50 POINTSSSS! Use trigonometric identities to verify that this expression is equal.

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

netineya [11]

The area of the shaded region is going to be the area of the rectangle minus the area of the square.

Area of a rectangle is L * W.
A = L * W
A = (x + 10)(2x + 5)
A = x(2x + 5) + 10(2x + 5)
A = 2x^2 + 5x + 20x + 50
A = 2x^2 + 25x + 50 .....this is the area of the rectangle

area of a square is : A = a^2...where a is one side
A = (x + 1)^2
A = (x + 1)(x + 1)
A = x(x + 1) + 1(x + 1)
A = x^2 + x + x + 1
A = x^2 + 2x + 1

now we subtract the area of the square from the area of the rectangle to get the area of the shaded region.

2x^2 + 25x + 50 - (x^2 + 2x + 1) =
2x^2 + 25x + 50 - x^2 - 2x - 1 =
x^2 + 23x + 49 <== the area of the shaded region

6 0

3 years ago

Write an equation for the line parallel to y= -2x+1 that contains (-2,5)

grin007 [14]

Answer:

y = - 2x + 1

Step-by-step explanation:

Parallels line have the same slope, when an equation is in the form y= mx + b, m is the slope. In this problem slope = - 2

Now with the slope what is missing is the y-intercept, the problem says that the line contains the point (-2, 5), replacing that point in the equation you can solve it to find the y-intercept

y = mx + b

5 = (-2)(-2) + b

5 = 4 + b

1 + b

y = - 2x +1

5 0

3 years ago

An article claims that 12% of trees are infested by a bark beetle. A random sample of 1,000 trees were tested for traces of the

inna [77]

Answer: 0.6812

Step-by-step explanation:

Let p be the population proportion of trees are infested by a bark beetle.

As per given: p= 12%= 0.12

Sample size : n= 1000

Number of trees affected in sample = 1000

Sample proportion of trees are infested by a bark beetle. = $\hat{p}=\dfrac{127}{1000}=0.127$

Now, the z-test statistic : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

So, $z=\dfrac{0.127-0.12}{\sqrt{\dfrac{0.12\times 0.88}{1000}}}$

$z=\dfrac{0.007}{\sqrt{\dfrac{0.1056}{1000}}}\\\\\\=\dfrac{0.007}{\sqrt{0.0001056}}\\\\\\=\dfrac{0.007}{0.010276}\approx0.6812$

Hence, the value of the z-test statistic = 0.6812 .

7 0

4 years ago

Kanesha wants to find out if people in her community would support turning an unused park into a dog park. Which populations wou

inysia [295]

The most likely populations that Kanesha can pick an appropriate sample for the survey is: people who live near the unused park.

When running a survey, it is important to use a sample that represents the target population that can sufficiently provide answers to the questions you seek to ask.

Using the a sample from the right population will give you enough data to carryout a survey. The people living close to the unused park would definitely be affected by whatever establishment that is done in the unused park.

Therefore, the most likely populations that Kanesha can pick an appropriate sample for the survey is: people who live near the unused park.

Learn more about survey on:

brainly.com/question/14610641

7 0

2 years ago

Read 2 more answers

If 12y=75+5x+2x-1. What is the value of x

AleksandrR [38]

Answer:

x = $\frac{12y - 74}{7}$