Answers
The rigid transformation of the pre-image ΔABC, that produces the image ΔDEF is option E as follows;
E. [tex]R_{(90^{\circ},\,(0,\, 0))}[/tex]
What is a rigid transformation?A rigid transformation is one in which the distances between each pair of points on the pre-image is preserved on the image, such that the pre-image and the image have the same size.
The coordinates of the vertices of ΔABC are;
A(-3, -3), B(-1, -4), C(-3, -4)
The coordinates of the vertices of ΔDEF are; D(-3, 3), E(-4, 1), F(-4, 3)
The formula for the rotation of a point (x, y) 90° clockwise about the origin is presented as follows;
Pre-image point [tex]{}[/tex] (Rotation 90° clockwise) Image point after rotation
(x, y) [tex]{}[/tex] ⇒ [tex]{}[/tex] (-y, x)
The points in the image ΔDEF of pre-image triangle ΔABC which corresponds to points on ΔABC are;
Vertex A in triangle ΔABC corresponds to vertex D on triangle ΔDEF
Vertex B in triangle ΔABC corresponds to vertex E on triangle ΔDEF
Vertex C in triangle ΔABC corresponds to vertex F on triangle ΔDEF
The transformation of (x, y) ⇒ (-y, x), (which is the transformation of a 90° clockwise rotation about the origin), on the vertices of ΔABC are;
A(-3, -3) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] D(-3, 3)
B(-1, -4) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] D(-4, 1)
C(-3, -4) [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex] F(-4, 3)
Therefore, the triangle ΔDEF can be obtained from the triangle ΔABC by a rotation of 90° clockwise about the origin.
The correct option is; E [tex]R_{(90^{\circ}, (0, \,0))}[/tex]
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Related Questions
During a one-month promotional campaign, Fran's Flix
gave either a free DVD rental or a
12-serving box of microwave popcorn to
new members. It cost the store $1 for each free
rental and $2 for each box of popcorn. In all, 59 new members were signed up and the
store's cost for the incentives was $103. How many of each incentive were given away?
Answers
If the store's cost for the incentives was $103.The amount of each incentive that were given away is: Free Rental 5, Box of popcorn 54.
How to find the incentive given?Let Free Rental = r
Let Box of popcorn = p
Total incentives:
r+p=59
r= 59-p Equation 1
r×1+p×2=103
r+2p=103 Equation 2
Put the value of r in (eq 2) from (eq 1)
r+2p=103 (eq 2)
59-p+2p=103
59+p=103
p=103-59
p=44
Put the value of p in (eq 1)
r=49-p...........(1)
r=49-44
r= 5
Free Rental = 5
Box of popcorn = 59 -5
Box of popcorn = 54
Therefore 5 and 54 incentive were given.
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Write your answer as a fraction in simplest form.
Answers
Answer:
17/10 (1.7)
Hope this helps!
Need help with this please
Answers
The value of 2[tex]\sqrt{12xy^{2} }[/tex] is 4y[tex]\sqrt{3x}[/tex].
According to the question,
We have the following expression:
[tex]2\sqrt{12xy^{2} }[/tex]
Now, we know that the square root of [tex]y^{2}[/tex] is y.
And the square root of 12 is [tex]2\sqrt{3}[/tex].
(More to know: we have the perfect square root of numbers. For example, the perfect square root of 36 is 6 and the perfect square root of 100 is 10. In the same way, there are perfect cube roots of numbers. For example, the perfect square root of 27 is 3.)
So, by putting the values of these terms in the square root, we have the following expression:
2*y*2[tex]\sqrt{3x}[/tex]
4y[tex]\sqrt{3x}[/tex]
Hence, the value of the given expression after solution is 4y[tex]\sqrt{3x}[/tex].
