On the accompanying grid, draw and label quadrilateral ABCD with points A(1,2), B(6,1), C(7,6), and D(3,7). On the same set of axes, plot and label quadrilateral A′B′C ′D′, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A′B′C′D′.
Answers
Answer: Refer to figure 1 for the diagram needed.
A ' = (-1, 2)
B ' = (-6, 1)
C ' = (-7, 6)
D ' = (-3, 7)
Area = 24 square units
============================================================
Explanation:
Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.
To reflect any given point over the y axis, we apply this rule
[tex](x,y) \to (-x,y)[/tex]
which means we change the sign of the x coordinate, but keep the y coordinate the same. For example, a point like A(1,2) moves to A ' (-1,2). The other points are handled in a similar fashion.
After all of the points have been reflected, you'll get what is shown in figure 1.
------------------
To find the area of quadrilateral ABCD, we can form a bounding box as small as possible around the quadrilateral. Refer to figure 2.
The area of rectangle FEHG is 6*6 = 36 square units
Then we subtract off the areas of these four outer triangles
Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.
Related Questions
You surprised your friends with a trip to a haunted house this weekend. The admission tickets were $8 per friend. You had to pay an additional $5 for parking and you spend $20 on food. You also got your friends a card that was $2 per friend. At the end of the night, you spent $105. How many of your friends did you bring to the haunted house?
Answers
Answer: 8
Step-by-step explanation:
Ok, start going backwards with the addition and substration which makes it:
105 – 25 = 80
Since you had to pay 8 and 2 for each friend so that makes the cost for a friend 10 so:
80 divided by 10 = 8
8 Friends is the answer.
Could you please help with this
Answers
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
2-7/9x=5/6 without fractions
Answers
Answer:
x=0.6 repeating (meaning 6 is repeating so this is a repeating decimal)
Lamar is a commercial real estate agent who earns a yearly salary of $82,500 plus a 2.5% commission on his total sales. If his total sales in one year are $3.75 million, what are Lamar’s earnings for that year?
Answers
Answer:
$176,250
Step-by-step explanation:
Multiply $3.75 million by Tomas commission on his total sales.
Since you can't multiply a percentage you have to turn the commission into a decimal by moving it two spaces to the left. (Note: if it doesn't have a decimal add one add the end of the number then move it two spaces to the left)
$3,750,000 x .025 or 0.025 = $93,750
Add $93,750 to Tomas yearly salary
$93,750 + $82,500 = $176,250
So
If Tomas sold properties that totaled $3.75 million in sales during one year, his earnings for that year would be $176,250
[tex]\frac{4x}{5}+\frac{5x}{6}[/tex]
Answers
To solve this issue, first we have to match the denominators, for this we have to take the LCM from the denominators 5.6, Then just solve the fraction normally, See:
[tex]\sf \dfrac{4x}{5}+\dfrac{5x}{6}\to LMC~(5,6)=30\\\\\\\sf =\dfrac{24x}{30}+\dfrac{25x}{30}\\\\\\\sf =\dfrac{24x+25x}{30}\\\\\\\boxed{\sf \frac{49x}{30}}[/tex]
Okay?!1. £1000 is invested for 2 years at 5% per annum with compound interest. Work out the total amount in the account after 2 years.
Answers
Answer:
A = £1102.50
Step-by-step explanation:
Use the compound amount formula:
A = P(1 + r)^t, where P is the principal, r is the interest rate as a decimal fraction, and t is the number of years.
Here A = £1000·(1 + 0.05)^2, which evaluates to A = £1102.50
What is six times a number in algebraic expression
Answers
Answer:
6(x)
Step-by-step explanation:
Answer:
6x
Step-by-step explanation:
x represents a number, it is also called a variable.
If there is 2 of x, it would be represented like this: 2x
If there is 1 of x, it would be represented like this: x
True or False:
Rachel used 12 centimeters of tape to wrap 3
presents.
Her unit rate is 12.
Select one:
True
O False
Check
No links.
Answers
Answer:
False
Step-by-step explanation:
The unit rate should be 9
Answer:
i think false
Step-by-step explanation:
if im wrong forgive if am right brainliest pls:)
What is 4 percent of $128.72 ?
Answers
Answer:
124.72
Step-by-step explanation:
Answer:
Step-by-step explanation:
4% of 128.72 = 0.04 * 128.72
= 5.1488
help me please!! and thank you
Answers
Answer:
(-2.5,3) is x1 y1 respectivelly. Apart from this, what part of the question are you struggling with?
The breadth of rectangle is 2cm .less then its length and its perimeter is 24cm.Find the length and breadth of rectangle
Answers
let Length=l
therefore breadth=l-2
A/Q
P=24
2(l+b)=24
2(l+l-2)=24
2(2l-2)=24
4l-4=24
4l=28
l=28/4
=7
Patrice and her husband are going on a 6-mile hike. So far they have hiked
3 miles. How much farther do Patrice and her husband have left to hike?
