What series of transformations to quadrilateral ABCD map the quadrilateral onto quadrilateral EFGH to prove that ABCD≅EFGH ?
a reflection across x-axis, and then a translation 4 units left
a reflection across x-axis, and then a translation 4 units right
a reflection across y-axis, and then a translation 4 units right
a reflection across y-axis, and then a translation 4 units left
Answers
Comparing the points to their mapped images compares A to E, B to F, C to G, and D to H. In each point, the y-coordinate switches signs and the x-coordinate is subtracted by 4.
Reflections across the x-axis will switch the sign of the y-coordinate, and reflections across the y-axis will switch the sign of the x-coordinate. Since the y-coordinates are the ones whose sign changed, the points must have been reflected across the x-axis.
Translations to the left will cause the x-coordinate to increase, and translations to the right will case the x-coordinate to decrease. Since the x-coordinate of every point was subtracted, this means that the translation must have been to the right.
The correct series of transformations is a reflection across the x-axis, and then a translation 4 units left.
Let's start by labeling the vertices of quadrilateral ABCD as follows:
A(2, 4)
B(4, 5)
C(5, 4)
D(4, 1)
If we reflect quadrilateral ABCD across the x-axis, the new coordinates of the vertices will be:
A'(2, -4)
B'(4, -5)
C'(5, -4)
D'(4, -1)
Now, if we translate quadrilateral A'B'C'D' 4 units left, the new coordinates of the vertices will be:
E(-2, -4)
F(0, -5)
G(1, -4)
H(0, -1)
These are the coordinates of the vertices of quadrilateral EFGH.
Therefore, it can prove that for the transformation to quadrilaterals ABCD≅EFGH by reflecting quadrilateral ABCD across the x-axis and then translating it 4 units left.
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Related Questions
Expand. Your answer should be a polynomial in standard form. (4−7y)(7+4y)
Answers
To expand (4−7y)(7+4y), apply the FOIL method to get the expanded form: 28 + 16y - 49y - 28y². Combine like terms to get the standard form: -28y² - 33y + 28.
Explanation:To expand the given expression (4−7y)(7+4y), we need to apply the distributive property (also known as the FOIL method in this case, which stands for First, Outer, Inner, Last):
First: Multiply the first terms in each binomial: 4 × 7 = 28.Outer: Multiply the outer terms: 4 × 4y = 16y.Inner: Multiply the inner terms: -7y × 7 = -49y.Last: Multiply the last terms: -7y × 4y = -28y².Combine the middle terms (16y and -49y) and arrange the polynomial in standard form, which is ordering terms from highest to lowest degree:
Expanded form: 28 + 16y - 49y - 28y²
Combine like terms: 28 - 33y - 28y²
Standard form: -28y² - 33y + 28
which is a better buy on apples? 5lbs for $5.25 or 10lbs for $10.25
Answers
What is 860,693 round to the nearest thousand
Answers
To round something to the nearest number place (e.g. tens, hundreds, thousands) you need to first identify the correct place with your problem 860,693
^
the thousands place is right here
To round it you need to take the number before it 860,693 and see if it
^
which is here
greater than or less than 5. If it is greater than 5 then you round up, if it is less than 5 then you round down.
So your answer is 861,000 because you round up.
Which unit should be used when measuring the length of a state border?
A.
centimeter
B.
kilometer
C.
meter
Answers
A state border is thousands of miles long (some of them). Meters would be too small of a measurement. Centimeters is even smaller. So the answer is B. Because this uses the least amount of numbers.
I hope this helps!
Hope this helps :)
Determine the volume of a cylindrical bucket if the diameter is 8.5 in. and the height is 11.5 in.
A. 652.2 in3
B. 2608.9 in3
C. 306.9 in3
D. 882.4 in3
Answers
Brainliest pls
We know that the volume,V of a cylinder is given by:
[tex] V=\pi r^2h [/tex]
where r is the radius, h is the height of the cylinder.
Now, it has been given to us that the diameter of the cylinder is 8.5 in. Therefore, the radius of the cylinder will be half it's diameter and will be, [tex] r=\frac{1}{2}\times 8.5=4.25 [/tex] in.
