Answer: All four answer choices would create congruent shapes.
===================================================
Explanation:
Reflections, rotations, and translations are considered rigid transformations. What this means is that they keep the same shape, but the shape has been moved in some fashion. As such, the "before" (preimage) and "after" (image) are congruent figures.
Imagine you drew a triangle on a clear piece of glass. If you took a picture of it from one side, then took another picture from the opposite side, then you'd get reflected versions of the triangle. Notice how the triangle has not moved at all. The camera has. Therefore, this proves that reflections keep the same exact shape. The only thing different is the orientation has swapped.
Now imagine you drew a triangle etched in stone. Grab your camera to take a picture of it. Then rotate the camera to get another picture. The two triangles are rotated copies of each other. They're the same exact triangle since the figure etched in stone hasn't changed. Only the camera has. This thought exercise proves rotations are a rigid transformation, aka an isometry.
Lastly, we'll go back to the triangle etched in stone to work with translations. A translation is any shifting. Take a picture of the triangle etched in stone. Then move the camera around to pan to another location (panning is when you keep your aim at the subject but move side to side, or up and down). Imagine the camera is stuck on a train track and can only aim one direction. The camera will take two pictures of the same triangle, of course the only difference is that they have shifted in the frame. Therefore, translations are the third final type of rigid transformation.
-----------------
Dilations are not rigid transformations, but only if the scale factor was something else than 1.
If the scale factor is less than 1, then the image shrinks.
If the scale factor is greater than 1, then the image enlarges.
If the scale factor is exactly 1, then the image doesn't change at all. This is because we multiplied all sides by 1. Multiplying by 1 doesn't change the number.
So because choice (2) mentions the scale factor is 1, this places it in the "rigid transformation" category and it's one of the four answers. Change the scale factor to anything else, and it wouldn't be an answer.
To make sure there is enough space for the donuts, Dave wants to add { inch to the minimum length, width, and height of the box. Including the additional space, what should be the length, width, and height of the new box, in inches? nter each answer in a separate response box.
The new length, width, and the height of the cuboid are (L+2) inches, (W+2) inches, and (H+2) inches respectively
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry. As the old length, width, and height are not given so we are assuming the length of the box is L, width is W, and height is H.
Dave wants to add 2 inches to the minimum length, width, and height of the box. Including the additional space. So the new length = (L+2) inches
New width = (W+2) inches
New height = (H+2) inches
Thus, the new length, width, and height are (L+2) inches, (W+2) inches, and (H+2) inches respectively.
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3. The value of a car in relation to the number of miles driven is given by the linear
function y = -9x + 55000.
a. Interpret the meaning of the rate of change and initial value for the linear function.
Answer:
General form of a linear equation: [tex]y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
A linear equation has a constant rate of change which is represented by the slope (m). It is the rate at which one quantity is changing with respect to another quantity.
Question 3Part (a)
Given equation: [tex]y=-9x+55000[/tex]
where:
y = value of car (in dollars)x = number of miles drivenThe rate of change (slope) is -9 and represents that for every 1 mile driven, the value of the car decreases by $9.
The initial value is the y-intercept (b) as this is the value when x = 0.
Therefore, the initial value of car is $55,000.
Part (b)
To find the number of miles at which the car be valued at $35,002, set the equation to $35,002 and solve for x:
[tex]\implies -9x+55000=35002[/tex]
[tex]\implies -9x=35002-55000[/tex]
[tex]\implies -9x=-19998[/tex]
[tex]\implies x=\dfrac{-19998}{-9}[/tex]
[tex]\implies x=2222[/tex]
Therefore, the car will be valued at $35,002 after 2,222 miles.
Question 4Given equation: [tex]y=0.39x+2.55[/tex]
where:
y = price of carrots (in dollars)x = weight (in oz)The rate of change (slope) is 0.39 and represents that for every increase of 1 oz of weight in carrots, the price of the carrots increases by $0.39
The initial value is the y-intercept (b) as this is the value when x = 0.
