An artist is laying out the design for a wall hanging on a coordinate plane. She uses polygon EFGH with vertices E (4, 4), F (−4, 4), G (−4, −4), and H (4, −4) to represent the finished piece. What is the area of this polygon?
Answers
Answer:
The area is 64squared units
Step-by-step explanation:
Given
[tex]E = (4,4)[/tex]
[tex]F = (-4,4)[/tex]
[tex]G = (-4,-4)[/tex]
[tex]H = (4,-4)[/tex]
Required
The area of the polygon
First, we plot the given coordinates on a plane (See attachment)
From the attachment, we can see that the 4 coordinates make up a square.
Where
[tex]EF = FG = GH = GE = 8\ units[/tex]
So, the area is:
[tex]Area = EF^2[/tex]
Substitute [tex]8[/tex] for [tex]EF[/tex]
[tex]Area = 8^2[/tex]
[tex]Area = 64[/tex]
Hence, the area is 64 squared units
Related Questions
in a survey of 1002 people, 701 said that they voted in a recent presidential election. voting records show that 61% of eligible voters actually did vote. find a 99% confidence interval estimate of the proportion of people who say that they voted
Answers
Answer:
The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623, 0.7369).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a survey of 1002 people, 701 said that they voted in a recent presidential election.
This means that [tex]n = 1002, \pi = \frac{701}{1002} = 0.6996[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6996 - 2.575\sqrt{\frac{0.6996*0.3004}{1002}} = 0.6623[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6996 + 2.575\sqrt{\frac{0.6996*0.3004}{1002}} = 0.7369[/tex]
The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623, 0.7369).
If a and b are angles lying in the 2nd quadrant such that cosa= -2/3 and cscb=2 find the following sin(a+b) and tan(a+b)
Answers
Both a and b lie in the second quadrant, which means
π/2 < a < π
π/2 < b < π
for which we have both cos(a) and cos(b) negative, while both sin(a) and sin(b) are positive. We're also given that
cos(a) = -2/3
csc(b) = 2 => sin(b) = 1/2
Now, recall the following identities:
• sin^2(x) + cos^2(x) = 1
• sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
• cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
• tan(x) = sin(x)/cos(x)
Now,
sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
… = √(1 - cos^2(a)) (-√(1 - sin^2(b))) + cos(a) sin(b)
* * where we take the negative square root because we expect cos(b) < 0 * *
… = - √(1 - (-2/3)^2) √(1 - (1/2)^2) + (-2/3) (1/2)
… = - √(1 - 4/9) √(1 - 1/4) - (2/3) (1/2)
… = - √(5/9) √(3/4) - 1/3
… = - (√5/3) (√3/2) - 1/3
… = -√15/6 - 1/3
… = -(√15 + 2) / 6
From the above, we know sin(a) = √5/3 and cos(b) = -√3/2. Then
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
… = (-2/3) (-√3/2) - (√5/3) (1/2)
… = √3/3 - √5/6
… = (2√3 - √5) / 6
and so it follows that
tan(a + b) = sin(a + b) / cos(a + b)
… = (-(√15 + 2) / 6) / ((2√3 - √5) / 6)
… = - (√15 + 2) / (2√3 - √5)
… = - (√15 + 2) (2√3 + √5) / ((2√3 - √5) (2√3 + √5))
… = - (2√45 + 4√3 + √75 + 2√5) / (12 - 5)
… = - (6√5 + 4√3 + 5√3 + 2√5) / 7
… = - (8√5 + 9√3) / 7
will the area be the same or different?
Answers
A teacher has a bag of marbles. There are 6 red, 6 blue, 8 green7 purple, and 8 yellow marbles in the bag. As the students enter the classroom, they draw a marble and keep it. If the first student in the room draws a yellowand the second draws a purple, what is the probability that the third student will draw a blue?
25%
18%
22%
33%
Answers
Answer:
18%
Step-by-step explanation:
Hope this helps :))
Answer:
the answer is 18%
hope this helps
Mr. Lauro decided to give a bonus point to the top 25% of students, a
remedial instruction to the bottom 25% of students and a chance for extra credit
to the middle 50% students.
1. Compute the median, lower quartile and upper quartile.
2. How many students will get bonus point that belong to the top 25%?
And who are those students?
3. Who are those students having a chance for extra credit?
4. How many students need to attend the remediation? Who are those
students?
please help po
wag po sana gawing tanga yung sagot
Answers
Answer:
Q1 = 23 ; median = 28 ; Q3 = 36
TOP 25% = 3 students (Pauleen ; Vic and Tito).