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the reflection of the point (8,0) across the x-axis is__
Answers
The reflection of the point (8,0) across the x-axis is (8, 0)
How to determine the image of the reflection?From the question, the point is given as:
Point = (8, 0)
Rewrite this point as
(x, y) = (8, 0)
The transformation is given as
Reflection across the x-axis
Mathematically, we have
(x, y) = (x, -y)
So,we have
Image = (8, 0)
Hence, the image of the reflection is (8, 0)
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Line v has an equation of y = -2x + 5. Perpendicular to line v is line w, which passes through
the point (6, -5). What is the equation of line w?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
Answer:
Line W's equation is y= 1/2x - 8
Step-by-step explanation:
lara writes the expression 1.5x 2.75y 3. maria writes the expression 3 1.5x 2.75y. which property can be used to prove the two expressions are equivalent?
Answers
The correct property is used to prove the two expressions are equivalent is;
''Commutative property''
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Lara writes the expression 1.5x + 2.75y + 3.
And, Maria writes the expression 3 + 1.5x + 2.75y.
Now,
Since, The commutative property states that;
a + b = b + a
So, Clearly, Here the commutative property used to prove the two expressions are equivalent, as;
⇒ 1.5x + 2.75y + 3 = 3 + 1.5x + 2.75y.
Thu, The correct property is used to prove the two expressions are equivalent is;
''Commutative property''
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answer the question is decreased or increased by what number
Answers
Answer:
Step-by-step explanation:
decrease by 10
Answer:
Step-by-step explanation:
increased by thirty tickets
use the arithmetic sequence 12,15,18,21...
what is the equation of the nth term of the sequence
Answers
Answer:
3n+9
Step-by-step explanation:
find the slope (15,8),(-17,9)
Answers
Please give brainly if correct :)
Answer: -1/32
Step-by-step explanation:
Use the slope formula: y2-y1/x2-x1
Apply that:
9-8/-17-15 = 1/-32 = -1/32
A biker cycles 9 miles 2/3 of an hour. The distance here varies directly with time. What is the constant of variation (It is the biker's rate.)
Answers
The constant of variation of the distance is 13.5 miles
How to determine the constant of variation?From the question, we have the following parameters that can be used in our solution:
Distance cycled = 9 miles
Number of hours = 2/3 of an hour
From the above parameter, we can calculate the constant of variation
The constant of variation is calculated as
Constant of variation = Distance cycled/Number of hours
Substitute the known values in the above equation
So, we have the following equation
Constant of variation = 9/(2/3)
Evaluate the quotient
Constant of variation = 13.5
Hence, the constant of variation is 13.5 miles per hour
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which expression shows how to write(3^4)^2 as a product?
Answers
(3⁴)² can be written as 3² × 3⁶.
What is Exponentiation?Exponentiation is the operation of doing multiplication repeatedly and it is written in the form aᵇ.
We have to write the given expression (3⁴)² as product of two numbers.
Now, (3⁴)² = 3⁸
We have the property of exponentiation,
aⁿ × aˣ = a^(n + x)
Thus 3⁸ = 3^(2+6) = 3² × 3⁶
Hence, (3⁴)² can be expressed as 3² × 3⁶.
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Find the midpoint of the segment with the
following endpoints.
(8, 2) and (1, 10)
Answers
Answer:
(4.5 , 6)
Step-by-step explanation:
Finding the midpoints of segment when endpoints are given:
To find the midpoints, add the x-coordinates and divide by 2 and add the y-coordinates and divide by 2.
(8 , 2) ⇒ x₁ = 8 ; y₁ = 2
(1 , 10) ⇒ x₂ = 1 ; y₂ = 10
[tex]\sf Mipoint\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\sf = \left(\dfrac{8+1}{2},\dfrac{2+10}{2}\right)\\\\\\=\left(\dfrac{9}{2},\dfrac{12}{2}\right)\\\\\\=(4.5,6)[/tex]
OA. 20
B.O
345WN-OX
O C. -10
D. 10
0 -1
-2
-5
-10
-17
-26
-37
1
What is the average rate of change for this quadratic function for the interval
from x = 4 to x = 6?
2
6
Answers
Answer:
C. -10
Step-by-step explanation:
Using the average rate of change formula,
[tex]\frac{-37-(-17)}{6-4}=-10[/tex]
Visitors to the amusement park must be at least 54 inches tall to ride the roller coaster. How tall might a visitor riding the roller coaster be?
Answers
Answer:
Step-by-step explanation:
The visitor might be exactly 54 inches or above 54 inches.
Find the slope and the y-intercept of the line.
3x-2y=-6
Write your answers in simplest form.
slope:
3
y-intercept: -6
2
X
08
Undefined
Ś
Answers
Step-by-step explanation:
convert equation to y = mx+c:
3x-2y= - 6
3x+6=2y
y=3/2x+6/2
y=3/2x+3
gradient/slope=3/2
y intercept = 3
Please mark as brainliest :))))0
Answer:
Step-by-step explanation:
y = mx + b , where "m" is a slope and "b" is a y-intercept
~~~~~~~~~~~~~~
3x - 2y = - 6
3x - 3x - 2y = - 3x - 6
- 2y = - 3x - 6
[tex]\frac{-2}{-2}[/tex] y = [tex]\frac{-3}{-2}[/tex] x + [tex]\frac{-6}{-2}[/tex]
y = [tex]\frac{3}{2}[/tex] x + 3
Slope: [tex]\frac{3}{2}[/tex]
y-intercept: 3
J.D. opened a savings account with $425. After
2 years, the total interest he earned was $10.20.
What was the annual interest rate?
Answers
The annual interest rate is 1.2%
The principal amount = $425
The total interest her earned = $10.20
The final amount = 425 + 10.20
= $435.2
Time period = 2 years
The simple interest
A = P(1 + rt)
Where A is the final amount
P is principal amount
r is the interest rate
t is the time period
Substitute the values in the equation
435.2 = 425(1 + r×2)
1 + 2r = 435.2 / 425
Divide the terms
1 + 2r = 1.024
2r = 1.024 - 1
2r = 0.024
r = 0.024/2
Divide the terms
r = 0.012
Then the percentage will be
r = 1.2%
Hence, the annual interest rate is 1.2%
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Use the diagram below
Answers
The measure of angle KJL from the given figure is 84°.
Given that, 3(m∠LJM)=2(m∠KJL) and m∠KJM=140°.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
Here, m∠KJM=m∠LJM+m∠KJL
Now, (m∠LJM)=2/3 (m∠KJL)
140°= 2/3 (m∠KJL) + m∠KJL
⇒ [2(m∠KJL)+3(m∠KJL)]/3 = 140°
⇒ 5m∠KJL=420°
⇒ m∠KJL=420°/5
⇒ m∠KJL=84°
Hence, the measure of angle KJL from the given figure is 84°.
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Draw a quadrilateral that has 2 separate pairs of equal length sides but is not a parallelogram.
Answers
A quadrilateral that has 2 separate pairs of equal length sides but is NOT a parallelogram is called a KITE.
What is a quadrilateral?
A quadrilateral is any polygon that has four sides and four vertices. They include;
Properties
Four sides (or edges)Four vertices (or corners), And internal angles that total 360 degrees make up a quadrilateral.What is a kite?
A quadrilateral is a polygon with four sides, commonly known as a kite. Four points on the plane must be "independent" in order for the kite to have four corners. As a result, none of the three are parallel to one another.
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Based on the graph, which of the following guarantees that an estimate using tangent line approximation will result in an overestimate? point of tangency near x = -2 point of tangency near x = 0 point of tangency near x = 2 point of tangency near x = 4
Answers
The value of x at which the tangent line approximation will result in an overestimate is given by:
Point of tangency near x = 0.
When does the tangent line approximation results in an underestimate and when does it results in an overestimate?The possible results for the tangent line approximation are given as follows:
Underestimate: tangent line is below the curve.Overestimate: tangent line is above the curve.The underestimate or underestimate depend on the second derivative of the function, as follows:
Second derivative positive: underestimate.Second derivative negative: overestimate.Hence, regarding the concavity, we have that the definitions are listed as follows:
Concave down: overestimate.Concave up: underestimate.On the graph given by the image at the end of the answer, the concave down point is given as follows:
x = 0.
Hence the correct option is:
Point of tangency near x = 0.
Missing InformationThe graph is given by the image at the end of the answer.
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What is true of any triangle created by points u, v, and any point on line r t other than s? it will be a right triangle. it will be an acute triangle. it will be an equilateral triangle. it will be an isosceles triangle.
Answers
For any triangle created by points u, v, and any point on the line r t other than s, it will be an isosceles triangle.
Isosceles triangle, in geometry, refers to a triangle that has at least two equal length sides. The isosceles triangle sometimes is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length. The triangle which has at least two sides of equal length includes the equilateral triangle as a special case. An isosceles triangle has two sides that are congruent to each other and the third side which is unequal to the other two sides is called the base of the isosceles triangle. The two angles opposite to the equal sides are congruent to each other. Hence, in the given situation, any triangle created by u, v, and any point on the line r t other than s, will be an isosceles triangle as the sides UR and UV will always be equal.
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a home-improvement store offers a new brand of lawn food that claims to reduce the number of weeds by 30% over a different brand of lawn food. to test the claim, a homeowner plans to use the new brand of lawn food on half of his lawn and the original brand on the other half. the homeowner will count the number of weeds that appear after a month on each half of the lawn. a neighbor explains that there may be confounding variables, such as shade, that might also explain the relationship. which statement best describes the effect of the confounding variables? because of confounding variables, the homeowner should only put the new lawn food on shady spots and the original brand on sunny spots. because shade is a primary cause of weed growth, the brand of lawn food used in shady or sunny spots will not affect the number of weeds. if the half of the lawn with the new lawn food shows fewer weeds after a month, this will prove the new lawn food is better at stopping weed growth. the parts of the lawn that receive the new lawn food may also get more shade than other parts of the lawn, and the shade might also cause fewer weeds.
Answers
Answer: D
Step-by-step explanation: The part of the lawn that receive the new lawn food may also get more shade than other parts of the lawn. And the shade might also cause fewer weeds
What is the slope of the line whose equation is
Oslope = 2
O slope = -9
O
slope = 0
Oslope = -1/2
y = 16?
Answers
Answer: slope = 0
Step-by-step explanation:
The equation of straight line can be expressed in the form y = mx + b, which is referred to as slope intercept form.
In this equation, m represents the slope of the line, y is the y-coordinate of an arbitrary point along the line and x is the x-coordinate of the same point, and b is the location where the line intercepts the y-axis of the graph.
if y = 16, then the slope of the line, m, must be 0.
y = mx + b
y = (0)x + b
y = b
In other words, the line described by the equation y = 16 is a horizontal line that passes through the y-axis at the point (0,16).
The surface area for a rectangular prism with a square base is given by the expression. 2s2+4sh, where side s is the side length of the square base and h is the height of the prism. What is the surface area in square feet of a rectangular prism with a square base, where s=4 feet and h=6 ?
Answers
Answer:
128 square feet
Step-by-step explanation:
2(4)^2 + 4 * 4 * 6 =
= 2 * 16 + 16 * 6 =
= 32 + 96 =
= 128 square feet
A cold water pipe can fill a swimming pool in 4 hrs, and a hot water pipe can fill it in 6 hrs. If cold water pipe is turned on and hot water pipe is turned on 3 hrs later, how long will it take for the pool to be filled?
Answers
Answer: 3 hours 36 minutes
Step-by-step explanation:
You can find out that the cold pipe fills up the pool by 1/4 every hour from the question. if you turn on the cold pipe for 3 hours, the pool would be filled 3/4 before you turn on the hot water. you also can find out that the hot pipe fills up the pool 1/6 every hour. so the next hour will continue to fill up the pool 5/12 until you turn off the water. you only need to fill up the pool 1/4 more so it will take a total of 3 hours and 36 minutes to fill up.
Simplify -4 (x + 1) + 6x write urr answer in factored form
Answers
x = 1
Step-by-step explanation:
[tex]{ \orange{ \tt{ - 4(x + 1) + 6x}}}[/tex]
Multiply -4 with (x+1) then the Eqⁿ becomes
[tex]{ \orange{ \tt{ - 4x - 4 + 6x}}}[/tex]
Step (1):- [tex]{ \red{ \sf{combine \: like \: terms}}}[/tex]
You can see the like terms i.e. -4x and 6x. Now, add this like terms.
[tex]{ \orange{ \tt{ - 4x + 6x - 4}}}[/tex]
[tex]{ = \orange{ \tt {2x - 4}}}[/tex]
Step (2):- [tex]{ \red{ \sf{ common \: factor}}}[/tex]
Take 2 as common in 2x-4 then,
[tex]{ \orange{ \tt{2(x - 2)}}}[/tex]
[tex]{ \orange{ \tt{2x - 2 = 0}}}[/tex]
[tex]{ \orange{ \tt{2x = 2}}}[/tex]
[tex]{ \blue{ \boxed{ \purple{ \sf{x = 1}}}}}[/tex]
helpppp................
Answers
Answer:
Step-by-step explanation:
Tips: All of the figures are prisms so always add prism to end.
2. Rectangular prism. Since it is a rectangle with the 3d dimensions added to it.
3. Hexagonal Prism. Since it is a hexagon with 3d dimensions added to it.
6. Triangular prism. Since it is a triangle with 3d dimensions added to it.
8. Also Triangular prism. Look above.
9. Rectangular prism. Since it is a rectangle with the 3d dimensions added to it.
10. Another Rectangular prism.Since it is a rectangle with the 3d dimensions added to it.
Ps. All the answers you created are correct!
T Mobile charges $20 for the 1st phone plan and $6 per line added. Jenny has at most $60 she can spend for family. Write an inequality to show how many lines she can have. a 20 + 6L ≤ 60 b 6 + 20L ‹ 60 c 20 + 6L > 60 d 6 + 20L ≥ 60
Answers
Answer:
A. 20 + 6L < 60
Step-by-step explanation:
It can't be B. or D. because 20L, not a thing in this problem. That leaves us with A. and C. being our only reasonable answers.
I chose A. because Jenny can't spend more than 60
Yuson spends $584 on equipment to start his own landscaping company. He charges $26 per hour. Write a linear equation in slope-intercept form to represent his profits, y, after working x hours.
Answers
The equation for profit in slope-intercept form is written as y = 26x - 584
Linear EquationA linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation is given as y = mx + c
m = slopec = y-interceptIn this problem, the constant or fixed value is the amount he spent on the equipment and the slope is the amount he charges per hour.
The equation of profit can be represented as y = 26x - 584
Where x = number of hours he worked.
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11. Write the equation of the line in point-slope form with a slope of -2
and passes through the point (2,-9). (YELLOW)
Answers
Joe is playing a game with a regular die. If the number that turns up is
even, he will gain 5 times the number that comes up. If it is odd, he will
lose 10 times the number that comes
up. He tosses a 3. Express the
results as an integer.
Answers
The required solution will be -30 which is expressed as an integer.
To represent this in a general context, we may utilize functions that are referred to in terms of the number tossed.
We know that if the number he gets is an even number, he will get 5 times the number.
As a result, the function for when the integer x is even is f(x) = 5x.
If the number is an odd number, he will lose 10 times the number.
As a result, the function for when the integer x is odd is f(x)=-10x.
Finally, Joe tosses a 3, which is an odd integer, hence the function we will represent is f(x) = - 10x.
⇒ f(3) = -10(3) = -30
Thus, the required solution will be -30 which is expressed as an integer.
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