2. Consider the following points.
A(-2,20) and P (10,-13)
AP undergoes the translation Tox(x,y), such that A (-28, 37) and P'(-16,4).
Part A: Complete the following algebraic description.
b
(x,y) → (x +
x= x
Part B: Which of the following statements is true?
A AP and A'P' have different locations.
B AP and A'P' have different shapes.
CAP and A'P' have different sizes.
D AP and A'P' have different directions.
Answers
Answer:
Transformation: (x,y) → (x - 26, y + 17) or
[tex]T _{-26,17}[/tex](x,y) [translation]
A, since the transformation of a translation simply changes the location of a certain figure because all the points of the figure are moved the exact same way. This is because a translation is a rigid transformation.
Explanation:
Let the preimage of points A and P be A(x1,y1), and P(x2,y2). And the image of points A and P be A'(x3,y3) and P'(x4,y4).
Given points A and P are A(-2,20) and (10,-13). And points A' and P' are A'(-28,37), and P'(-16,4). The translation is found by calculating the difference between these points for the figure. (x,y) → (( x + ((x3-x1) + (x4-x2))/2), (y + ((y3-y1) + (y4-y2))/2 )). If this does not match all the points in the transformation of the figure, than it is not a rigid transformation, and so it cannot be a translation.
The simple formula for the uniform translation of a figure is : (x,y) → ((x + (x2-x1), (y + (y2-y1)) . Where x2, and y2 are part of the image, while x1, and y1 are part of the preimage. This will get you from the preimage(1) to image(2) following a translation.
Given all the points, the more complicated work is shown here:
(x,y) → ((x + ((-28--2) + (-16-10))/2), (y + ((37-20) + (4--13))/2)) = (x,y) → ((x + (-26 + -26)/2),(y + (17 + 17)/2) = (x,y) → ((x - 26),(y + 17)) = (x,y) → (x - 26, y + 17).
When writing a transformation like a translation in a function, it will look like this: [tex]T _{∆x,∆y}[/tex](x,y). ∆x,∆y are just placeholders for the change in these variables that get you from the preimage to image.
Related Questions
in a survey 8 out of 32 students preferred vanilla ice cream if 252 students are surveyed how many should theoretically prefer vanilla ice cream make a prediction?
Answers
Answer:
63
Step-by-step explanation:
8 / 32 = 0.25
Multiply 0.25 with 252
0.25 * 252 = 63
This process simply applies the same ratio from the first test to the second test.
A coordinate plane is shown. Triangle PQR has vertices P at negative 6 comma 6, Q at negative 6 comma 3, and R at negative 3 comma 3. Triangle P prime Q prime R prime has vertices at P prime negative 2 comma 2, Q prime at negative 2 comma 1, and R prime at negative 1 comma 1. What is the scale factor of dilation?
Answers
Answer:
The scale factor of dilation from ΔPQR to ΔP'Q'R' is 1/3
Step-by-step explanation:
The given information are;
The vertices of ΔPQR are;
P(-6, 6), Q(-6, 3), and R(-3, 3) and the coordinates of ΔP'Q'R' are P'(-2, 2), Q'(-2, 1), and R'(-1, 1)
Given that the length, l, of each side of the triangles is given by the formula for calculating length given the vertices we have;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For side PQ, we have;
(x₁, y₁) = (-6, 6), (x₂, y₂) = (-6, 3)
Given that the points have equal y-values, the length is the difference of their x-values as follows;
[tex]l_{PQ}[/tex] = 6 - 3 = 3
Similarly, length QR is the difference in the y-values, since the x-values are equal. therefore, we have;
[tex]l_{QR}[/tex] = -3 - (-6) = 3
Length PR is given as follows;
(x₁, y₁) = (-6, 6), (x₂, y₂) = (-3, 3)
[tex]l_{PR} = \sqrt{\left (3-6 \right )^{2}+\left (-3-(-6) \right )^{2}} = \sqrt{18} = 3\cdot \sqrt{2}[/tex]
[tex]l_{PR}[/tex] = 3·√2
For P'Q', we have
P'(-2, 2), Q'(-2, 1)
[tex]l_{P'Q'}[/tex] = 2 - 1 = 1
[tex]l_{P'Q'}[/tex] = 1
For Q'R', we have
Q'(-2, 1), R'(-1, 1)
[tex]l_{Q'R'}[/tex] = -1 - (-2) = -1 + 2 = 1
[tex]l_{Q'R'}[/tex] = 1
For P'R', we have;
P'(-2, 2), R'(-1, 1)
[tex]l_{P'R'} = \sqrt{\left (1-2 \right )^{2}+\left (-1-(-2) \right )^{2}} = \sqrt{2} = \sqrt{2}[/tex]
[tex]l_{P'R'}[/tex] = √2
Therefore, given that we have
PQ/(P'Q') = PR/(P'R') = 3/1 = 3 and QR/(Q'R') = 3·√2/(√2) = 3
The scale factor of dilation from ΔPQR to ΔP'Q'R' = 1/3.
Given that 1 pound equals 16 ounces, how many pounds are in 116 ounce -) A) 6.75 pounds B) 7.25 pounds 7.5 pounds D) 7.75 pounds
Answers
Answer:
B)7.25
Step-by-step explanation:
16x7.25=116
HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!
Answers
I got 2 : 3. You didn’t give answer choices but after you commented the answer choices I was able to determine that 2:3 is the answer.
Two pounds of raw materials are needed to produce one product. The desired ending balance of raw materials is 10% of the of the next month's production needs. (Refer to your answer in Activity Sheet 05). The beginning inventory of raw materials is 4,000 pounds and raw material cost per unit is P 0.50/per pound.
Answers
Answer:
Purchases= production + desired ending inventory - beginning inventory
Step-by-step explanation:
Giving the following information:
Two pounds of raw materials are needed to produce one product.
The desired ending balance of raw materials is 10% of the next month's production needs.
The beginning inventory of raw materials is 4,000 pounds.
The raw material cost per unit is $0.50 per pound.
To calculate the direct material purchase required for a given month, we need the production for each month. I will provide the formula and a small example to guide an answer.
To calculate the purchase required, we need to use the following formula:
Purchases= production + desired ending inventory - beginning inventory
For example:
Production:
January= 5,000 units
February= 4,500 units
Direct material purchases January:
Production= 5,000*2= 10,000
Desired ending inventory= (4,500*2)*0.1= 900
Beginning inventory= (4,000)
Total purchase in pounds= 6,900
Total direct material cost= 6,900*0.5= $3,450
how many triangles in the figure?
26
25
24
27
Answers
Frederick is training for a triathlon and wants to focus on swimming this week. He can swim 25 yards in 23 seconds. He set up a proportion to determine how long it would take him to swim 175 yards at this rate. Which proportions can be used to determine how long it would take him to swim 175 yards?
Answers
Answer:
161secsStep-by-step explanation:
If Frederick can swim 25 yards in 23 seconds, then:
25 yards = 23 seconds
To determine how long it will take him to swim 175yards, we will say:
175 yards = x
Equating both expression:
25 yards = 23 seconds
175 yards = x
Cross multiply
25x = 23*175
25x = 4025
Divide both sides by 25
25x/25 = 4025/25
x = 161 secs
This means that it will take Frederick 161 secs to swim 175 yards
Find the measure of angle b
Answers
Answer:
130°
Step-by-step explanation:
a straight line is 180°
so you have
180°-50°= 130°
b and 50 are supplementary angles (they add up to 180), so create an equation by adding them up to equal 180:
b + 50 = 180
we want the x by itself, so subtract both sides by 50 to get:
b = 130°
Divide n by 5 then add 6
Answers
Answer:
n+30/5
Step-by-step explanation:
Simplify n/5
n/5+6
Rewrite the whole as an equivalent fraction
2.1 Add an integer to a fraction
Rewrite the whole as a fraction using 5 as the denominator: 6= 6/1=6×5/5
Equivalent fraction: the fraction thus generated looks different but has the same value as everything.
2.2 sum of the two equivalent fractions add two equivalent fractions that now have a common denominator
Combine the numerators, place the sum or difference over the common denominator, and then reduce to the lowest terms of possible:
n+6×5/5=n+30/5
PLS TELL ME WHICH ONE IS TRUE PLS DONT LIE
Answers
2/5(10x+25)
Simplify
Brainly
Answers
Answer:
4x+10
Step-by-step explanation:
Select the correct answer.
To bake one cake, Drew uses 18 ounces of flour. He has 850 ounces of flour. Let y represent the ounces of flour left and x represent the number of cakes he has baked. When the situation is modeled on a graph, what are the slope and the y-intercept of the line representing this situation?
A.
slope = 850 and y-intercept = 18
B.
slope = 18 and y-intercept = 850
C.
slope = -18 and y-intercept = 850
D.
slope = 850 and y-intercept = -18
Answers
Answer:
The answer is C, hope that helps:)
Step-by-step explanation:
Victor runs 3 laps around the track every 5 minutes. How many laps does Victor run in 1 minute?
Answers
Answer:
Victor runs 0.6 of a lap in 1 minute
Step-by-step explanation:
From the question;
3 laps = 5 minutes
x laps = 1 minute
3 * 1 = 5 * x
3 = 5x
x = 3/5
x = 0.6
Victor runs 0.6 of a lap in a minute
The lowest temperature ever recorded on Earth was $-89.2\degree\text{C}$ at Soviet Vostok Station in Antarctica. The highest temperature ever recorded was $56.7\degree\text{C}$ at Greenland Ranch in California. What is the difference between the highest and lowest recorded temperatures?
Answers
Answer:
145.9°C
Step-by-step explanation:
Given that :
Lowest temperature recorded (Soviet Vostock station Antarctica) = - 89.2°C
Highest temperature recorded (Greenland Ranch California) = 56.7°C
Difference between the highest and lowest recorded temperature :
(Highest temperature - lowest temperature)
(56.7°C - (-89.2°C))
= 56.7°C + 89.2°C
= 145.9°C
Name the slope of a line parallel to y = -3x -2
Answers
Can anyone do this question?
Answers
Answer:
its simple 5.90
Step-by-step explanation:
can yall help me plz
Answers
Answer:
lol girl i have this one too and im trying to do cuz no one cam to help me so im going to try and then i will see if i help you
Step-by-step explanation:
Answer:
just add thos and then put then to geter and you get 3x+1^2
Step-by-step explanation:
Pls Help me. I will mark brainlist.
Answers
Answer:
The second answer
Step-by-step explanation:
Because if you subtract a negative from an equation you get positive (two negatives make a positive)
The book contains 200 thin sheets of paper.
The student wants to find the average mean, thickness of a sheet of paper in the book
Describe how he can determine such a small distance using only a ruler.
Answers
Answer:
Measure all the sheets together and divide by 200
Step-by-step explanation:
An average mean is the sum of something divided by how many things there are. In this case, it is the sum of the thickness of 200 pages, divided by the number of pages, 200.
Please Help! Will mark brainliest!
Answers
Answer:<EBA=103
Step-by-step explanation:
72+31=103
Answer:
[tex]\boxed {\tt C. \ m \angle EBA=103}[/tex]
Step-by-step explanation:
∠EBA is made up of 2 angles: ∠ABC and ∠EBC
If we want to find the measure of ∠EBA, we should add the measure of ∠ABC and ∠EBC.
m∠EBA= m∠ABC+m∠EBC
The measure of angle ABC is 72. The measure of angle EBC is 31. (m∠ABC=72 and m∠EBC=31)
m∠EBA= 72 + 31
Add.
m∠EBA=103
The measure of angle EBA is 103 and choice C is correct.
Solving each proportions 10/8=n/10
Answers
Answer:
n=12.5
Step-by-step explanation:
10/8=n/10
multiply the denominator and numerators 10 ad 10=100 divide by 8=12.5
If f(x)=ax²+bx+c and f(1)=6,f(2)=11,f(3)=18 find the value of a,b,c
Answers
f(x) = ax² + bx + c
f(1) = 6
f(2) = 11
f(3) = 18
Find:value of a,b,c
Solution:Substitute x = 1 , 2 , 3 in the given polynomial.
★ f(1) = a(1)² + b(1) + c
⟹ 6 = a + b + c -- equation (1)
Similarly,
★ f(2) = a(2)² + b(2) + c
⟹ 11 = 4a + 2b + c -- equation (2)
★ f(3) = a(3)² + b(3) + c
⟹ 18 = 9a + 3b + c -- equation (3)
Subtract equation (1) from (2).
⟹ 4a + 2b + c - (a + b + c) = 11 - 6
⟹ 4a + 2b + c - a - b - c = 5
⟹ 3a + b = 5 -- equation (4).
From equation (3) ,
⟹ 18 - c = 9a + 3b
⟹ 18 - c = 3(3a + b)
Substitute the value of 3a + b from equation (4).
⟹ 18 - c = 3 * 5
⟹ 18 - 15 = c
⟹ 3 = c
substitute the value of c in equation (1).
⟹ 6 = a + b + 3
⟹ 6 - 3 = a + b
⟹ 3 = a + b -- equation (5)
Subtract equation (5) from equation (4).
⟹ 3a + b - (a + b) = 5 - 3
⟹ 3a + b - a - b = 2
⟹ 2a = 2
⟹ a = 1
Substitute a value in equation (5).
⟹ 1 + b = 3
⟹ b = 3 - 1
⟹ b = 2
Therefore,
a = 1
b = 2
c = 3.
I hope it will help you.
Regards.
What algebraic expression could represent the average of 2x, x + 3, and 6x?
Answers
Answer:
3x+1
Step-by-step explanation:
(2x+x+3+6x)/3
9x+3/3
3x+1
The final result is a simplified algebraic expression 3x + 1 that represents the average of 2x, x + 3, and 6x.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The average of 2x, x + 3, and 6x can be represented by the algebraic expression (2x + (x + 3) + 6x)/3.
This expression takes the sum of 2x, x + 3, and 6x, and then divides that sum by 3, which is the number of terms being averaged.
Alternatively, the average can be represented by (2x + x + 6x + 3) / 3 = (9x + 3) / 3 = 3x + 1.
In either case, the final result is a simplified algebraic expression that represents the average of 2x, x + 3, and 6x.
Learn more about Expressions here :
brainly.com/question/21751419
#SPJ2
Using these clues, make a quadilateral. Write the name and each side. What is the perimeter?
1. rectangle with sides 7 feet
2. 7feet
3. 10 feet
4. 10feet
Answers
The name of my shape is a parallelogram. The sides are:
7 feet7 feet10 feet10 feetThe perimeter is 34 feet because:
Step 1: Add smaller groups.
10 + 10 = 20
7 + 7 = 14.
Step 2: Add the two numbers.
14 + 20 = 34.
Hope this answer helps you!
they only said simplify and i guessed the answer as undefined
Answers
when 3+3x-5-8x is simplified, the result is?
Answers
Answer:
−5x−2
Step-by-step explanation:
rewrite the quadratic function f(x) = (2x -3)(x+4) in standard form
Answers
Answer:
f(x) = 2x^2+5x-12
Step-by-step explanation:
do any of you know how to do algebra 2 ?
Answers
Answer: Were is the math problem at?
Maggie‘s brother is 11 years younger than four times her age. The sum of their ages is 54. How old is Maggie?
Answers
Answer:
Maggie is 13
Step-by-step explanation:
Honestly, I just kept trying ages starting from 10 because I knew it wasn't going to be less than that. Then I did whatever age, in this case 13, and multiply it by 4. Then minus 11 from that number. Then take that end number and add it to the beginning number(maggies age) and you should get 54.
Math Equation Explanation:
13*4 = 52 (Maggies Age) x 4
52-11= 41 The question stated that Maggie's brother was 11 -------------------------------------years younger than her age times 4.
41 + 13 =54 The sum of both their ages.
A carpenter has less than 120 minutes to spend painting furniture each day. Today, he has spent 30.5 minutes painting a desk. Now he will paint x chairs, each of which takes 12.5 minutes. What is the maximum number of chairs the carpenter can paint?
Answers
Answer:
Maximum number of chairs is 7.
Step-by-step explanation:
We are told he has less than 120 minutes to spend painting furniture each day.
Now he has spent 30.5 minutes painting a desk.
Also, he wants to paint "x" number of chairs with each chair taking 12.5 minutes.
Thus, we have;
30.5 + 12.5x < 120
Subtract 30.5 from both sides to get;
12.5x < 120 - 30.5
12.5x < 89.5
x < 89.5/12.5
x < 7.16
Thus, maximum number of chairs he can paint is 7