Therefore, the initial cost of the carrots is $2.55.
Part (b)
To find the weight of carrots you can buy for $6.06, set the equation to $6.06 and solve for x:
[tex]\implies 0.39x+2.55=6.06[/tex]
[tex]\implies 0.39x=6.06-2.55[/tex]
[tex]\implies 0.39x=3.51[/tex]
[tex]\implies x=\dfrac{3.51}{0.39}[/tex]
[tex]\implies x=9[/tex]
Therefore, you can buy 9 oz of carrots for $6.06
Part (c)
To find out how much it costs to buy 21 oz of carrots, substitute x = 21 into the equation and solve for y:
[tex]\implies y=0.39(21)+2.55[/tex]
[tex]\implies y=10.74[/tex]
Therefore, it costs $10.74 to buy 21 oz of carrots.
The ratio of boys to girls in the 8th grade is 5:6. If there are 75 boys in the 8th grade, how many are girls?
Answer:
There are 15 girls
Step-by-step explanation:
Given:- Ratio of boys to girls = 5:3
And, the number of boys = 75
let the girls be 5x and boys be 3x
so, 5 × 75 { given }
x = 75/5 = 15
6x= 6 × 15 = 90
6x/6 = 90/6 = 15
---~ Hope this helps~---
Mrs. Welloff has just passed away, she has a $1,000,000 life insurance policy and her beneficiaries are her son and 3 grandchildren. She will leave 50% of her estate to her son and the other 50% to her three grandchildren equally. How much money will they each receive?
Son_______________
Grandchild #1_______________ Grandchild #2_______________ Grandchild #3_______________
Answer:
Step-by-step explanation:
1/2 of 1,000,000 is 500,000
the son will get 500,000$
now 500,000 divided by 3(since it's 3 grandkids) is
166666.66, because it's money, and you have to round to the nearest cent.
one will get 166666.67, but it doesn't matter who.
so
grand #1 = 166666.66$
grand #2 = 166666.66$
grand #3 = 166666.67$
what is the equation of a parabola with a vertex at (6,4) and a=2?
Answer:
y = 2x² - 24x + 76
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here a = 2 and (h, k ) = (6, 4 ) , then
y = 2(x - 6)² + 4 ← in vertex form
expand factor using FOIL
y = 2(x² - 12x + 36) + 4 ← distribute parenthesis by 2
y = 2x² - 24x + 72 + 4
y = 2x² - 24x + 76 ← in standard form
for the given literal equation z=a/b + c/d .solve for D
An equation is formed of two equal expressions. The given literal equation z=(a/b)+(c/d) is d=cb/(zb-a).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given literal equation z=(a/b)+(c/d) can be solved for D as,
z-(a/b) = (c/d)
(zb-a)/b = c/d
d = cb/(zb-a)
Hence, The given literal equation z=(a/b)+(c/d) is d=cb/(zb-a).
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Please help me on this my moms mad at m e because i dont know
Vicky has a spinner divided into 9 equal sections that are labeled 1 though 9. She wants to compare the theoretical probability and the experimental probability of spinning an odd number. She spins the spinner 10 times and records the results in this list.
{2, 4, 1, 8, 7, 5, 3, 4, 1, 9}
**Note - There are 3 answers. You must select 3 answers.**
The theoretical probability of spinning an odd number is equal to ______. The experimental probability of spinning an odd number is equal to ______. Therefore, the theoretical probability of spinning an odd number is _____ the experimental probability of spinning an odd number.
Select 3 correct answer(s)
Question 7 options:
1/5
5/9
2/3
3/5
1/2
less than
greater than
The theoretical probability of spinning and odd number will be 5/9.
How to calculate the probability?The theoretical probability of spinning and odd number will be:
Number of odd numbers / Total number
= 5/9
The experimental probability of spinning an odd number is equal to:
= 5/10 = 1/2
Therefore, the theoretical probability of spinning an odd number is greater than the experimental probability of spinning an odd number.
