, you can find the length and width by determining what two numbers multiply to equal 3.66..., with one number being two times larger than the other number. The way I tend to think of this is that if one number is double the other, then the smaller number is one third of the sum of the two numbers (since the smaller number represents one part of the sum, and the other represents two parts of the sum, which is double the smaller number).

Since the length and width combine to be the divided perimeter, 3.66..., that means two thirds of 3.66... is the longer side (the length), and then the one third of 3.66... is the shorter side (the width). This means the length is 2.44... and the width is 1.22...

Finally, you can solve for the perimeter by dividing the perimeter by two and then subtracting the length squared. The written equation looks like this:

A = P $\frac{1}{2}$ - L²

(A = area, P = perimeter, L = lenth)

Now just insert the numbers into the equation and solve!

The area of the rectangle is 2.99cm²

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3 years ago

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Lelechka [254]

Answer:

$\huge\boxed{\sf Slope = \frac{5}{2} }$

Step-by-step explanation:

<u>Take any two points or coordinated from the graph.</u>

Let's take (2,2) and (0,-3)

So,

$\sf (x_{1},y_{1}) = (2,2)\\\\(x_{2},y_{2}) = (0,-3)$

Hence,

$\sf Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\Slope = \frac{-3-2}{0-2} \\\\Slope = \frac{-5}{-2} \\\\Slope = \frac{5}{2} \\\\\rule[225]{225}{2}$

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2 years ago

Read 2 more answers

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chose

Nookie1986 [14]

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)

Step-by-step explanation:

Notation and definitions

n=50 represent the sample size

$\bar X= 27.2$ represent the sample mean

$s=5.83$ represent the sample standard deviation

m represent the margin of error

Confidence =88% or 0.88

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by $\alpha=1-0.88=0.12$ and $\alpha/2 =0.06$ . The degrees of freedom are given by: