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3 years ago

A square is changed into a new rectangle by increasing its width by 2 inches and decreasing its length by 2

1 answer:

5 0

Answer: The area of the square is 64 square inches and the area of the new rectangle is 60 square inches. The square's area is 4 inches larger than the rectangle.

Step-by-step explanation: If a side length of the square measures 8 inches, then its area can be calculated as follows;

Area = L x W

The length and the width both measure 8 inches (all sides of a square are equal in length).

Area = 8 x 8

Area = 64

Also, the the new rectangle is formed by increasing the width of the square by 2 inches (that is 8 + 2 = 10), and decreasing the length by 2 inches (that is 8 - 2 = 6). The area of the new rectangle is calculated as follows;

Area = L x W

Area = 10 x 6

Area = 60

Therefore the area of the square is 64 square inches and the area of the rectangle is 60 square inches. The area of the square is 4 inches larger than that of the rectangle.

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Help please........................

yawa3891 [41]

A dilation means that a shape is expanded or shrunk by a scale factor. The scale factor is 4, so all the points are multiplied by 4 to reflect this expansion.

A reflection over the y-axis means that the y-values in the points change their sign from positive to negative, and vice versa.

Therefore, the points will become the following:
A''(12,-12), B''(-4, -12), C''(-16,-4), D''(0, -4)

This new shape will be similar to the original shape, since it shares the same shape, but not the same size.

The answer is A.

7 0

4 years ago

Factor the expression completely -7r-35x

bogdanovich [222]

7 is the most common in this expression.

therefore to factorise, you will choose the most common factor.

the answer will be -7(r+5x)

7 0

3 years ago

If the lesser of the two consecutive even integers is five more than half the greater, what are the two integers?

Marina CMI [18]

The integers are 12, 14.

Solution:

Let the even consecutive integers be x and x + 2.

Lesser number = x and Greater number = x + 2

Lesser number = Half of greater number + 5

$$\Rightarrow x = \frac{1}{2} (x + 2) + 5$

$$\Rightarrow x = \frac{x + 2}{2} + 5$

To add the numbers, denominators must be same. So multiply 5 by $\frac{2}{2}$ .

$$\Rightarrow x = \frac{x + 2}{2} + \frac{10}{2}$

$$\Rightarrow x = \frac{x + 12}{2}$

Multiply by 2 on both sides, we get

⇒ 2x = x + 12

Subtract x from both sides.

⇒ x = 12

Lesser number = 12

Greater number = 12 + 2 = 14

Hence the integers are 12, 14.

7 0

3 years ago

How many days are there in a normal year?

MAXImum [283]

In a non-leap year, there are 365 days, in a leap year there are 366 days.

6 0

4 years ago

Read 2 more answers

State legislators propose cutting funding to public universities. College administrators oppose this, claiming that across the s

zimovet [89]

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of sample 1

x2 = sample mean of sample 2

s1 = sample standard deviation for sample 1

s2 = sample standard deviation for sample 2

n1 = number of samples in sample 1

n2 = number of samples in sample 2

From the information given,

x1 = 934.1

s1 = 120.52

x2 = 1302.2

s2 = 178.6

For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18

z = 2.552

x1 - x2 = 934.1 - 1302.2 = -368.1

√(s1²/n1 + s2²/n2) = √(120.52²/10 + 178.6²/10) = √(1452.50704 + 3189.796)

= 68.13

Margin of error = 2.552 × 68.13 = 173.87

Therefore, confidence interval =

-368.1 ± 173.87

8 0

4 years ago