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please help me. please solve
Answer:
x = 3
Step-by-step explanation:
7x + 3 = 24 ( subtract 3 from both sides )
7x = 21 ( divide both sides by 7 )
x = 3
Help me pls this is due today and I need the answers a soon as possible!!!
Answer:
You can find the given attachment
How many different outcome pairs are possible from rolling a sixteen-sided and a twenty-sided
dice at the same time?
The number of the possible combinations from rolling a sixteen-sided and a twenty-sided dice at the same time is 320.
What is the combination?The arrangement of the different things or numbers in a number of ways is called the combination.
The possible outcomes for dice with 16 sides:-
{ 1,2,3,4,5,6,...............16}
The possible outcomes for dice with 20 sides:-
{ 1,2,3,4,5,6,...............20}
So the number of the possible pairs will be:-
= 16 x 20
= 320 pairs.
Therefore the number of the possible combinations from rolling a sixteen-sided and a twenty-sided dice at the same time is 320.
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The credit card industry works similar to the cigarette industry. what reasons caused culture to change its view of cigarettes over the past few decades? what do you think would need to happen to change america's view of credit cards?
The credit card industry and cigarette industry are very similar in terms of negative influence on personal finances.
What is credit card?A credit card is a sort of payment card that uses a line of credit rather than the account holder's cash deposits to make purchases.
Tobacco use can have a negative impact on personal finances due to the sheer high price of tobacco products, wasted pay owing to sickness absence, plus hospitalization rates due to the higher risk of illness associated with smoking use.
If you let that debt grow, you may find that the amount of interest you owe equals or even exceeds your original principal, forcing you to spend a lot just to pay it off.
Thus, the credit card industry and cigarette industry are very similar in terms of negative influence on personal finances.
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Akeem will record the time it takes him to run 1 mile each day for 7 days. In order to meet his fitness challenge, his mean running time for 7 days must be 9 minutes or less. A list of Akeem's running times, in minutes, for the first 6 days is shown.
9.4, 9.0, 9.1, 8.9, 8.5, 8.8
The time Akeem runs on days must be 9.3 minutes or less than 9.3 minutes if the mean running time for 7 days must be 9 minutes or less.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have:
Akeem will record the time it takes him to run 1 mile each day for 7 days. In order to meet his fitness challenge, his mean running time for 7 days must be 9 minutes or less.
Here we are assuming that it is required to find the time Akeem runs on the 7th day.
Let's suppose Akeem runs x minutes on the 7th day.
Mean running time ≤ 9
The mean:
[tex]\dfrac{(9.4+9.0+9.1+8.9+8.5+8.8+x)}{7} \leq 9[/tex]
[tex]\dfrac{(53.7+x)}{7} \leq 9[/tex]
53.7 + x ≤ 63
x ≤ 9.3 minutes
Thus, the time Akeem runs on days must be 9.3 minutes or less than 9.3 minutes if the mean running time for 7 days must be 9 minutes or less.
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division equation where 13 is quotient with the dividend a whole number and a unit fraction is the divisor
The division equation that has a quotient of 13 is 1/1/13 = 13
How to determine the equation?The given parameters are:
Quotient = 13Dividend = Whole numberDivisor = Unit fraction i.e. 1/n where n is an integer.A division equation is represented as:
Dividend/Divisor = Quotient
Substitute 13 for the Quotient
Dividend/Divisor = 13
Recall that:
Unit fraction = 1/n
So, we have:
Dividend/1/n = 13
Let n = 13.
So, we have:
Dividend/1/13 = 13
This gives
13 * Dividend = 13
Divide both sides by 13
Dividend = 1
So, we have:
1/1/13 = 13
Hence, the division equation is 1/1/13 = 13
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Find the equation of the line that passes through the point (-2, 3) and is parallel to the line whose equation is y = 2x + 1. = 1 1.
Answer:
Step-by-step explanation:
Daniels garage is 8ft long by 10 ft wide. His living room is twice as long and twice as wide as his garage. Daniels house is 3 times as long and 4 times as wide as his living room. What is the total perimeter of his house?
Answer:
The perimeter of his house: 256 ft
Step-by-step explanation:
length of living room = 2 x length of garage
=2 x 8 ft
=16 ft
width of living room = 2 x width of garage
= 2 x 10 ft
= 20 ft
daniel house length = 3 x length of L.R
= 3 x 16 ft
=48 ft
daniel house width = 4 x width of L.R
= 4 X 20 ft
= 80 ft
preimeter of rectangle = 2[l + b]
= 2[ 48 +80 ]
= 256 ft
perimeter of house = 256 ft
raymond wants to know the costs of buying different numbers of songs for his mp3 player the cost of each song is the same let s represent the possible number of songs ramond could buy let d represent the amount of money
The values of s in correspondence with the values of d are as indicated in the answer below.
What are the missing values of s and d?It follows from the complete task content that the missing values in Raymond's table are required.
From the first row, it follows that 2 MP3 songs goes for 2.58.
On this note, the ratio of d to s; d/s = 2.58/2.
Ultimately, the missing values can be evaluated by just substituting d and s into the equation for each case.
Remarks:
Fill in the table for all missing values of s and d.
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Help now please !!!!
Answer:
Im sorry if you get this wrong but it should be the opposite like -3, -2 since its going on the other side for the y axis?
Step-by-step explanation:
A bag contains 7 red, 3 yellow, and 4 blue marbles. What is the probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first?
A) 11/14
B) 1/7
C) 2/13
D) 75/91
Answer:
2/13
Step-by-step explanation:
4/14 × 7/13 when i simplify it becomes 2/13!!!
The probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first is 2/13.
What is Probability?Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of getting a blue marble at the first try is,
Probability(Blue) = Number of blue marbles / Total number of marbles
= 4 / 14
The probability of getting a red marble at the second try is,
Probability(Red) = Number of Red marbles / Total number of marbles
= 7 / 13
The probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first is,
Probability = Probability(Blue) × Probability(Red)
= (4/14) × (7/13)
= 2/13
Hence, the probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first is 2/13.
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What is the sum? startfraction 3 over x endfraction startfraction 4 over x squared endfraction startfraction 3 x 4 over x cubed endfraction startfraction 7 over x endfraction startfraction 3 x 4 over x squared endfraction startfraction 7 over x x squared endfraction
The expressions are algebraic expressions, and the sum of the expressions 3/x and 4/x² is [tex]\frac{3x + 4}{x^2}[/tex]
How to determine the sum?The expression is given as:
[tex]\frac{3}{x} + \frac{4}{x^2}[/tex]
Take the LCM of the expressions
[tex]\frac{3}{x} + \frac{4}{x^2} = \frac{3x + 4}{x^2}[/tex]
The above expression cannot be further simplified
Hence, the sum of the expressions 3/x and 4/x² is [tex]\frac{3x + 4}{x^2}[/tex]
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Answer:
C on edge
Step-by-step explanation:
3x+4/x^2
Which statement describes the following expression? 2 x (1,635 ÷ 101)
2 times the value of 1,635 minus 101
2 times the value of 1,635 times 101
2 times the value of 1,635 divided by 101
2 times the value of 1,635 plus 101
Answer:
2 times the value of 1635 divided by 101.
hope it helps :))
6. Geographic Trends Janice has been offered
a job in Chicago where her current salary of
$30,000 will increase by 20 percent. Before
ct
accepting the position, Janice wants to
understand her potential cost of living. She
estimates that rent will be $1,500 per month.
She will have to take the train to and from
work, which will be $3.50 round trip daily. Her
food cost will be $75 per week. If Janice works
5 days a week for 52 weeks per year, what
will her annual income be after paying rent,
transportation, and food?
The annual income of Janice when she accepts new job in Chicago be after paying rent, transportation, and food is, $409190.