The height, h=11.5 inches
Therefore, applying the formula we will get:
Volume, V=[tex] \pi (4.25)^2(11.5)\approx652.57 in^3 [/tex]
Thus, out of the given options, Option A is the correct option.
A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week. How many weeks does one bag last?
Answers
Final answer:
To find out how many weeks a 3 lb bag of cat food will last for a cat that eats 3/4 lb per week, divide the total weight of the bag by the weekly consumption. One 3 lb bag lasts for 4 weeks.
Explanation:
The question asks how many weeks a bag of cat food will last if the cat eats 3/4 lb each week and the bag is 3 lbs. To find the answer, we need to divide the total weight of the bag by the amount eaten each week.
Here's the step-by-step calculation:
Total weight of cat food per bag: 3 lbsThe amount of cat food the cat eats per week: 3/4 lbNumber of weeks one bag lasts = Total weight of cat food per bag \/ The amount of cat food the cat eats per weekNumber of weeks one bag lasts = 3 lbs / 3/4 lb = 4 weeksTherefore, one bag of cat food will last for 4 weeks.
A wooden disk is shaped like a cylinder with a radius of 20.2 millimeters, and a height of 3.9 millimeters. What is the surface area of the wooden disk to thenearest whole millimeter?
Answers
-4x-15y=-17
-x+5y=-13
[tex] - 4x - 15y = - 17 \\ - x + 5y = - 13[/tex]
Answers
we are given the following system of equations
[tex] - 4x - 15y = - 17[/tex]
[tex] - x + 5y = - 13[/tex]
if you look at the x variables in both equations you can see that we can easily eliminate them by multiplying the bottom equation by -4 as so
[tex] - 4x - 15y = - 17[/tex]
[tex] - 4( - x + 5y = - 13)[/tex]
simplify and we get
[tex] - 4x - 15y = - 17[/tex]
[tex]4x - 20y = 52[/tex]
now we can combine like terms on each side with the x's cancelling and get
[tex] - 35y = 35[/tex]
now divide off -35
[tex]y = - 1[/tex]
great now we can go back to our original system and pick a equation and substitute y back in to find x lets use
[tex] - x + 5y = 13[/tex]
so now we substitute y and get
[tex] - x + 5( - 1) = 13[/tex]
[tex] - x - 5 = 13[/tex]
[tex] - x = 17[/tex]
[tex]x = - 17[/tex]
now we put x and y into one coordinate (x,y)
so now our FINAL ANSWER IS
(-17,-1)
The area of a rectangle playgrond is 78 square meters. If the length of the playground is 13 meters, what is its width?
Answers
78 = length * 13
[tex] length = \frac{78}{13} [/tex] use a calculator to find out the answer then,
Answer:
6 meters.
Step-by-step explanation:
Let w represent width of the rectangle.
We have been given that the area of a rectangle playground is 78 square meters. The length of the playground is 13 meters.
We know that area of a rectangle is width times length of rectangle. We can represent our given information in an equation as:
[tex]\text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
[tex]78\text{ m}^2=13\text{ m}\times \text{Width}[/tex]
[tex]13\text{ m}\times \text{Width}=78\text{ m}^2[/tex]
[tex]\frac{13\text{ m}\times \text{Width}}{13\text{ m}}=\frac{78\text{ m}^2}{13\text{ m}}[/tex]
[tex]\text{Width}=6\text{ m}[/tex]
Therefore, the width of the rectangle is 6 meters.
Evan's mother used 1/3 pound of beef, 1/2 pound of shrimp, and 3 pounds of pasta to make dinner for 4 people.
Use this information to answer ALL FOUR PARTS below.
Question:
Part A:
Each person will receive an equal share of beef with none left over. What is the amount, in pounds, of each serving of beef?
Part B:
Each person will receive an equal share of shrimp with none left over. What is the amount, in pounds, of each serving of shrimp?
Part C:
Each person will receive an equal share of pasta with none left over. What fraction represents the amount, in pounds, of each serving of pasta?
Part D:
Evan only ate 1/2 of the pasta that he received. What is the amount, in pounds, of pasta did Evan eat? Explain how you got this answer step-by-step using math vocabulary.
