Rectangle WXYZ with vertices W(-7,2), X(5,2), Y(5,-6), and Z(-7,-6) a. dilation with scale factor of 1/4 using (-7,6) as the center b. reflection in the y-axis
Answers
The location of the vertices of the image of the rectangle WXYZ, following the dilation and reflection transformations are;
a. (-7, 5), (-4, 5), (-4, 3), (-7, 3)
b. (7, 5), (4, 5), (4, 3), (7, 3)
What is a dilation transformation?A dilation transformation involves the scaling of the dimensions of of the pre-image to get the dimensions of the image.
The points on the rectangle WXYZ are;
W(-7, 2), X(5, 2), Y(5, -6), and Z(-7, -6)
The scale factor of the dilation = 1/4
The center of dilation = (-7, 6)
The steps to perform the calculation of the dilation are as follows;
Translate the center of dilation, (x, y) and the points on the vertices of the rectangle to the origin using the rule, (-x, -y)Dilate the image of the rectangle, following the translation, using the scale factor and the origin as the center of dilationTranslate the image obtained following the dilation to the original location, using the rule (x, y), to get the image of the dilation about a center (x, y)The coordinates of the rectangle following a translation rule of (7, -6) are;
W(-7, 2) ⇒ T₍₇, ₋₆₎ ⇒ W'(0, -4)
X(5, 2) ⇒ T₍₇, ₋₆₎ ⇒ X'(12, -4)
Y(5, -6) ⇒ T₍₇, ₋₆₎ ⇒ Y'(12, -12)
Z(-7, -6) ⇒ T₍₇, ₋₆₎ ⇒ Z'(0, -12)
Dilating the image W'X'Y'Z' by a scale factor of 1/4, centered at the origin, we get;
W'(0, -4) ⇒ [tex]D_{1/4}[/tex] ⇒ W''(0, -1)
X'(12, -4), ⇒ [tex]D_{1/4}[/tex] ⇒ X''(3, -1)
Y'(12, -12) ⇒ [tex]D_{1/4}[/tex] ⇒ Y''(3. -3)
Z'(0, -12) ⇒ [tex]D_{1/4}[/tex] ⇒ Z''(0, -3)
Translating the above points, using the rule, (-7, 6), we get;
W''(0, -1) ⇒ T₍₋₇, ₆₎ ⇒ W'''(-7, 5)
X''(3, -1) ⇒ T₍₋₇, ₆₎ ⇒ X'''(-4, 5)
Y''(3. -3) ⇒ T₍₋₇, ₆₎ ⇒ Y'''(-4, 3)
Z''(0, -3) ⇒ T₍₋₇, ₆₎ ⇒ Z'''(-7, 3)
The coordinates of the rectangle WXYZ following the dilation by a scale factor of 1/4 with the center of dilation at (-7, 6) are;
(-7, 5), (-4, 5), (-4, 3), and (-7, 3)b. The image following the reflection of a point (x, y), over the y-axis is (-x, y)
The coordinates of the image after a reflection across the y-axis are;
W'''(-7, 5) ⇒ [tex]R_{y-axis}[/tex] ⇒ W''''(7, 5) = R(7, 5)
X'''(-4, 5) ⇒ [tex]R_{y-axis}[/tex] ⇒ X''''(4, 5) = S(4, 5)
Y'''(-4, 3) ⇒ [tex]R_{y-axis}[/tex] ⇒ Y''''(4, 3) = T(4, 3)
Z'''(-7, 3)⇒ [tex]R_{y-axis}[/tex] ⇒ Z''''(7, 3) = U(7, 3)
The vertices of the image following the dilation by a scale factor of 1/4, and a reflection across the y-axis are; (7, 5), (4, 5), (4, 3), and (7, 3)Learn more on dilation transformation here: https://brainly.com/question/16690760
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Related Questions
A rectangle is 10.8 meters wide and has an area of 181.44 square meters. What is the length of the rectangle?
Answers
The length of the above given rectangle is 16.8m.
Explain the shape rectangle?An enclosed 2-D form called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposing sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.Rectangle's surface area. A = l × b. Once the length and breadth of a rectangle are known, its area may be computed. The area of the rectangle may be calculated as a square unit by multiplying the length and width.Given data :
area of square = 181.44 m
rectangle wide = 10.8 m
Length of the rectangle = ?
