PLEASEE HELPP!
Use the following figure to answer BOTH parts the question
(a) Describe in words a sequence of transformations that maps ∆ to ∆′′′.
(b) Write an ordered-pair rule for each transformation in the sequence.
Answers
Transformation involves changing the position of a shape
The sequence that maps ∆ABC to ∆A′B′C′ is reflection across the y-axis, followed by horizontal and vertical shiftsThe ordered pair rule is: [tex](x,y) \to (-x,-1,y-2)[/tex](a) The sequence that maps both triangles
From the figure the coordinates of both triangles are:
[tex]A = (-5,0)[/tex]
[tex]B = (-2,1)[/tex]
[tex]C = (-4,2)[/tex]
[tex]A' = (4,-2)[/tex]
[tex]B' = (1,-1)[/tex]
[tex]C = (3,0)[/tex]
Start by reflecting triangle ABC across the y-axis.
The rule of this transformation is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]A = (5,0)[/tex]
[tex]B = (2,1)[/tex]
[tex]C = (4,2)[/tex]
Next, translate the triangle 1 unit left and 2 units down
The rule of this transformation is:
[tex](x,y) \to (x,-1,y-2)[/tex]
So, we have:
[tex]A' = (4,-2)[/tex]
[tex]B' = (1,-1)[/tex]
[tex]C = (3,0)[/tex]
Hence, the sequence that maps ∆ABC to ∆A′B′C′ is reflection across the y-axis, followed by horizontal shift to the left by 1 unit, and vertical shift down by 2 units
(b) The ordered pair rule
In (a), we have:
[tex](x,y) \to (-x,y)[/tex] ---- reflection
[tex](x,y) \to (x,-1,y-2)[/tex] --- translation
Combine both transformations, so we have the following ordered pair:
[tex](x,y) \to (-x,-1,y-2)[/tex]
Hence, the ordered pair rule is: [tex](x,y) \to (-x,-1,y-2)[/tex]
Read more about transformation at:
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Related Questions
5. Find mTOS in the figure below.
Answers
Applying the definition of a linear pair, m∠TOS = 52°
Recall:
Linear pair are two angles on a straight line whose sum equals 180°.
Given:
m∠TOU = 128°m∠SOV = (4x + 8)°m∠TOU + m∠TOS = 180° (linear pair)
Substitute128° + m∠TOS = 180°
Subtract 128° from both sides of the equationm∠TOS = 180° - 128°
m∠TOS = 52°
Thus, applying the definition of linear pair, m∠TOS = 52°
Learn more about linear pair on:
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Factorise fully the following:
2x^2-8x
6x+9x^3
12x^3-4x^2
Answers
Step-by-step explanation:
1- 2x(x -4)
2- 3x(2-3x)
3- 4x²(3x-1)
given the line y=-2x - 1 and the point (4,4) find the equation of the line perpendicular to the given line. PLEASE! Helppp
Answers
Answer:
(-6,-5)
Step-by-step explanation:
y2-y1
x2-x1
subtract then you get the answer
Evaluate the expression shown below and write your answer as a mixed number in simplest form.
Answers
Answer:
-5 13/25
Step-by-step explanation:
This is what my calculator got me
What is the slope and y-Intercept of the equation 3(y – 2) + 6(x + 1) - 2 = 0?
A. Slope = -2, y-intercept = 2/3
B Slope = 2, y-intercept =2/3
C Slope = -2, y intercept = -2/3
D Slope = 2, y intercept= -2/3
E Slope = -2, y intercept = 3/2
Answers
Answer:
A. Slope = -2, y-intercept = 2/3Step-by-step explanation:
Convert the given equation into slope-intercept form:
3(y - 2) + 6(x + 1) - 2 = 03y - 6 + 6x + 6 - 2 = 03y + 6x - 2 = 03y = - 6x + 2y = - 2x + 2/3The slope is -2, the y-intercept is 2/3
Correct choice is A
⇒ 3(y - 2) + 6(x + 1) - 2 = 0
⇒ 3y - 6 + 6x + 6 - 2 = 0
⇒ 3y = -6x + 2
⇒ y = (-6x + 2)/3
⇒ y = -2x + ⅔
FINAL ANSWER :Slope = -2
Y - intercept = +⅔
Answer :Option (a) is the correct answer .
3. If you are calculating the acceleration of an object, and it has a speed of 30 km/hr
and the time is measure in hours what are the units for acceleration?
I
Answers
We want to see which units we should use for acceleration in the given scenario, the units that we must use are km/h², or kilometer per hour squared.
So we know that acceleration is the rate of change of the velocity (in the same way that velocity is the rate of change in position).
Note that position is represented only with distance units, like km.
And to get a velocity you use the units km/h (that tell you how many kilometers your position changes in one hour).
Similarly, the rate of change of the velocity will be (velocity)/time.
(km/h)/h = km/h²
Which is kilometers per hour squared.
If you want to learn more about acceleration, you can read:
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Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3% of his total sales in dollars, X, which can be represented by g(x) = 185 +0.03x. Jim is paid $275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) = 275 +0.025%. Determine the value of x, in dollars, that will make their weekly pay the same.
Answers
Answer:
$18,000.
Step-by-step explanation:
When their weekly pay is the same:
185 + 0.03x = 275 + 0.025x
0.03x - 0.025x = 275 - 185
0.005x = 90
x =90/0.005
x = 18,000
why do you need to find the number that is halfway between 1 and 1 1/2
Answers
Answer:
Lets just say we are finding the halfway point is very needful because; it means that we can find the amount of flour used for 1 while egg.
We are told there is a need to find the Number that is halfway between 1 and 1½.
Step-by-step explanation:
Rafael writes an expression to represent “a number, n, decreased by thirty-one.” Then he evaluates that expression if n = 29. Which statements are true about the expression and its evaluation? Check all that apply.
The correct expression is 31 minus n.
This is a subtraction expression.
This is an addition expression.
To evaluate, substitute 29 for the variable in the expression.
To evaluate, substitute 31 for the variable in the equation.
To evaluate the expression, add 31 to 29.
The correct expression is n minus 31.
To evaluate the expression, subtract 31 from 29.
Answers
Answer:
The correct expression that can be represented by n decreased by thirty-one is n - 31
let
The unknown number = n
n decreased by thirty-one
= n - 31
If n = 29
n - 31
= 29 - 31
= -2
The correct expression is 31-n.
False
This is a subtraction expression.
True
This is an addition expression.
False
To evaluate, substitute 29 for the variable in the expression
True
To evaluate, substitute 31 for the variable in the equation.
False
To evaluate the expression, add 31 to 29.
False
The correct expression is n - 31
True
To evaluate the expression, subtract 31 from 29.
True
Step-by-step explanation:
the answer is a b e g f hop this helps u
Solve for x please help me ****
Answers
Answer:
x =10
Step-by-step explanation:
In a parallelogram, opposite sides are congruent
QT = RS
2x - 10 = x
Add 10 to both sides
2x = x + 10
subtract 'x' from both sides
2x -x = 10
x = 10
Graph x <3
Please help me
Answers
Answer:
Step-by-step explanation:
my Christmas present to you
Answers
Answer:
yay thx
Step-by-step explanation:
merry xmas
A diver descends 3.2m in 5min. what was his average rate of descent in metres per minute?
Answers
Divide distance by time:
3.2 meters / 5 minutes = 0.64
The descent was -0.64 meters per minute
Answer:
.64
Step-by-step explanation:
Whenever you see x per y that means that you're looking at a ratio, which can be expressed as a fraction.
It would look like 3.2/5
The rate of descent may not be consistent, but on average it's reflected by the ratio and so you can just cut 3.2 meters into five equal parts to see, on average, how far the diver descended every minute.
Parallelogram ABCD has vertex coordinates A(0, 1), B(1,3), (4,3), and D(3,1). It is translated 1 unit to the right and 3 units down and then rotated 180°clockwise around the origin. What are the coordinates of A?
Answers
Answer:
A'(-1, 2)
Step-by-step explanation:
Translation 1 right and 3 down is accomplished by the transformation ...
(x, y) ⇒ (x +1, y -3)
Rotation 180° is accomplished by ...
(x, y) ⇒ (-x, -y)
Then the composition of transformations gives ...
(x, y) ⇒ (-x -1, -y+3)
The transformed coordinates of A(0, 1) are ...
A(0, 1) ⇒ A'(-0 -1, -1 +3) = A'(-1, 2)
The average rate of population decline between 2004 and 2014 is 1.45 thousand deer per year. If the population continued to decline at this rate, in which year would the population have reached 225 thousand deer? Explain your reasoning.
Answers
Answer:
in 155 years it would reach 225 thousand deer
Step-by-step explanation:
Please answer this ASAP
Solve for y.
30y=20y+60
A: y= -6
B: y= 6
C: y= 1.2
D: y= -1.2
Answers
Thirty times 6 equals to 20 times 6 plus 60
PLEASE HELP.
A group of bacteria has a population of 100,000. The growth rate is 20%. How much bacteria will there be in 10 years? Use the exponential formula.