Extra credit students : (students whose score range between 23 and 36. (score of 23 is not included).
Remediation = 4 students (Pia, Joey, Ryan and Allan
Step-by-step explanation:
Given the scores :
35, 23, 42, 36,36,27,42,28,35,18,42,25,27,18,20
Ordering the scores in ascending order :
18, 18, 20, 23, 25, 27, 27, 28, 35, 35, 36, 36, 42, 42, 42
The lower quartile :
Q1 = 1/4 * (n+1)th term
Q1 = 1/4 * 16 = 4th term
Q1 = 23
The median :
Q2 = 1/2 * (n+1)th term
Q2 = 1/2 * 16 = 8th term
Q2 = 28
The upper quartile :
Q3 = 3/4 * (n+1)th term
Q3 = 3/4 * 16 = 12th term
Q3 = 36
The top 25% refers to the student who scored beyond the 75 percentile score :
Number of students = (15th - 12th) = 3 students students who scored 42
Pauleen ; Vic and Tito.
The middle 50% gets extra credit : This is the interquartile range :
This are the students whose score range between 23 and 36. (score of 23 is not included)
Students who have to attend the remedial class are those in the lower quartile, student with score of 23 and below.
4 students and they are : Pia, Joey, Ryan and Allan
Aysha got a dress that was on 20% off of the original price of $25.40. How much did she get the dress for?
Answers
Answer:
20.32$
Step-by-step explanation:
25.40×.20 = 5.08
25.40- 5.08 = 20.32
so the answer would be 20.32$
At a city council meeting, there 101 people present, and 66 were elderly.
If you talked to six random people there, what is the percent chance that exactly three is elderly? (Round
to the nearest hundredth of a percent.)
Answers
Answer:
23.63% chance that exactly three is elderly
Step-by-step explanation:
The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
101 total people means that [tex]N = 101[/tex]
Sample of 6 means that [tex]n = 6[/tex]
66 elderly means that [tex]k = 66[/tex]
If you talked to six random people there, what is the percent chance that exactly three is elderly?
This is P(X = 3). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,101,6,66) = \frac{C_{66,3}*C_{35,3}}{C_{101,6}} = 0.2363[/tex]
0.2363*100% = 23.63%
23.63% chance that exactly three is elderly
if topic A is very sensitive, while topic B is not sensitive at all, which of the following statements is most likely true when surveying people on the two topics?
A. Topic b requires an anonymous answer form, while topic A does not.
B. Both topic A and topic B require an anonymous answer form.
C. Topic A requires an anonymous answer form, while topic B does not.
D Neither topic A nor topic B requires an anonymous answer form.
Answers
Answer:
C.
Step-by-step explanation:
Most people do not want personal information about sensitive topics revealed about themselves, so Topic A requires anonymity.
With non-sensitive topics, people are usually comfortable with revealing their identity, so Topic B doesn't require anonymity.
Solve the system of equations and choose the correct answer from the list of options. (4 points)
x + y = −3
y = 2x + 2
five over 3 comma 4 over 3
negative 5 over 3 comma negative 4 over 3
negative 3 over 5 comma negative 3 over 4
3 over 4 comma 3 over 5
Answers
Answer:
The answer is B
Step-by-step explanation:
What times 1/4 = 4/3
Answers
4/3 x 4/1 = 16/3
Answer:
answer is 16/3
Step-by-step explanation:
let the number be x
1/4*x=4/3
x=4/3*4/1
x=16/3
now checking the answer .In place of x put 16/3
1/4*16/3
16/12
4/3
hence 16/3 times 1/4 is 4/3
Express as a trinomial. .
Answers
Answer:
6x^2-17x-14
Step-by-step explanation:
See the steps below:)
Julie has 21 colored pencils and 27 crayons. What is the ratio of crayons to colored pencils?
Answers
Based off that assumption it would be
9:7
9:7 is the ratio of crayons to colored pencils.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
The ratio of crayons to colored pencils can be found by dividing the number of crayons by the number of colored pencils:
The ratio of crayons to colored pencils = 27/21
Simplifying this ratio by dividing both the numerator and denominator by 3, we get:
The ratio of crayons to colored pencils = 9/7
Therefore, the ratio of crayons to colored pencils is 9:7.
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PLZ HELP!!!
I will give you brainliest
Answers
Answer:
141
Step-by-step explanation:
CD = | 4-(-2)| = 6
DB = |3-(-7)| = 10
area of a right triangle
A = (leg 1 x leg2)/2 = (6 x 10)/2 = 30
EB = |3-(-3)| = 6
EF = |-8-(-2)| = 6
area of a square = side^2
A = 6^2 = 36
segment G(and a point with same x coordinate of H)
|8-3| = 5
segment H(and the same point)
|-10-(-8)| = 2
A = (5x2)/2 = 5
segment I(and the same point)
|-8-6| = 14
Area of a rectangle
A = base x width
A = (5 x 14) = 70
total area = 70 + 5 + 36 + 30 = 141
A line has a slope of 1/2 and goes through the point (2,-1). What is the equation of this line in slope intercept form.
Answers
Answer:
y=1/2x-1
Step-by-step explanation:
the slope-intercept form is y=mx+b where m is the slope and b is the y-intercept
- we know that the slope is 1/2 and that the y-intercept if the point (2,-1) is -1 so....
The admission fee at a small fair is $2.00 for children and $4.00 for adults on a certain day 30 people enter the fair and $100 is collected collected how many children and how many adults attended and justify higher and how you know your response make sure to label your variables and state your solution in a complete sentence
Answers
Answer:
20 adults and 10 children
Step-by-step explanation:
We need to find the total amount of adults and children for 30 total people (adults + children) and only 100$ for them. 30 adults is 120$. We need to take off double the amount of money that would bring it to 100$ because the cost for each child is half of an adult. That way, we have 80$ of adults, and when we fill in the rest with children, we get to 100$ total and 30 total people.
Answer:
10 children 20 adults
Step-by-step explanation:
children = c
adult = 2c (double than children)
2(c) + 4(2c) = 100
10c = 100
c = 10 10 children
30-10 = 20 20 adults
$2(10) = $20
$4(20) = $80
$20+$80 = $100
Choose all of the zeros of the function f(x) = 2x² + 5x – 3.
-3, -0.5, 0.5, 1, 3 << those are the answer choices.
Answers
Answer:
-3. and -0.5
Step-by-step explanation:
i hope that helps
Consider a student loan of $22,000 at a fixed APR of %6 for 25 years.
Answers
Answer:
$33000
Step-by-step explanation:
Given data
Principal= $22,000
Rate= 6%
Time= 25 years
The interest to be paid is
Simple interest= PRT/100
Simple interest= 22000*6*25/100
Simple interest=3300000/100
Simple interest=$33000
Hence the total simple interest paid is $33000
THIS IS DUE IN LIKE 5 MINUTES I WILL GIVE YOU BRAIN THING IF ITS CORRECT PLEASE HELP NO LINKS THIS IS VERY IMPORTANT I WILL GIVE YOU BRAIN THING IF ITS CORRECT
Answers
Answer: A
Step-by-step explanation:
Answer:
a.30
b.12
i cant figure out the rest i am so sry im
trying to figure it out tho
- What is the volume of a square pyramid with height 15m and slant height 17m?
A 85 m2
B 320 m2
C 1280 m2
D 3840 m2
Answers
Answer:
c ) 1280 m^3
here,
slant height (s)= 17m
vertical height ( h)= 15m
length (a)= ?
so,
s^2 = (a/2)^2 + h^2
(17)^2 = (a/2)^2 + 15^2
64 = (a/2)^2
8^2= (a/2)^2
8×2 = a so a = 16
Now we know
volume of pyramid
= 1/3 × a^2 × h
= 1/3 × 16^2 × 15
= 1/3 × 256 × 15
= 1280 m^3
Using the extreme value theorem, what are the
minimum and maximum values of f(x)?
O minimum value = 1; maximum value = 6
O minimum value = 2; maximum value = 6
minimum value = -1; maximum value = 3
O minimum value = -2: maximum value = 3
Answers
Answer:
A
Step-by-step explanation:
Edge
The option A, O minimum value = 1; maximum value = 6 is correct.
We have given that,
Using the extreme value theorem, what are the minimum and maximum values of f(x).
What is the extreme value theorem?Extreme Value Theorem An important application of critical points is in determining possible maximum and minimum values of a function on certain intervals.
Therefore, The option A, O minimum value = 1; maximum value = 6 is correct.
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A cable is 60 meters long. How long is the cable in decimeters?
Be sure to include the correct unit in your answer.
Answers
Answer:
600 decimeters
Step-by-step explanation:
multiply the meter length by 10
60x10=600
Reggie needs 24 feet of rope to make a tire swing. He has 10 yards of rope. Is this enough for him to make his swing? Explain.
Answers
Answer:
8 yards < 10 yards
He has enough.
Step-by-step explanation:
1 yard = 3 feet
y yards = 24 feet
[tex]\frac{1}{3} :\frac{y}{24}[/tex]
y · 3 = 1 · 24
3y = 24
3y ÷ 3 = 24 ÷ 3
y = 8
24 feet = 8 yards
8 yards < 10 yards
Find the length of the third side. If necessary, write in simplest radical form.
3√5
Answers
Answer:
3
Step-by-step explanation:
We can use the Pythagorean thorem to solve this question
leg = [tex]\sqrt{hypotenuse^2 - leg^2} = \sqrt{(3\sqrt{5})^2 - 6^2} = \sqrt{45 -36} = \sqrt{9} = 3[/tex]
is 12:8 and 18:12 equivalent?
Answers
Answer:
no
Step-by-step explanation:
18 is not a multiple of 12
and 12 is not a multiple of 8
Find ad please help aghhhh due today
Answers
Answer:
AD = 6m
Step-by-step explanation:
Sin(30) = AD / 12
Sin(30) * 12 = AD
6 = AD
Hope this helps!
Find AD.
[tex] \sf a. \: 2\sqrt{3} \: m[/tex]
[tex] \sf b. \: 3 \sqrt{3} \: m[/tex]
[tex] \sf c. \: 6 \: m[/tex]
[tex] \sf d. \: 6 \sqrt{3} [/tex]
____________________
Solution :-Given Information :-∠DCB = 30°∠BDC = 90°∠ABC = 90°BC = 12 mTo Find :-The Length of AD Calculation :-Here, Sin θ is 30°
Sin = [tex] \bf \frac{perpendicular}{hypotenuse} [/tex]
Here, θ is 30°
Substituting the values, We get,
∴ Sin ( 30 ) = [tex] \sf \frac{AD}{BC} [/tex]
Substituting the value of BC as 12, We get,
⇒ Sin ( 30 ) = [tex] \sf \frac{AD}{12} [/tex]
Transposing 12 to Left Hand Side, We get,
⇒ Sin ( 30 ) × 12 = AD
Calculating further, We get,
⇒ AD = 6 m
∴ AD = 6 m
____________________Final Answer :-The Length of AD is 6 m
____________________These tables represent a quadratic function with a vertex at (0,3). What is the
average rate of change for the interval from x = 7 to x = 8?
х
Interval
0
1
2
у
3
2
-1
-6
-13
--22
--33
Average rate
of change
-1
1-2
-3
1-2
-5
1-2
-7
]-2
-9
13-2
-11
O to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
3
4
5
6
O
A. -15
B. -61
C.-2
D. -46
Answers
Answer:
These tables represent a quadratic function with a vertex at (0,-1) what is the average rate of change for the interval from x=7 to x=8?
B.-15
Step-by-step explanation:
The average rate of change from 7 to 8 = -15
How to determine the average rate of change?The average rate of change of a quadratic function is calculated using:
Rate = (f(b) - f(a))/(b - a)
The interval is from x = 7 to 8.
So, we have:
(a,b) = (7,8)
The equation becomes
Rate = (f(8) - f(7))/(8 - 7)
Evaluate the difference
Rate = (f(8) - f(7))/1
This gives
Rate = f(8) - f(7)
From the table, we have:
Rate from 5 to 6 = -11 where the constant is -2
So, we have:
Rate from 6 to 7 = -11 - 2
Rate from 6 to 7 = -13
Also, we have:
Rate from 7 to 8 = -13 -2
Rate from 7 to 8 = -15
Hence, the average rate of change from 7 to 8 = -15
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7th grade math problem please help !!
Answers
Answer:
136 units^2
Step-by-step explanation:
Does anyone know why I can't access or see the homepage for this website?
It hasn't loaded in 20 minutes and my internet connection is fine.
Answers
may i get some help please
Answers
Answer:B
Step-by-step explanation:
They are alternate angles due to them being on opposing sides from one another and corresponding as they are equal and opposing
Hope this helps
the difference of four times a number and 23 is 5 less than the number. Find the number
Answers
Answer:
I think it could be 28 because 28 minis 5 is 23