A rectangle with a length of x + 5 has a perimeter of 4x + 14. 1. Write the expression for the width of the rectangle in terms of x.
2. Suppose the perimeter of the rectangle is 42 inches. What are the length and
width of the rectangle?
3. Write the expression for the area of the rectangle in terms of x.
4. What is the area of the rectangle when x = 7?
Show how t get the answer

1. Width = x + 2

2. Length = 12; width = 9

3. x² + 7x + 10

4. 108

Step-by-step explanation:

perimeter = 4x + 14

length = x + 5

1. Perimeter of a rectangle = 2(length + width)

4x + 14 = 2{(x + 5) + width}

4x + 14 = 2x + 10 + 2width

4x + 14 - 2x - 10 = 2width

2x + 4 = 2width

Width = (2x + 4)/2

Width = x + 2

2. Perimeter of a rectangle = 2(length + width)

42 = 2{(x + 5) + (x + 2)}

42 = 2x + 10 + 2x + 4

42 = 4x + 14

42 - 14 = 4x

28 = 4x

x = 28/4

x = 7

length = x + 5

= 7 + 5

= 12

Width = x + 2

= 7 + 2

= 9

3. Area of the rectangle = length × width

= (x + 5)(x + 2)

= x² + 2x + 5x + 10

= x² + 7x + 10

4. Area of the rectangle = x² + 7x + 10

When x = 7

x² + 7x + 10

= 7² + 7(7) + 10

= 49 + 49 + 10

= 108

see explaination

Step-by-step explanation:

Using the formulla that

sum of terms number of terms sample mean -

Gives the sample mean as \mu=17.954

Now varaince is given by

s^2=\frac{1}{50-1}\sum_{i=1}^{49}(x_i-19.954)^2=9.97

and the standard deviation is s=\sqrt{9.97}=3.16

b) The standard error is given by

\frac{s}{\sqrt{n-1}}=\frac{3.16}{\sqrt{49}}=0.45

c) For the given data we have the least number in the sample is 12.0 and the greatest number in the sample is 24.1

Q_1=15.83, \mathrm{Median}=17.55 and Q_3=19.88

d) Since the interquartile range is Q_3-Q_1=19.88-15.83=4.05

Now the outlier is a number which is greater than 19.88+1.5(4.05)=25.96

or a number which is less than 15.83-1.5(4.05)=9.76

As there is no such number so the given sample has no outliers