Answers
Answer:
200,000 i don't know apologies if it's wrong
Step-by-step explanation:
100,000*.20*10
200,000*10
200,000
Place the fraction 1/2 on the number line.
Answers
Answer:
in the middle
Step-by-step explanation:
I did this before
is y in y + 2z + 45 + 5x a constant?
Answers
Answer:
See below
Step-by-step explanation:
No, a constant is a number without a variable ( variables are represented with a letter )
y is a variable as it is a letter.
The constant in y + 2z + 45 + 5x would be 45 as it has no variable.
[tex]41 \times 28 - 36 \div 32 + 17 \times 21 - 18 = [/tex]
answere please
Answers
Answer:
The answer is 1485.875.
Step-by-step explanation:
[tex]\large{\tt{\underline{\underline{\pink{SOLUTION:}}}}}[/tex]
To solve the above equation we will follow the BODMAS rule.
[tex]\blue\star[/tex] BODMAS is an order of mathematic operations.[tex]\blue\star[/tex] BODMAS rule is to be followed while solving expressions in mathematics.It stands for :
[tex]\purple\star[/tex] B = bracket[tex]\purple\star[/tex] O = order of power[tex]\purple\star[/tex] D = division[tex]\purple\star[/tex] M = multiplication[tex]\purple\star[/tex] A = addition[tex]\purple\star[/tex] S = subtractionSolving this question by bodmas rule :
[tex]\begin{gathered}\quad{\sf{ = 41 \times 28 - 36 \div 32 + 17 \times 21 - 18}}\\\\\quad{\sf{ = 41 \times 28 - \dfrac{36}{32} + 17 \times 21 - 18}}\\\\\quad{\sf{ = 41 \times 28 - 1.125+ 17 \times 21 - 18}}\\\\\quad{\sf{ = 1148 - 1.125+ 357 - 18}}\\\\\quad{\sf{ = (1148+ 357) - (1.125 + 18)}}\\\\\quad{\sf{ = (1505) - (19.125)}}\\\\\quad{\sf{ = 1505- 19.125}}\\\\\quad{\sf{ = 1485.875}}\end{gathered}[/tex]
Hence, the answer is 1485.875.
[tex]\rule{300}{2.5}[/tex]
please i need help asap
Answers
Answer: d. Shift units up
Step-by-step explanation:
f(x) = 3^x + 2 means that it must go up by two units.
4/9 7/21 change to percent
Answers
Answer:
Hi there, your answers here are 44% and 33%.
To convert 4/9 to a percent, first we can write it as a decimal - 0.44444444444. To get this decimal, we divide 4 by 9. Then, we multiply this decimal by 100 to get 44.4444444444, or roughly 44%.
To convert 7/21 to a percent, first we can write it as a decimal - 0.33333333333. To get this decimal, we divide 7 by 21. Then, we multiply this decimal by 100 to get 33.3333333333, or roughly 33%.
16. (-4, -3), (-2, 2)
Answers
Answer:
16. 5/2
Step-by-step explanation:
Rise/run
2- (-3)=5
-2- (-4)=2
rise/run= 5/2 (Five over two)
One triangle weighs how much
Answers
Answer:
13
Step-by-step explanation:
ANSWER FAST 20 POINTS
Answers
Answer: A
Step-by-step explanation:
The answer is A because, if you look at the line on the graph it’s a dotted line.
This means it’s either a < or >. Next you can see the y-intercept is -1, which actually doesn’t help you because all the answers hace the same y-intercept but still good to know. Finally if you use rise or run you can find the slope to be -2x.
Just did the math and the person who answered first is I believe is correct.
A cannonball shot from a cannon has projectile motion.
true or false
need a answer please
Answers
The ratio of boys to girls in a group is 2:1. If there are 26 more boys than girls, work out how many boys there are.
Answers
Answer : 52 boys : 26 girls
Step - by - step explanation :
Now we can guess, whatever number we put HAS to be 26 more boys than girls and it has to follow the 2 boys : 1 girl ratio . . .
26 boys : 13 girls <-- this follows the 2:1 ratio but is NOT 26 more boys than girls
52 boys : 26 girls <-- this follows the 2:1 ratio and has 26 more boys than girls ! :D
please answer thisss
Answers
Answer:
ask assistance from someone close to you,it's a practical question.
Plzzzz help meeeee plzzzzzzzz
Answers
Answer:
$0.70
Step-by-step explanation:
70cents is the same as 70/100. so, this would be 0.70.
Hope this helps!
For f(x)=−2x+4, find f(x) when x=−3.
Answers
x = –3
Substitute -3 into f(x) = –2x +4.
f(-3) = –2(–3) + 4
f(-3) = 6 + 4
f(-3) = 10