Length of the rectangle = 10.8 x _____ = 181.44
= 181.44 / 10.8 = 16.8m
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ignore my dirty computer again please lol, last one help please :))
Answers
Answer: -2
Step-by-step explanation:
Let the number be w
3*(w+5) = 9
Expanding, we get 3w + 15 = 9
3w = 9 - 15 = -6
w = -6/3 = -2
Please help!! I’ll give brianliest!
Answers
Answer:
4/19
Step-by-step explanation:
Jar a: 3/8
Jar b: 1/11
8+11 = 19
3+1= 4
4/19
Choose the most accurate relationship between ∠1 and ∠2. A horizontal line is shown with a ray extending upward from a point near the center of the line. A second line runs diagonally from the lower left to the upper right, intersecting the line at the point of origin of the upward pointing ray. The angle formed by the two lines below the horizontal line on the left is labeled 1. The angle formed just left of the horizontal line and upward pointing ray is labeled 2. The angle just right of the upward ray formed by the upward ray and diagonal line is labeled 4. The angle formed just right of the diagonal line and above the horizontal line is labeled 5. The angle formed below the horizontal line and just right of the diagonal line is labeled 6. A. adjacent B. linear pair C. supplementary D. vertical
Answers
The relation between angles ∠1 and ∠2 will be the adjacent angles. Then the correct option is A.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The property of angles are as follows:
Two angles are said to be supplementary angles if their sum is 180 degrees.When two lines intersect, then their opposite angles are equal.If the total of two angles is 180 degrees, they are said to be linear angles.In math, two points are nearby in the event that they have a typical side and a typical vertex.The relation between angles ∠1 and ∠2 will be the adjacent angles. Then the correct option is A.
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The complete question is attached below.
Which box-and-whisker plot represents this data: 6, 7, 9, 9, 20, 22, 26, 28, 29, 30?
Answers
Median = 22, Lower Quartile = 9, Upper Quartile = 28,
Interquartile Range = 19, Lower Whisker = 6 , Upper Whisker = 30
Step 1: First, arrange the data in numerical order:
6, 7, 9, 9, 20, 22, 26, 28, 29, 30
Step 2: Calculate the median (middle value):
Median = 22
Step 3: Calculate the lower quartile (Q1):
Q1 = 9
Step 4: Calculate the upper quartile (Q3):
Q3 = 28
Step 5: Calculate the lower whisker (lowest value):
Lower whisker = 6
Step 6: Calculate the upper whisker (highest value):
Upper whisker = 30
Step 7: Plot the data points:
6, 7, 9, 9, 20, 22, 26, 28, 29, 30
Step 8: Draw the boxplot:
The boxplot should have a box with the lower whisker at 6, the lower quartile (Q1) at 9, the median at 22, the upper quartile (Q3) at 28, and the upper whisker at 30.
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Which inequality is true?
A number line going from negative 3 to positive 3 in increments of 1.
One-fourth less-than negative 1 and StartFraction 2 Over 4 EndFraction
Negative 2 and three-fourths less-than negative 1 and one-half
Negative 2 and one-fourth greater-than negative 1 and one-fourth
Negative three-fourths greater-than 1 and three-fourths
Answers
The inequality is true.
Inequality is one that leads to unequal or biased outcomes and is an unjust distribution of resources and opportunities. It leads to an increased resolution of the opportunities and resources. Has a socio and political-economic structure.
Thus the answer is 3 to +3 in increments of 1 5/6 to -1/3 21/3 >21/6.
The inequality makes the comparisons between no. or the expressions in the terms of greater or less depending on how numbers are arranged on the number line.
A number line that is going from the negative 3 to positive 3 and is in increasing order.
The second one shows the positive value of 5/6 towards decreasing and a negative value of the -1/3 hence is also correct The third one depicts the 2 and one-third greater than 2 and one half.
Hence the option 1, 2, and 3 are true.
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(complete solution) can someone help me here please thank you everyone! lovelots
Answers
Hope it helps.
If you have any query, feel free to ask.
What is the size of an exterior and interior angle of a regular 15 sided polygon?
Answers
The size of an exterior and interior angle of a regular 15-sided polygon is 24° and 156° respectively.
To find the size of each interior angle of a regular polygon you need to find the sum of the interior angles first.
If the number of sides is n, then the sum of the interior angles is:
S = 180 (n-2)
This formula derives from the fact that if you draw diagonals from one vertex in the polygon, the number of triangles formed will be 2 less than the number of sides. Each triangle has 180°.
This form of the formula derives from drawing triangles in the polygon by drawing lines from a central point to each vertex. In this way the number of triangles is the same as the number of sides, but the angles at the centre are not required, so 360° is subtracted.
Once you have the sum of all the interior angles you divide by the number of sides to find the size of each interior angle.
Each interior angle of a regular polygon with n sides:
θ = 180°(n-2)/n
Put n = 15
∴ θ = 180°(15-2)/15 = 156°
Each exterior angle of a regular polygon with n sides:
β = 180° - θ
Put θ = 156°
∴ β = 180° - 156° = 24°
Thus, the size of an exterior and interior angle of a regular 15-sided polygon is 24° and 156° respectively.
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y[tex]y\leq -\frac{1}{3} x+3 \\y\geq 3x+2[/tex]
Answers
The common region between both inequalities shows the possible solution sets.
What is inequality? Differentiate between equation and expression? inequality : An inequality is used to make unequal comparisons between two expressions or numbers.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the system of inequality as -
y ≤ (- 1/3)x + 3
y ≥ 3x + 2
Refer to the graph of the inequalities attached. The common region to both the inequalities represent the possible solution sets.
Therefore, the common region between both inequalities shows the possible solution sets.
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Shamus owes his parents $162. he pays them 60% of the $45 he earns as a soccer referee each week. how many weeks will it take Shamus to pay back all of the money he owes his parents?
HELP ITS DUE TOMORROW
Answers
A race car drove around a circular track that was 0.3 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.
504.46 feet
252.23 feet
160.66 feet
80.34 feet
Answers
The radius of the circular track is 252.23 feet
What is an equation?An equation shows the relationship between numbers and variables in an expression.
The circumference of a circular object is length of the complete arc of the object. It is given as:
Circumference = 2π * radius
A race car drove around a circular track that was 0.3 mile. If 1 mile = 5,280 feet:
0.3 mile = 0.3 miles * 5280 feet per mile = 1584 mile
Let r be the radius of the track, hence:
1584 = 2πr
r = 1584/2π
r = 252.23 feet
The radius is 252.23 feet
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Answer: 252.23 feet
The first person to answer was correct!
Step-by-step explanation:
I took the quiz so you don't have to! <3
The value of n is both 5 times as the value of m and 36 more than the value than value of m. What are the values of n and m?Explain.
Answers
The values of n and m in the expression are 45 and 9 respectively.
How to find the values of variables in equations?The value of n is both 5 times as the value of m and 36 more than the value than value of m. Therefore, the values of n and m can be found as follows:
Using equations,
n = 5m
n = 36 + m
By substitution,
5m = 36 + m
5m - m = 36
4m = 36
divide both sides by 4
m = 36 / 4
m = 9
Let's find the value of n.
n = 5(9)
n = 45
Therefore,
n = 45 and m = 9
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What is the value of log 7 to the base 49?
Answers
The value of log_49 7 is approximately 0.1845. The value of log_49 7 can be calculated by dividing the logarithm of 7 by the logarithm of 49.
log_49 7 = log(7) / log(49) = 0.1845
The value of log_49 7 can be calculated by dividing the logarithm of 7 by the logarithm of 49. When this calculation is performed, the result is approximately 0.1845. This calculation can be used to determine the logarithmic value of a number to a given base. In this case, the base is 49 and the number is 7. This means that the logarithmic value of 7 to the base 49 is approximately 0.1845.
The value of log_49 7 is approximately 0.1845. The value of log_49 7 can be calculated by dividing the logarithm of 7 by the logarithm of 49.
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How much more would a person pay for a 4 T shirt at T shirt connection than at Al’s T shirts shops?
1.49
5.96
20.47
22.97
Answers
Answer: 5.96
Step-by-step explanation: the bottom two are too much and the first is by far too less
Point-slope form
Complete the point-slope equation of the line through (-2, 6) and (1, 1).
Use exact numbers.
y-6=
Answers
The point slope equation of the line from the given points (-2, 6) and
(1, 1) is 3y+5x = 8 .
What is equation of straight line ?
The equation of straight line as follows , y = mx+b .
where m is the slope .
Given ,
To find the point slope equation of the line
from the given points (-2, 6) and (1, 1).