3
Answers
Answer:
3 miles
Step-by-step explanation:
6 total miles
3 miles done
6 (total) = 3 (done) + x (unknown)
x = 6 - 3
x = 3
3 miles left to hike
what is the answer help
Answers
Answer:
1
Step-by-step explanation:
y=-x-1
when it is perpendicular, it is the opposite then flip the fractions so 1 and if you flip 1 it is still 1
Plzzzz help mee I forgot how to do it
Answers
Answer:
100011 is the base number.Step-by-step explanation:
Best of luck friendIf you guys know how to do this lemme know, thanks :))
Answers
Answer:
A 65
Step-by-step explanation:
x = -5
y = -8
-5 - 5 (-8)^2 / -5 = -325 / -5
= 65
Answer:
65
Step-by-step explanation:
So, this expression is asking us to solve an equation when x = -5 and y = -8.
When asked to solve problems like this, all we have to do is plug in the numbers accordingly
[tex]\frac{x-5y^2}{x} ---->\frac{(-5)-5(-8)^2}{(-5)}[/tex]
Now, we can simplify using PEMDAS
[tex]\frac{-5-5(64)}{-5} = \frac{-5-320}{-5} = \frac{-325}{-5} = 65[/tex]
Please correct me if i'm wrong :)
An envelope is 6 in. wide and 4 in. high. Will a card with an 8 in. diagonal fit in it? Identify the correct explanation.
A) Because 7.2 < 8, it is possible that the card fits in the envelope.
B) Because 8.9 > 8, it is possible that the card fits in the envelope.
C) Because 7.2 < 8, it is NOT possible that the card fits in the envelope.
D) Because 8.9 > 8, it is NOT possible that the card fits in the envelope.
Answers
= 6^2 + 4^2
=36 + 16
= 52
A^2= 52
Sqrt A^2 = sqrt 52
A = 7.2
Since the envelopes diagonal is 7.2 inches and the card’s diagonal is 8 inches and 7.2<8. Your answer is c)
ℎ ℎ 22 2 22 2− 3 +10
Answers
Answer:
wouldn't the answer be 9
Step-by-step explanation:
Answer:
22h^2 + 33 (added) . h⋅h⋅22,2,22,2−3+10 (subtracted)
Step-by-step explanation:
I don't understand what you want so I will list lots of answers hopefully it helps. Please message under my answer for more solutions so I can help you but I hope this started to help you.
When a child is more than two standard deviations underweight for his or her age, the child is suffering from a condition called _____.
Answers
I’ll give brainliest, thanks and 5 stars
the diameter of a pool is 28 m. the circumference of the deck is 101 m. what is the area of the pool and deck?
Answers
Answer:
ok
Step-by-step explanation:
soln,
d=28m
r=d/2=28/2
=14m
now,
[tex]\pi {r}^{2} [/tex]
22/7×(14×14)
22/7×196
=616m^2
7x-2y=-29
9x+10y=13
emliantion substuion methd
Answers
Answer:
(-3, 4)
Step-by-step explanation:
5(7x - 2y = -29)
35x - 10y = -145
9x + 10y = 13
44x = -132
x = -3
7(-3) - 2y = -29
-21 - 2y = -29
-2y = -8
y = 4
Riley is saving up to buy a new television. She needs a total of $1,164.38. Riley has saved $200.66 already and earns $80.31 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answers
2. Now we can divide $963.72 by how much Riley earns in a week $80.31 to find the number of weeks: 12 weeks
Answer: 12 weeks
Hope this helps!
(-1, 5) (3,y) m=5 whats the value of my and whats the slope <3
Answers
Answer:
slope: 5
y = 25
Step-by-step explanation:
slope is m, and m = 5, so slope is 5.
y-5=5(x+1)...........set up point slope form
y-5=5x+5............distribute 5
y=5x+10..............add 5 to both sides
y=5(3)+10............plug in 3
y=25.....................simplify
Step-by-step explanation:
I am not sure you posted the question correctly.
m is the slope already. this comes from the point slope form
y - y1 = m(x - x1)
where x1, y1 are the coordinates of a point on the line.
so, the slope is 5 (and cannot be <3).
so, using the first point we get
y - 5 = 5(x - -1) = 5(x + 1) = 5x + 5
therefore
y = 5x + 10
for (3, y) we put 3 in as x
y = 5×3 + 10 = 15 + 10 = 25
it is (3, 25) for m = 5.
David is a salesman for a local Ford dealership. He is paid a percent of the profit the dealership makes on each car. If the profit is under $800, the commission is 25%. If the profit is at least $800 and less than $1,000, the commission rate is 27.5% of the profit. If the profit is $1,000 or more, the rate is 30% of the profit. Find the difference between the commission paid if David sells a car for a $1,000 profit and the commission paid if he sells a car for a $799 profit?
Answers
Answer:
At the city museum, child admission is $5.90 and adult admission is $9.20. on sunday, 144 tickets were sold for a total sales of $1136.70 . how many adult tickets were sold that day?
