Plot the vertices (-2, -8), (-2, 2), and (8, 2).
What is the last vertex of the rectangle?
What is the area of the rectangle?
square units
Answers
Answer:
(8, -8)100 square unitsStep-by-step explanation:
The diagonals of a rectangle have the same midpoint, so for points A, B, C, D, we must have ...
(A+C)/2 = (B+D)/2
D = A + C - B
D = (-2, -8) +(8, 2) -(-2, 2) = (-2+8+2, -8+2-2)
D = (8, -8)
__
The side lengths are 2-(-8) = 10, and 8-(-2) = 10. The area is the product of the side lengths, so is 10×10 = 100 square units.
_____
Comment on side lengths
When the end points of one side are on the same vertical line, the length of that side is the difference of y-coordinates. When the points lie on the same horizontal line, the side length is the difference of x-coordinates.
Answer:
the last vertex is (8,-8)
the area of the rectangle is 100 square units
Step-by-step explanation:
Related Questions
Solve the system of equations by elimination.
2x + 2y = -2
3x - 2y = 12
Answers
5x = 10
x = 2
2(2) + 2y = -2
4 + 2y = -2
2y = -6
y = -3
Which of the following choices describes volume?
a
The amount of juice a carton can hold.
b
The weight of a bowling ball.
c
How tightly the molecules in a glass of water are packed together.
d
The temperature that must be reached for ice to melt.
Answers
Answer:
C. How tightly the molecules in a glass of water are packed together
Step-by-step explanation:
Volume of a substance is different according to the state of the matter.
So for a water molecule, the volume of the the water is definite and can be measured by the container which is the glass cup
So volume can be the measure of how tight the molecule of that substance ate together.
Anna and Lionel share $675 in the ratio 4 : 5 Lionel gives 3/5 of his share of the money to his mother. How much money does Lionel give to his mother?
Answers
Answer:
$225
Step-by-step explanation:
Total share ratio = 4+5 = 9
Lionel's ratio = 5
Lionel's share = (5/9) × 675
= $375
Lionel's mum = (3/5) x 375
= $225
The graph below is the graph of a function.
True or false
Answers
Answer:
False
Step-by-step explanation:
there is more than one y-value for some x-values
Please answer this correctly
Answers
Write a 3×3 matrix A which A^2 is diagonal while A is not diagonal ?
Answers
Consider the matrix
[tex]A=\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}[/tex]
Multiplying A by itself has the effect of swapping the first and second rows:
[tex]A^2=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}[/tex]
which is diagonal, while A itself is not.
Please do only 9, 11, and 13 . These are on probability and it’s only 3 questions.
Answers
9: What is the probability of beef tips being the preferred new menu item?
To find the probability of a customer preferring beef tips over the other menu items, divide the quantity of customers that preferred beef tips over the total number of customers that participated in the survey:
28 / (42 + 28 + 30) = 28/100 = 28%
There is a 28% chance that beef tips is the new preferred menu item.
11: Out of a similar group of 375 customers, predict how many more customers will prefer chicken carbonara to shrimp scampi.
There are 100 customers that participated in the pre-existing survey. A grand total of 375 participants in a similar survey would mean that each food's preference would grow in a similar fashion.
100 * 3.75 = 375
You can then multiply each response group by 3.75 to find how many people prefer chicken carbonara and shrimp scampi.
42 * 3.75 = 157.5
30 * 3.75 = 112.5
Then, subtract the quantities to find out how many more people prefer chicken to shrimp.
157.5 - 112.5 = 45 people.
13: Predict the number of times that Giorgianna's name will be drawn in 32 weeks. Round to the nearest whole number.
There are five people in the group, and one is chosen as the team leader every week. 1 divided by 5 is .2, so the probability of being chosen as team leader is 20%.
You can multiply 0.2 by 32 to represent how many times the experiment will be run. The product is 6.4 times, so Giorgianna's name will likely be drawn 6 times within 32 weeks.
Answer:
9.) 7/ 25. 11). 45. 13) 6
Step-by-step explanation:
Explanation shown below;
For 13;
The probability of chosen Georgianna is 1/5
The number of times the draw would be conducted would be 32
Hence Georgianna would be chosen [ 1/5. * 32 = 6. 4 = 6[to the nearest whole]
What is the value of 2(x+y)-(x-z) ifx=2, y=1, and z=-3
Answers
Answer:
2(2+1)-[2-(-3)]
(2×3)-5
6-5=1
**10 POINTS PLEASE HELP**
The perimeter of △PQR is 44 cm, and △PQR ~ △WXY. If PQ = 12 and XY + WY = 24, what is the perimeter of WXY? Complete the explanation.
Since the perimeter of △PQR = 44, QR + PR = 44 − PQ, or ____ cm. This is proportional to the sum XY + WY, because the two triangles are (similar or congruent)
so their corresponding sides are (not proportional or proportional). Their ratio is 24:__ , or 3:__ , which is the same ratio as their perimeters, 3/___ = P/44, so P = ___ cm.
Answers
Answer:
Since the perimeter of ΔPQR = 44, QR + PR = 44 - PQ, or 32 cm. This is proportional to the sum XY + WY, because the two triangles are similar so their corresponding sides are proportional. Their ratio is 24:32 or 3:4, which is the same as their perimeters, 3/4 = P/44, so P = 33 cm.
Step-by-step explanation:
The given parameters are;
ΔPQR ~ ΔWXY
Perimeter of ΔPQR = 44
PQ = 12
XY + WY = 24 based on position is proportional to QR + PR
However, the perimeter of ΔPQR = PQ + QR + PR = 44
Therefore, QR + PR = 44 - PQ = 44 - 12 = 32
Hence, XY + WY = 24 based on position is proportional to QR + PR = 32
If XY:QR = WY:PR we get (XY + WY):(QR + PR) (common factors)
∴ (XY + WY):(QR + PR) = 24:32 = 3:4
By extension, (WX + XY + WY):(PQ + QR + PR) = 3:4
Where: WX + XY + WY = P and PQ + QR + PR = 44 we have;
P:44 = 3:4 or 3/4 = P/44
From which P = 44 × 3/4 = 33 cm.
Given the inequality 2x − 8y ≤ 24. Which best describes the half-plane that is the solution?
Hint: Rewrite inequality solving for y.
Question 3 options:
The half-plane lying below the line y = 14x − 3, not including the line y = 14x − 3.
The line y = 14x −3 and the half-plane lying above it.
The line y = 14x − 3 and the half-plane lying below it.
The half-plane lying above the line y = 14x − 3 , not including the line y = 14x − 3.
Answers
Answer:
The line y = 1/4x −3 and the half-plane lying above it.
Step-by-step explanation:
I attached the work to your problem. Please see the attachment.
In asking all 349 second graders in a school district, it is found that on average, these second graders have 2.5 pets. Is this number a parameter or a statistic and why?
Answers
Answer:
Parameter
Step-by-step explanation:
A statistic describes a sample. A parameter describes a population. Since the entire population of second graders in the district is surveyed, this is a parameter.
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
Answers
Answer:
168 adult tickets were sold
Step-by-step explanation:
Multiply the amount of students by the cost of the student ticket (82 times 3.75) which equals 307.5 . Subtract that from the total amount earned (2071.5) and you get 1764. Divide that by the cost of an adult ticket (10.50), and you'll get the amount of adults who attended, which is 168.
Answer:
168 Adult tickets were sold
Step-by-step explanation:
Vote me brainliest
if X/4 = x+1/5, then x =
Answers
Answer:
as written, -4/15with parentheses, 4Step-by-step explanation:
As the problem is written, you have ...
[tex]\dfrac{x}{4} =x+\dfrac{1}{5}\\\\5x=20x+4\qquad\text{multiply by 20}\\\\-15x=4\\\\x=-\dfrac{4}{15}[/tex]
__
If you add parentheses to include x in the numerator, then you have ...
x/4 = (x +1)/5
[tex]5x=4(x+1)\qquad\text{multiply by 20}\\\\5x -4x = 4\qquad\text{eliminate parentheses, subtract 4x}\\\\x=4[/tex]
__
Additional comment
We include the second working because it is a fairly common mistake to neglect to put parentheses around a numerator or denominator. The solutions to such problems are not often fractions, so we suspect you intend the latter form.
A rectangle has a length of x + 2 and a width of x-2, and
has an area of 60 square units. Find the length and width
of the rectangle.
Answers
Answer:
L = 10, W = 6
Step-by-step explanation:
(x-2)(x+2) = 60
[tex]x^{2}[/tex] - [tex]2^{2}[/tex] = 60
[tex]x^{2}[/tex] = 60 + 4 = 64
x = [tex]\sqrt{64}[/tex] = 8 or -8
-8 rejected
thus length is 8 + 2 = 10, width is 8-2=6
The length is 10 units and width is 6 units.