What is the total cost?Total cost or the final cost is the summation of all the cost spend while buying any good or taking any service.
Janice has been offered a job in Chicago where her current salary of $30,000 will increase by 20 percent. Thus, his new salary is,
[tex]S=\dfrac{100+20}{100}\times30000\\S=36000[/tex]
He gets 6000 thousand extra after increment. Her annual income is,
[tex]S=36000\times12\\S=432000[/tex]
Before accepting the position, Janice wants to understand her potential cost of living.
She estimates that rent will be $1,500 per month. Thus, the She will have to take the train to and from work, which will be $3.50 round trip daily. Her food cost will be $75 per week.Janice works 5 days a week for 52 weeks per year. Her annual income be after paying rent, transportation, and food is,
[tex]S=432000-1500\times12-3.50\times5\times52-75\times52\\S=409190[/tex]
Thus, the annual income of Janice when she accepts new job in Chicago be after paying rent, transportation, and food is, $409190.
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What is the volume of the can? SHOW WORK.
Answer:
[tex] V_{can} = 480\: cm^3[/tex]
Step-by-step explanation:
Height of the can (h) = 12 cmArea of top (A) [tex]=40\: cm^2[/tex][tex]V_{can} = Area * Height[/tex][tex]\implies V_{can} = 40 * 12[/tex][tex]\implies V_{can} = 480\: cm^3[/tex]Gary has 5 cm of string his project uses 1,750 mm how many more millimeters of string does Gary need
Answer:
1,700mm
Step-by-step explanation:
1,750mm=175cm
5cm=50mm
1,750-50=1,700mm
gary's project uses 1,750 which is equal to 175 cm he already has 5cm of string which is equal to 50mm so he will need 1,700mm of string or 170cm
i hope this helps please feel free to point out any mistakes that i might have made
What is the range of this function?
-3 -5
0 -2
4 3
7 8
A(-5,-3,-2,0,3,4,7,8)
B (-5,-2,3,8)
C (-3,3)
D(-3,0,4,7)
Answer:
B (-5, -2, 3, 8)
Step-by-step explanation:
Remember this because you'll probably need it
The range consists of all the y-values that make up a function. Since all of the y-values are [-5, -2, 3, 8], the answer is B
26. Figure B is the image of Figure A.
after a dilation with center (0,0) and a
reflection across the y-axis. What is the
scale factor of the dilation?
The scale factor of dilation is [tex]\LARGE \frac{1}{4}[/tex].
What is scale factor?When describing an enlargement you must state by how much the shape has been enlarged or reduced.
Area of triangle B =[tex]\frac{1}{2} * b *h[/tex]
= 0.5 x 2 x 3
= 3 units
Area of triangle A =[tex]\frac{1}{2} * b *h[/tex]
= 0.5 x 4 x 6
= 12 units
Scale factor =[tex]\frac{Area of \; triangle B}{Area of\; triangle A}[/tex]
=[tex]\frac{3}{12}[/tex]
= [tex]\frac{1}{4}[/tex]
Hence, the scale factor of dilation is [tex]\LARGE \frac{1}{4}[/tex].
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I need help please! I will name the brainliest!
PLEASE HELP !!! These box plots show daily low temperatures for a sample of days in two different towns. Which statement is the most appropriate comparison of the spreads? Town A 10 15 20 30 55 Town B 5 20 30 40 55
Answer: 20
Step-by-step explanation:
I need help, what is 9^-2+181-69? this is math
Answer:
193
Step-by-step explanation:
9^2 = 81+181=262-69= 193
probability questions
pls help
-
[3 x 25 – 13 × (-2)] + 23
(-22 + 32) - 3
Give your answer in simplest form.
Enter
What
Answer:
type this in M
a
t
h
w
a
y
Step-by-step explanation:This
will give the answer promise
Answer:
1029
Step-by-step explanation:
124 + 23 x 10 - 3 = 147 7 =1029