Answers
Part B: 1/2 / 4 = 1/8. Each person gets 1/8 pound of shrimp.
Part C: 3 / 4 = 3/4. Each person gets 3/4 pound of pasta.
Part D: If we're talking about pasta, then Evan ate 3/8 pound of pasta. Half of 3/4 (the amount of pasta given to everyone) is 3/8, so if Evan ate 1/2 of his share (3/4), he ate 3/8 pounds of pasta.
Hope this helps! Have an awesome day :)
Is it 2.20? Because if the square root is 2.23 then you’d find the value of the nearest hundredth?
Answers
The square root of 5 is approximately 2.236
You want to find the hundredths place, so you'll need to look at the thousandths place.
The thousandths place is 6, which is more than 5, so you will round 2.236 up to 2.24
The square root of 5 to the nearest hundredth is 2.24
Hope this helps =)
Picture is attached need help fast thanks
Answers
[tex] \sqrt[3]{ 8^{x} } [/tex]
Verbally we can say we are taking cube root of [tex] 8^{x} [/tex]. Cube root is equivalent to raising the power to [tex] \frac{1}{3} [/tex].
So, we can say we raising [tex] 8^{x} [/tex] to the power [tex] \frac{1}{3} [/tex].
In expression form, this will be:
[tex] ( 8^{x} )^{ \frac{1}{3} } \\ \\ = 8^{ \frac{x}{3} } [/tex]
Therefore, third option is the correct answer
Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.
Answers
The triangle is right-angled with the legs DE (horizontal) and DF (vertical).
see the attached figure
Hence
the circumcenter is the mid-point of the hypotenuse EF,
point E (8,3) point F(1,-5)
Fin the mid-point
Xm=(8+1)/2----------> Xm=4.5
Ym=(-5+3)/2----------> Xm=-1
the mid-point is (4.5,-1)
the answer is
the circumcenter is the point (4.5,-1)
The circumcenter of triangle DEF has coordinates [tex](4.5,-1)[/tex]
EXPLANATION
The circumcenter of triangle DEF is the point where all the three perpendicular bisectors of the three sides of the triangle intersect.
Let us find the perpendicular bisector of any two sides, because the third one will also meet these two perpendicular bisectors at the same point.
The perpendicular bisector of ED passes through the midpoint of the line connecting D(1,3) and E(8,3).
We must therefore find the midpoint to obtain,
[tex]N=(\frac{1+8}{2},\frac{3+3}{2})=(4.5,3)[/tex]
The slope of ED is
[tex]n=\frac{3-3}{8-1}=0[/tex].
The slope of the perpendicular bisector is the negative reciprocal of the slope of ED
[tex]slope=-\frac{1}{0}[/tex] which undefined.
The equation of a line that has an undefined slope is given by
[tex]x=x_1[/tex].
Therefore the equation of the perpendicular bisector of ED is [tex]x=4.5--(1)[/tex]
We must also find the equation of the perpendicular bisector of DF.
The midpoint of D(1,3) and F(1,-5) is [tex]M=(\frac{1+1}{2}, \frac{3+-5}{2})=(1,-1)[/tex]
The slope of DF is
[tex]m=\frac{-5-3}{1-1} =\frac{-8}{0}[/tex] this is an undefined slope but let us keep it like this for now.
The perpendicular bisector will have a slope that is the negative reciprocal of this undefined slope
[tex]slope=-\frac{1}{\frac{-8}{0}}= \frac{0}{8}=0[/tex]. This means that the slope is parallel to the x-axis.
The equation of lines that are parallel to the x-axis is given by the formula,
[tex]y=y_1[/tex].
Therefore the equation of the perpendicular bisector is [tex]y=-1--(2)[/tex].