Length = x+2
Width = x-2
Area = 60
Area = Length × Width
Therefore, (x+2)(x-2) = 60
x²-2x+2x - 4 = 60
Collect like terms
x² = 60+4.
x² = 64.
Therefore, in order to get the value of x, we'll find the square root of 64
x² = 64.
x = ✓64
x = 8
Length = = x+2 = 8+2 = 10
Width = x-2 = 8-2 = 6
In conclusion, the length is 10 units and width is 6 units.
Read related link on:
https://brainly.com/question/7153878
Need help
Pleaseeeee
Answers
Answer:
164 m^2
Step-by-step explanation:
You can think of the shaded area in different ways. One of the ways is the entire outer colored rectangle minus the area of the small white rectangle inside.
The large colored rectangle is 12 m by 15 m.
The inner rectangle is 8 m tall. The width is 12 m - 5 m - 5 m = 2 m
A = 12 m * 15 m - 2 m * 8 m
A = 180 m^2 - 16 m^2
A = 164 m^2
You are paid $10.65/hr. Your deductions are FICA (7.65%), federal tax withholding (9.9%), and state tax withholding (7.35%). Your housing and fixed expenses are $493.68/month. How many hours per month must you work to be sure those expenses are paid?
62 hours
64 hours
68 hours
66 hours
Answers
Answer:
The first option; You must work about 62 hours.
Step-by-step explanation:
The total percent that you pay in taxes is 24.9%.
That means that you keep 75.1% of the money that you earn. We can write the following equation to determine the number of hours, h, that it will take to earn 493.68.
0.751(10.65)h = 493.68
Just divide by 0.751 and 10.65 and you will get the number of hours needed.
Answer:
A.) 62 hours
Step-by-step explanation:
I took the consumer math test :)
Complete the recursive formula of the arithmetic sequence -15,-11,-7,-3
Answers
Answer:
c(1)=-15
c(n)=c(n-1)+4
Step-by-step explanation:
how do you change the equation 10q−5r=30 so that r is the independent variable?
Answers
Answer:
r=2q-6
Step-by-step explanation:
10q-5r=30
Subtract 10q from both sides:
-5r=30-10q
Divide both sides by -5:
r=2q-6
Hope this helps!
How are the functions f (x) = 16 Superscript x and g (x) = 16 Superscript one-half x related
Answers
Answer:
g(x) is f(x) expanded horizontally by a factor of 2
Step-by-step explanation:
Given:
f(x) = 16^x
g(x) = 16^(x/2)
__
Replacing x in a function with x/k expands the graph horizontally by a factor of k. Here, it seems we have ...
g(x) = f(x/2)
so g(x) is a horizontal expansion of f(x) by a factor of 2.
Answer:
c). The output values of g(x) are the square root of the output values of f(x) for the same value of x.
Step-by-step explanation:
Suzanne owns a small business that employs 555 other people. Suzanne makes \$100{,}000$100,000dollar sign, 100, comma, 000 per year, and the other 555 employees make between \$40{,}000$40,000dollar sign, 40, comma, 000 and \$50{,}000$50,000dollar sign, 50, comma, 000 per year.
A dot plot has a horizontal axis labeled, Salary, in thousands of dollars, marked from 40 to 100, in increments of 2. 1 dot is plotted above each of the following values: 40, 42, 44, 46, 48, 100. The dot above 100 is shaded purple.
Suzanne decides to leave the company and keep the other 555 salaries the same.
A dot plot has a horizontal axis labeled, Salary, in thousands of dollars, marked from 40 to 100, in increments of 2. 1 dot is plotted above each of the following values: 40, 42, 44, 46, 48.
How will removing Suzanne's salary from the data set affect the mean and median?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The mean will decrease and the median will increase.
(Choice B)
B
The median will decrease and the mean will increase.
(Choice C)
C
Both the mean and median will decrease, but the median will decrease more than the mean.
(Choice D)
D
Both the mean and median will decrease, but the mean will decrease more than the median.
Answers
Answer:
d
Step-by-step explanation:
Statistics can be extremely valuable, but you must also make sure that the sample and questions are unbiased. Design a pair of questions that are related to the same healthcare issue: one that is unbiased and another that would result in a bias in one direction or the other.
Examples:
a. Do you think that the rate of type II diabetes diagnoses will increase over the next 10 years?
b. Given the large increase in childhood obesity in the United States, do you think that type II diabetes diagnoses will increase over the next 10 years?
Discuss why it is important to create a truly unbiased sample and survey questions.
Answers
Answer:
Do you think the rate of death due to pandemic will rise over the next month?
Considering the increase in death rate due to pandemic over the last 2 months, there will be an increase over the next 4 months?
Step-by-step explanation:
It is important to create a truly unbiased sample and survey questinos so that the results are authentic and can be generalized to represent a population.
You are ready to buy a house, and you have $31,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding (0.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you?
Answers
Answer:
$ 140,104.96
Step-by-step explanation:
The amount the bank will the individual is the present value of the total mortgage payment.
monthly mortgage payment=28%*$36,000/12=$840
the payment is meant for 30 years but 360 months i.e 12*30
the amount of loan is the present value of $840 monthly for 360 months with 0.5% interest rate per month
=pv(rate,nper,-pmt,fv)
rate is 0.5%
nper is 360 months
pmt is $840 per month
fv is the total payments which is unknown
=pv(0.5%,360,-840,0)=$140,104.96
The loan amount is closest to $ 140,104.96
What is 3/10 out of $60
Answers
3/10 out of $60 equals $18
60/10= 6
6*3=18
Answer = $18
The equation of a circle is given below.
9
x^2+ (y - 7.5)^2 =9/49
What is its center?
Answers
Answer:
(0, 7.5)
Step-by-step explanation:
Compare the equation to the standard-form equation of a circle:
(x -h)^2 +(y -k)^2 = r^2 . . . . . . . center at (h, k); radius r
You will notice that ...
h = 0
k = 7.5
The center is (h, k) = (0, 7.5).
5b + 1 is at most 51
Answers
Step-by-step explanation:
5(10)+1
50+1
51
10 could be one possible answer
Find the mean and median of these data: 3, 4, 10, 12, 18, 20.
Answers
Answer:
the median is 10 and 12
the mean is 11.17
Step-by-step explanation:
Mean=11.16
Median=11
look at the attached picture
Hope it will help you...
Good luck on your assignment..
~pragya
Linear Equations: Solve for x given "-2x + 7 = 13"
Answers
Answer:
x = -3
Step-by-step explanation:
-2x + 7 = 13
-2x = 13 - 7
-2x = 6
x = 6/-2
x = -3
Solution: x=−2.5 y=0.5
Solution: x=2 y=2.
The slope is?
Answers
Answer:
1/3
Step-by-step explanation:
We have (x₁, y₁) = (-2.5, 0.5) and (x₂, y₂) = (2, 2). The formula for slope is
(y₂ - y₁) / (x₂ - x₁). When we plug these values in we get (2 - 0.5) / (2 - (-2.5)) =
1.5 / 4.5 = 1 / 3. Hope this helps!
Let A, P, and D by n x n matrices. Mark each statement true or false. Justify each answer.
a. A is diagonalizable if A = PDP^-1 for some matrix D and some invertible matrix P. Choose the correct answer below.
O The statement is true because the columns of P are the n linearly independent eigenvectors of A.
O The statement is false because A must have n distinct eigenvalues for the matrix D and P to exist.
O The statement is true because if A = PDP^-1, then A is diagonalizable by definition.
O The statement is false because the symbol D does not automatically denote a diagonal matrix.
Answers
Answer:
Correct answer is the 4th answer.
Step-by-step explanation:
By definition, a matrix is called diagonalizable if there exists some invertible matrix P and a diagonal matrix D such that AP = PD, which is equivalent to having A = PDP^-1.
We are not told that D is a diagonal matrix, hence, it could be any matrix. If A=PDP^-1 for some matrix D that is not diagonal, it doesn't imply that A is diagonalizable. Consider the following case: Let us take A a non diagonalizable matrix. Take D = A and P = identity matrix of size n. Then, this equation holds, but A is still not diagonalizable.
6 plus 6 plus 6 time 2 equals?
Answers
Answer:
48
Step-by-step explanation:
6+6+6=24 (6*3)
24*2=48
Answer:
36
Step-by-step explanation:
6 + 6 + 6 = 18
18 x 2 =36
:3