Step-by-step explanation:
The required difference between the commission paid is $100.25 when David sells a car for a $1,000 profit and for a $799 profit.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have to determine the difference between the commission paid if David sells a car for a $1,000 profit and the commission paid if he sells a car for a $799 profit
The profit = $1,000
The profit is $1,000 or more, the rate is 30% of the profit.
So, the commission paid :
⇒ 30% of $1,000 = $300
The profit = $799
The profit is under $800, the commission is 25%.
So, the commission paid :
⇒ 25% of $799= $199.75
The required difference between the commission paid :
⇒ $300 - $199.75 = $100.25
Learn more about the percentages here:
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What is the slope of the line ?
Answers
Answer:
[tex]m=\frac{4}{5}[/tex]
Step-by-step explanation:
You can calculate the slope with just 2 points, so find 2 points on the line that land perfectly on the grid.
I'll use (-2, 0) and (3, 4) here
To calculate slope:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
where (x1, y1) is your first point and (x2, y2) is your second. Technically they can go in any order, but I think its generally easier to consider first-to-last as left-to-right.
Plug in those 2 points and solve:
[tex]m=\frac{4-0}{3--2}\\m=\frac{4}{5}[/tex]
Think of slope as rise over run. A slope of [tex]\frac{4}{5}[/tex] means it rises 4, and goes over 5. It's also literally rise over run, as the top number (rise) is over the bottom number (run).
1 (a) The price of a newspaper increased from $0.97 to $1.13 Calculate the percentage increase.
Answers
Answer:
16.49%
Step-by-step explanation:
0.97+16.49%=1.129953
The percentage increase is 16.49%
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100)
We are given that the price of a newspaper increased from $0.97 to $1.13
WE need to find the percentage increase.
Therefore,
Intital price = 0.97 ( 1.13 - 0.07)
= 0.16 / 0.97 x 100
= 16/0.97
= 16.49
0.97+16.49% = 1.129953
Learn more about percent here:
https://brainly.com/question/11549320
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Use the vertical-line test to determine whether each graph represents a function.
Answers
Answer:
14) Not a function 15) Function 16) Function
Step-by-step explanation:
The vertical line test is when you draw a line on the graph to see if it passes the function. The rule is that you can only have one intersection per line
for number 14, if you draw a line, it intersects the function twice each time
for 15, no matter what kind of vertical line you draw, each line will only intersect the function once and the same for 16 (except 16 is more of a linear function)
Answer:
Well a function can’t be on the same one as each other so thats why the vertical line test is used.
For number 14 if you’d draw a vertical line, you’d see there would be 2 answers So that can’t be a function.
For number 15, if you draw a vertical line, none of the given have 2 questions so number 15 is a function.
Whilst in number 16 if you’d draw a vertical line, there wouldn’t be anything that have 2 answers of that overlap. So it is a function
express 10500 in terms of its prime factors .
determine the smallest positive number P such that 10500P is a perfect cube
Answers
Answer:
Below
Step-by-step explanation:
Dividing by prime numbers :
2 | 10500
2 | 5250
3 | 2625
5 | 875
5 | 175
5 | 35
7.
So 10500 = 2*2*3*5*5*5*7
To find the smallest positive cube we need to multiply by 2 ( to get 3 2's in the prime factors), another 2 3's and another 2 7's
That is P = 2*3*3*7*7 = 882.
The perfect cube is 2^3*3^3*5*3*7^3 = 9261000.
choose the correct description of the system of equations. 3x-y=5 6x=2y+5 A.Consistent and independent B.Consistent and dependent C.Inconsistent D.Inconsistent and dependent
Answers
Answer:
C. inconsistent
Step-by-step explanation:
3x - y = 5 6x = 2y + 5 Solve for y
3x - 5 = y 6x - 5 = 2y
3x - 5 = y [tex]\frac{6x}{2} - \frac{5}{2} = \frac{2y}{2}[/tex]
3x - 5 = y 3x - 2.5 = y
Slope = 3 Slope = 3 Same slope
y-intercept: -5 y-intercept: 2.5 Different intercepts
not solution set
Please help I’m begging you
Answers
Answer:
y = 9
Step-by-step explanation:
The line "y = 9" is parallel to the x-axis and passes through (0,9).
When the Johnson family lights candles at 5:00 PM, each candle is 8 inches tall. The height of each candle changes by -3/4 inch for each hour that it burns. How tall will each candle be at 11:00 PM when the Johnsons put the candles out for the night?
Each candle will be___inches tall.
Answers
From the information given, it can be deduced that the length of the candle at 11:00PM will be 3.5 inches tall.
Since the family lights candles at 5:00 PM and offs them by 11:00PM, the difference in hours will be 6 hours.
Therefore, the length of the candles at 11:00PM will be:
= 8 - (3/4 × 6)
= 8 - 4.5
= 3.5
In conclusion, the correct option is 3.5 inches tall.
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Answer: 3.5
just did it
Step-by-step explanation: