Find the composition of
transformations that
map ABCD to EHGF.
Reflect over the y-axis,
then translate
(x-2, y+[ ? ]).
Answers
Answer:
[(x + 6), (y + 1)]
Step-by-step explanation:
Vertices of the quadrilateral ABCD are,
A → (-5, 2)
B → (-3, 4)
C → (-2, 4)
D → (-1, 2)
By reflecting the given quadrilateral ABCD across x-axis to form the image quadrilateral A'B'C'D',
Rule for the reflection of a point across x-axis is,
(x, y) → (x , -y)
Coordinates of the image point A' will be,
A(-5, 2) → A'(-5, -2)
From the picture attached, point E is obtained by translation of point A'.
Rule for the translation of a point by h units right and k units up,
A'(x+h, y+k) → E(x', y')
By this rule,
A'(-5 + h, -2 + k) → E(1, -1)
By comparing coordinates of A' and E,
-5 + h = 1
h = 6
-2 + k = -1
k = 1
That means
Rule for the translation will be,
[(x + 6), (y + 1)]
For the given graph, the translation rule is (x, y) ⇒ (x+(-4), y+(-4))
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which a graph is modified to give a variation of the proceeding graph.
The graphs can be translated or moved about the xy-plane
After point D is reflected across the y-axis, its coordinates are
D(-1, 2) ⇒ D'(1, 2)
This is the point that gets translated to F(-3, -2). The translation is
F -D' = (-3, -2) -(1, 2)
= (-3-1, -2-2)
= (-4, -4)
Then the translation rule is (x, y) ⇒ (x+(-4), y+(-4))
Hence, for the given graph, the translation rule is (x, y) ⇒ (x+(-4), y+(-4))
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Related Questions
Un terreno Forma rectangular mide X +4 de alto y de base X +10 indica la expresión algebraica que expresa el área del terreno
Answers
Answer:
X^2+14x +40
Step-by-step explanation:
La base es x+4 y la altura es x+10 multiplicas la base por la altura
if p(q) = q^2 4q- 12 then what is p(-1)
Answers
(1): "q2" was replaced by "q^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring q2-4q-12
The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .
-12 + 1 = -11
-6 + 2 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization
Equation at the end of step
1
:
(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : q+2 = 0
Subtract 2 from both sides of the equation :
q = -2
Solving a Single Variable Equation:
2.3 Solve : q-6 = 0
Add 6 to both sides of the equation :
q = 6
Supplement : Solving Quadratic Equation Directly
Solving q2-4q-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = q2-4q-12
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Aq2+Bq+C,the q -coordinate of the vertex is given by -B/(2A) . In our case the q coordinate is 2.0000
Plugging into the parabola formula 2.0000 for q we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 12.0
or y = -16.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
Vertex at {q,y} = { 2.00,-16.00}
q -Intercepts (Roots) :
Root 1 at {q,y} = {-2.00, 0.00}
Root 2 at {q,y} = { 6.00, 0.00}
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
B.
Step-by-step explanation:
You just remove 3 zeros from 10.
10 —> 1 —> 0.1 —> 0.01 :)
of the field of view to figure the estimated length of the
cell. If the number of cells is 50 and the diameter you are
observing is 5 millimeters in length, then one cell is 0.1
millimeter long. Measured in microns, the cell would be
1,000 microns in length.
please help me!
ty ty :)
Answers
Answer:
y-2 = -11 (x-5)
Step-by-step explanation:
2 is the y value of the point, 5 is the x value and -11 is the m value.
Slope point form: y-y1 = m(x-x1)
Hope that helps
HELP ME WITH THIS PLEASEEE !
Answers
Answer:
34 i think i got it really wrong but...
Step-by-step explanation:
Eva spent $11.61 downloading songs, and each song cost $1.29. Four students wrote and solved equations to find s, the number of songs that she downloaded. Which student wrote and solved the equation correctly?
Seba’s work:
1 dollar and 29 cents = 11 dollars and 61 cents. S = 10.
Ari’s work:
1 dollar and 29 cents = 11 dollars and 61 cents. S = 9.
Erick’s work:
StartFraction s Over 1 dollar and 29 cents EndFraction = 11 dollars and 61 cents. S = 14.98.
Daniel’s work:
StartFraction s Over 1 dollar and 29 cents EndFraction = 11 dollars and 61 cents. S = 9.
Answers
Answer:
1.29s = 11.61
s = 9
Step-by-step explanation:
1.29s = 11.61
s = 11.61/1.29
s = 9
Answer:
The correct answer is Ari's work
Step-by-step explanation:
right on edge
Welcome!^^
lesson 5 practice problems
Answers
Answer:
Step-by-step explanation:
ok ill help but can soke one help me too
Which values from the set negative 6, negative 4, negative 3, negative 1, zero, 2, satisfy this inequality?
Negative one half x, plus 3, is greater than or equal to 5.
Answers
Answer:
- 6
Step-by-step explanation:
- [tex]\frac{1}{2}[/tex] x + 3 ≥ 5 ( subtract 3 from both sides )
- [tex]\frac{1}{2}[/tex] x ≥ 2 ( multiply both sides by 2 to clear the fraction )
- x ≥ 4
Multiply both sides by - 1, reversing the symbol as a result of multiplying by a negative quantity.
x ≤ - 4
The only value from the set which satisfies the inequality is
x = - 6
I need these answers for a worksheet I have and I would appreciate it if someone would help me out.
Question 1. You can combine like terms to ________ an expression.
Question 2. All ______ are like terms and can be combined.
Question 3. Terms with the same _____ are considered like terms.
Answer choices:
Constants
variables
simplify
Answers
All CONSTANTS are like terms and can be combined.
Terms with the same VARIABLE are considered like terms
pls help pls no links?
Answers
[tex]\dfrac{3^{15}}{3^3} = 3^{15 -3} = 3^{12}[/tex]
will mark brainliest (2 possible answers pls) ( NO LINKS OR ANSWERS WITH NO EXPLANATION)
Answers
Answer:
P = 22.22
Step-by-step explanation:
It takes 5 minutes to fill an empty aquarium to a depth of
5/8
meters. What is the unit rate in minutes per meter?
Answers
Answer:
1/8 meters per minute
Step-by-step explanation:
5/8 ÷ 5
I hope this helps!!
Which expression can be used to find the surface area of the following triangular prism?
5
5
2.
11
8.
Answers
Answer:
214.
Step-by-step explanation:
To get Surface area take
(cross section area) × 2 +(perimeter of crossection area × length)
the cross section area is a triangle
so area of a triangle =1/2 base times height
1/2×8×2=8
let's get perimeter of cross section
the cross section is still at triangle so let's find its perimeter.
5+5+8=18
18×length of which is 11
18×11=198
and 188 + 16=214. that's the answer
maybe you can get a expression from the work that I've just done cuz I can't see the answers clearly in the picture you have taken.if you don't mind just send the picture back then I'll get the answer.
No files or links please!
graph y= -4/3 x+2 using the slope and y-intercept
slope: 3
y-intercept: (0,-2)
Answers
Answer as a each as an algebraic expression.
Answers
Answer:
is saying the half of q is 9 so you have to find out the value of q and when you find out the value for example x=18 the half of 18 is 9 I don't know if you undertand my explication
Step-by-step explanation:
18 the half of 18 is 9 because 9+9=18
Whats the answer to these questions?
Answers
Answer:
Answer is in the attached file.
Solve for x in the equation X2 - 12%+ 36 = 90.
X
X = 6+3/10
Ox=6+2/7
<
= 12+ 3922
X= 12+3/10
X=
Answers
Answer:
x = 6 ± 3√
Step-by-step explanation:
Step-by-step explanation:Since this is an unfactorable expression, apply the Quadratic Formula, -b ± √b² - 4ac\2a,
The solutions to the equation are:
x = 6 + 3 √(10) or x = 6 - 3 √(10)
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
x² - 12x + 36 = 90
Subtracting 90 from both sides.
x² - 12x - 54 = 0
To solve for x, we can use the quadratic formula.
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation
ax² + bx + c = 0.
In this case, a = 1, b = -12, and c = -54.
Substituting these values into the formula.
x = (-(-12) ± √((-12)² - 4(1)(-54))) / 2(1)
x = (12 ± √(144 + 216)) / 2
x = (12 ± √(360)) / 2
x = 6 ± 3 √(10)
Therefore,
The solutions to the equation are:
x = 6 + 3 √(10) or x = 6 - 3 √(10)
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you use a garden hose to fill a wading pool if the water level rise 12 centimeters every 5 minutes and you record the data point of (15,y) what is the value of y
Answers
so 5 x 12 = 60
Please help :)
M is the midpoint of segment AT.
Solve for X and AM
Answers
So AM = TM
<=> 5x = 3x + 4 <=> 5x - 3x = 4
<=> 2x = 4 <=> x = 2
The answer: x = 2
Ok done. Thank to me :>
Help me find three different ratios that are equivalent to 3:11!! I need a explanation too!
Answers
3 * 2 and 11 * 2 which would be 6:22 and is still equal to the ratio 3:11. Your explanation can be the when divided by 2 or the number you multiplied by, you would get the original ratio
Examples:
6:22
9:33
12:44
An equation of a line is y = 3x -7. What would the SLOPE of a line parallel to this equation be?
Answers
Answer:
3
Step-by-step explanation:
If two lines are parallel then their slope is the same
y=mx+b
m= slope
b= y-intercept
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY
Answers
Answer:
See image
Step-by-step explanation:
Use Pythagorean Theorem
a^2 + b^2 = c^2
See image
Manolo and Annalisa make handbags. Manolo made 16 handbags the first day and 12 each day after
that. Annalisa made 8 the first day and 12 each day after that.
Answers
Based on the amount being made by Manolo and Annalisa every day, the amount both made on the various days were:
Annalisa made 8 bags on Day 1Manolo had made 40 bags by Day 3Annalisa is said to have made 8 bags on the first day so this is the number of bags that should be put in the table for having been made in the first day.
Manolo made 16 bags on the first day and then 12 bags each day after that. The total number of bags made by the third day by Manolo would be:
= 16 + 12 + 12
= 40 bags
In conclusion, Annalisa made 8 bags on Day 1 and Manolo had made 40 bags on the 3rd day.
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Plz help me thx
Simplify:
Answers
Answer:
4
Step-by-step explanation:
note that [tex]\sqrt{x^2}[/tex] = x , then
[tex]\sqrt{(2-\sqrt{5})^2 }[/tex] + [tex]\sqrt{(2+\sqrt{5})^2 }[/tex]
= 2 - [tex]\sqrt{5}[/tex] + 2 + [tex]\sqrt{5}[/tex] ← collect like terms
= 4
Mr Jibril wants to fill a rectangular container measuring 8 m by 5 m by 2 m completely with gravel. Gravel costs $26 per cubic metre. He has only $1500. How much more money will Mr Jibril need to pay for the gravel?
Answers
9-(1-3y)=4+y-(3-y), find y
Answers
Answer:
-7 is the answer!! :) hope this helps
Graph y=2x+5 on the plane
Answers
Answer:
Incorrect
Step-by-step explanation:
for your slope go down two to the right one
What is the value of q
Answers
Answer:
Triangles QST and RST are similar. Therefore, the following is true:
q s
--- = ---- This results in 10q=rs.
r 10
Also, since RST is a right triangle, 4^2 + s^2 = q^2.
Since QST is also a right triangle, s^2 + 10^2 = r^2.
4 s
Also: ---- = ----- which leads to s^2 = 40
s 10
Because of this, 4^2 + s^2 = q^2 becomes 16 + 40 = 56 = q^2
Then q = sqrt(56) = sqrt(4)*sqrt(14) = 2*sqrt(14) (answer)
HELP!!!
42 is the product of 6 and y
Answers
Answer:
7
Step-by-step explanation:
Divide the 42 by 6 to get your answer. 42/6=7
This also works in reverse. 6*7=42
The answer: 42 is the product of 6 and y=7
Ok done. Thank to me :>
Ok here’s another question
Answers
Answer:
20 necklaces
Step-by-step explanation:
If Elizebeth is starting off w/10 necklaces we can find on the graph that $10 buys an additional 10 necklaces. Now knowing that information we can add 10 necklaces to our original necklaces and get 20 necklaces. We can also find that our unit rate of change is 10 dollars : 10 necklaces or 1 dollar : 1 necklace. Knowing this can help us solve future problems like how many necklaces can Elizebeth get for x dollars.