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ipn [44]
3 years ago
13

The rectangle below has an area of x^2-25x 2 −25 square meters and a length of x+5x+5 meters. What expression represents the wid

th of the rectangle?
Mathematics
1 answer:
iris [78.8K]3 years ago
3 0

Answer:  x - 5

Step-by-step explanation:

Since, the area of the rectangle = x^2 - 25=(x+5)(x-5)

Length of the rectangle = x+5

Let the width of the rectangle = b

Thus, the area of the rectangle = (x+5)\times b

⇒ (x+5)\times b=(x+5)(x-5)

⇒  b=\frac{(x+5)(x-5)}{(x+5)}

⇒ b=x-5

Therefore, the expression that shows the width of the rectangle = x-5

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In terms of x, find an expression that represents the area of the shaded region. The outer square has side lengths of (x+5) and
VLD [36.1K]
The area of the outer square = (x+5)² = x² + 10x + 25

The area of the inner square = (x-2)² = x² - 4x + 4

The area of the shaded region = (x² + 10x + 25) - (x² - 4x + 4)
                                                   = x² + 10x + 25 - x² + 4x - 4
                                                   = 14x + 21  square units
6 0
3 years ago
In a survey, 28 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped
Rina8888 [55]

Answer:

The 80% confidence level estimate for how much a typical parent would spend on their child's birthday gift is between $33.954 and $35.246.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution should be used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 28 - 1 = 27

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.8}{2} = 0.9. So we have T = 1.314

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.314\frac{2.6}{\sqrt{28}} = 0.646

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 34.6 - 0.646 = $33.954

The upper end of the interval is the sample mean added to M. So it is 34.6 + 0.646 = $35.246

The 80% confidence level estimate for how much a typical parent would spend on their child's birthday gift is between $33.954 and $35.246.

3 0
3 years ago
Solve the system of linear equations by graphing. y = –5/2x – 7 x + 2y = 4 What is the solution to the system of linear equation
muminat

ANSWER

(–4.5, 4.25)

EXPLANATION

The first equation is

y =  -  \frac{5}{2}x - 7

This function is in the slope-intercept form

The second equation is:

x + 2y = 4

2y =-x+ 4

y =  -  \frac{1}{2}x + 2

The graph of the two functions are shown in the attachment.

The point of intersection represents the solution to the system of equations they represent.

The solution is

(–4.5, 4.25)

4 0
3 years ago
14. In a game, Theodore received a handful of coins (pennies, nickels, dimes, and quarters) as a prize. When he got home, he fou
quester [9]

Answer:

Step-by-step explanation:

.

3 0
4 years ago
Determine the gcf. 2y^10, 5y^4, 6y^5
Sonja [21]

Answer:

y^4

Step-by-step explanation:

2y^10, 5y^4, 6y^5

We first need to find the factors of each term

2y^10 = 2*yyyyyyyyyy

5y^4 = 5yyyy

6y^5 = 3*2 yyyyy

The greatest common factor  is the largest term that appears in all the terms

The greatest common factor is yyyy  = y^4


8 0
4 years ago
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