First we have to find slope,
so slope = y2-y1 / x2-x1
This is (1-6)/(1-(-2)) = -5/3
Now that you know the slope you can use that for the point-slope equation
The point-slope equation is y-y1 = m(x-x1). If we start with y-6, the x value is -2 (from our point (-2,6)
y-6 = -5/3 (x-(-2))
y-6 = -5/3 (x+2)
3(y-6) = -5(x+2)
3y - 18 = -5x -10
3y+5x = 18-10
3y+5x = 8
Hence, The point slope equation of the line from the given points (-2, 6) and (1, 1) is 3y+5x = 8 .
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What are the four rules of maths?
Answers
Addition, subtraction, multiplication, and division are the four fundamental mathematical operations.
Even the most complex mathematical theories use addition, subtraction, multiplication, and division. So one of the keys to developing a grasp of math, and particularly algebra, is to master them. These (and other) procedures are now easily performed thanks to electronic calculators, but these tools can also lead to a dependence that makes truly understanding mathematics challenging. Calculators can be useful for double-checking answers, but if you rely on one too much, you risk missing out on the kind of challenging mental exercises that can improve your ability to not just do math but also grasp what you are doing completely.
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| a-b | - |c + d | if a =-5, b=4.c =1, d =-3
Answers
Answer:
Step-by-step explanation:
[tex]|-5-4| - |1+-3|[/tex]
|-9| - |-2|
9-2
7
HURRY Match the information on the left with the appropriate equation on the right. Ccrg
Answers
Answer:
y=3x-10 (perpendicular)
y=-3x+9 (parallel)
Step-by-step explanation:
perpendicular means that the slope is opposite, the opposite of -1/3x is 3x
to find the y intercept, you plug in the points into the equation
2=3(-4)+b
2=-12+b
-10=b
y=3x-10
parallel means that the slope is the same
you do the same thing as before
3=-3(2)+b
3=-6+b
9=b
y=-3x+9
jacob and elizabeth are 210 feet apart when they begin walking directly toward one another. jacob travels at a constant speed of 2.5 feet per second and elizabeth travels at a constant speed of 4.5 feet per second. let t represent the number of seconds that have elapsed since jacob and elizabeth started walking toward one another. write an expression in terms of t that represents the number of feet jacob has traveled since he started walking toward elizabeth.
Answers
The number of feet Jacob has traveled since he started walking toward Elizabeth is 2.5t .
Let the distance between Jacob and Elizabeth is 210 feet
Distance = speed x time
Jacob is walking at the constant speed of 2.5 feet per second
and Elizabeth is walking at a constant speed of 4.5 feet per second
Let the distance traveled by jacob be x and distance traveled by Elizabeth be (210 - x)
Let t be time passed when they both started walking towards each other
So the time taken by Jacob to cover x amount of distance is t
so by formula Distance = speed x time
x = 2.5 x t
So number of feet jacob has traveled since he started walking toward elizabeth is 2.5t.
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
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Primo car rental agency charges $21 per day plus $0.30 per mile. Ultimo car rental agency charges $22 per day plus $0.65 per mile. Find the daily mileage for which the Ultimo charge is twice the Primo charge.
Answers
The daily mileage for which the Ultimo charge is twice the Primo charge is 40.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Primo charges = $21 per day plus 0.30 per mile.
Ultimo charges = $22 per day plus $0.65 per mile.
let x equal the number of miles.
Ultimo Charge = twice Primo Charge
22 + 0.65x = 2(21 + 0.3x)
22 + 0.65x = 42 + 0.60x
42- 22 = 0.65x - 0.60x
20 = 0.5x
x= 20/0.5
x= 40
Hence, the daily mileage is 40.
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70 POINTS TRIANGLE THEOREMS Solve problem 7 & 8 for finding angle A please and show work
Answers
Answer:
I got 34 for number 8
Step-by-step explanation:
I'm not sure what number 7 is but hope this helped
(the work on top is where I started on 7)
8 a 1000 meters make up 1 km. what is the decimal number for 356 meters? what is the lowest fractional form of this decimal number? decimal number: in lowest fractional form:
Answers
Answer:
45
Step-by-step explanation:
45
a coin that is cm in diameter is tossed onto a by grid of squares each having side length cm. a coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position. given that the coin lands in a random position so that no part of it is off the grid, what is the probability that it is in a winning position?
Answers
The probability that it is in a winning position will be 0.8036.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A coin that is 2 cm in diameter is tossed onto a grid of squares each having a side length of 4 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position.
Then the probability of winning is calculated as,
P = [a² - πd² / 4] / (a²)
P = [4² - 3.14 x 2² / 4] / (4²)
P = (16 - 3.14) / 16
P = 0.8036
The probability that it is in a winning position will be 0.8036.
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In trapezoid ABCD, the parallel sides AB and CD have lengths 8 and 20 units. The height of the trapezoid is 12 units. Points E and F are midpoints of sides AD and BC, respectively. What is the area of quadrilateral EFCD in square units.
Answers
The area of the quadrilateral EFCD is 102 sq. units.
What is a trapezoid?A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, In trapezoid ABCD, the parallel sides AB and CD have lengths 8 and 20 units. The height of the trapezoid is 12 units. Points E and F are midpoints of sides AD and BC, respectively.
We know that, A trapezoid midsegment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.
Length of EF = AB + DC / 2 = 28/2 = 14 units.
Since, EF is the midsegment therefore, height of the quadrilateral EFCD = 12/2 = 6 units.
Area of the quadrilateral EFCD = (14 + 20 / 2) x 6 = 102 sq. units.
Hence, the area of the quadrilateral EFCD is 102 sq. units.
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Algebra 1 whats number 16
Answers
Answer: A positive 18
hope this helps any
Answer:
Step-by-step explanation:
z^2 = 1
3 *1 = 3
PLUG IN:
3((-1)^2)-(3*-5)
3-(-15)
3+15= 18
The answer is A
How do you write a function given the vertex and a point?
Answers
The formula to write the function with vertex and point is y = a(x−h)² + k
The term function is referred as a relationship between inputs where each input is related to exactly one output and the function has a domain and codomain or range.
Here we have to write a function given the vertex and a point.
As we all know that the general form of the function is written as follows:
=> f(x) = ax² + bx + c
While in the given question, here we have the value of vertex and the point of the graph, then the general form of the equation is rewritten as, follows:
=> f(x) = a(x−h)² + k
Here the terms (h, k) refers the vertex and a refers a constant multiplier.
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Solve the system of equations using elimination.
−2x + 3y = 13
x + y = 11
(−5, 1)
(−3, 3)
(3, 8)
(4, 7)
Answers
Answer:
(4,7)
Step-by-step explanation:
-2x + 3y = 13
-3(x + y = 11)
take the whole bottom equation and multiply by -3 to eliminate the 3y
-2x + 3y = 13
-3x -3y = -33
cancel out 3y
-2x = 13
-3x = -33
add -2 to -3 and 13 to -33
to get -5x = -20
divide -5 on both sides
x = 4
then you can do the exact same steps to find the y coordinates, but if x is 4 then the coordinate point is (4,7)
A trapezoid has an area of 104 square
centimeters. If one base measures 12 centimeters
and the height is 8 centimeters, what is the length of
the second base?
Answers
The formula for the area of a trapezoid is (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the bases, and h is the height.
Describe the trapezoid shape.
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
We know that the area is 104 square centimeters and the height is 8 centimeters, we can use that to find the length of the second base.
104 = (1/2)(b1 + b2) * 8
104 = (1/2)(12+b2) * 8
104 = (1/2)(12+b2) * 8
104 = 6 + 4b2
98 = 4b2
b2 = 98/4 = 24.5 cm
The second base of the trapezoid is 24.5 cm.
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12. two boxes contain a total of 175 screws. one box has 6 times more than the other. how many screws are in the large box? a 100 b 125 c 150 d 200
Answers
Two boxes contain a total of 175 screws. one box has 6 times more than the other. 150 screws are in the large box. So the answer is C. 150.
The given problem can be solved by using algebra. Let x be the number of screws in the smaller box. Then, the larger box has 6x screws. We know that the total number of screws in both boxes is 175, so we can set up the equation:
x + 6x = 175
7x = 175
x = 25
So, the smaller box has 25 screws and the larger box has 6x = 6(25) = 150 screws.
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What is the average speed of a train Travelling 240 km in 4 hours?
Answers
The average speed of a train travelling 240 km in 4 hours is 60 km/h.
Distance = 240 km
Time = 4 hours
Speed = Distance/Time
Speed = 240 km/4 hours
Speed = 60 km/h
The average speed of a train is calculated by dividing the total distance travelled by the total time taken to travel that distance. In this case, the train has travelled a total distance of 240 km in 4 hours. We can calculate the average speed of the train by dividing 240 km by 4 hours. This gives us an average speed of 60 km/h. This means that the train travelled an average speed of 60 km/h for the entire journey. This speed is the average speed of the train, which means that it could have been travelling faster or slower than this at different times during the journey.
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