The perpendicular bisectors will intersect at, [tex](4.5,-1)[/tex]
Hence the circumcenter is [tex](4.5,-1)[/tex]
how do you multuply monominails (sorry if i spelled it wrong)
a^3 *v^4
Answers
mono = one
nomial = name
so monomial translates to "one name"
As for the actual question of multiplying monomials, there isn't anything we can do here. The reason why is because the bases 'a' and 'v' are different. If they were both the same letter, then we'd be able to add the exponents. However that is not the case here. So we'd just leave it as a^3*v^4
If both terms had the same base (ex. were both a), then we could add the exponents and have a^7
Find the area of the triangle that has a base of 16 yd and a height of 9 yd
Answers
72=(9x16)/2
b is the base and h is height.
1/2(16)(9)
1/2(144)
72.
The area is 72 yd²
10 POINTS AND BRAINLIEST!1
Identify the following numbers as Irrational (I) or Rational (R).
a. ¾ ______
b. 1/3 ______
c. 4√4 ______
d. .3333 ______
e. 0.3¯0.3¯ _____
f. ππ _____
g. -3/4 ______
h. -4.32 _____
i. 12−−√12 _____
Answers
The table shows data for a random sample of 20 students out of middle school. Use the sample to draw an inference about each measure. Explain your reasoning.
Answers
If there is a 30% increase in the operation charge for using a service,$82.70 remains to be paid.how much is the original bill ?
Answers
1/4x+y=5 what is the slope
Answers
slope is -1/4
y=ax+b
y=-1/4x+5
a=-1/4 , so -1/4 is slope
b=5, so b is y-intercept
We subtract by 1/4x on both sides and get y = -1/4x + 5. So, the slope is -1/4.
---
Hope this helps!
Natalia is drawing a rectangle. She wants the width to be at least 10 inches and the perimeter to be no more than 72 inches.
A.) write a system of inequalities that can be used to solve this problem.
B.) give a possible length and width for the rectangle.
C.) give a length and width that cannot be used for the rectangle.
Answers
W >= 10
2L + 2W <= 72
B) To give a possible length and width, we don't need to solve the system. We can plug use numbers that will satisfy the equations above.
One possible solution would be W = 12 and L = 10. In this case, the width is greater than 10, and the perimeter is 44 which is less than 72.
C) One answer that would NOT work is W = 5 and L = 10 because width is less than 10.
Another example would be W = 20 and L = 18 because the perimeter would be greater than 72.
Natalia's problem involves creating a system of inequalities with limitations on width and perimeter. Possible rectangle dimensions follow this system, such as a width of 10 inches and a length of 26 inches. Dimensions that don't comply, like a width of 9 inches or a width of 10 inches with a length of 27 inches, are not feasible.
Explanation:To address Natalia's rectangle problem, we need to create a system of inequalities based on her requirements for width and perimeter. Let's denote the width as w and the length as l. The inequalities should look like this:
w ≥ 10 (The width must be at least 10 inches)2l + 2w ≤ 72 (The perimeter must be no more than 72 inches)Possible dimensions for Natalia's rectangle that satisfy these inequalities could be a width of 10 inches and a length of 26 inches. In this case, the perimeter would be 2(10) + 2(26) = 72 inches, which is the maximum allowed.
Impossible dimensions would include a width of 9 inches, as this is less than the minimum required width, or a width of 10 inches with a length of 27 inches, which would make the perimeter 2(10) + 2(27) = 74 inches, exceeding the maximum permitted perimeter.
Increasing a number by 10% is the same as multiplying it by y. What is the value of y? Express your answer as a decimal to the nearest tenth.
Answers
If f=6 and g=8, what does h equal
Answers
The value of h in this given alphabetical series is 10.
What is an arithmetic sequence?The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
Given, f=6 and g=8
Since, there is no additional data is given I will assume this is the question of Alphabetic sequence.
In Alphabet Series section, a string of alphabets, either in a single file or in combination form a sequence. This sequence comes together following a definite rule. The candidate is expected to detect this rule and answer the questions at the end.
So,
the value of f = 6 and g = 8
Since, Alphabetic order after f and g is h, i ,j, k, l, .....
And common factor is 2
Thus,
The value of h = 8+2 = 10
The value of i = 10+2 = 12
The value of j = 12 +2 =14
And so on
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Rachael is a nurse. She earns 12 vacation days after working 768 hours. How many hours does Rachael need to work to earn 1 vacation day? Remember to include units! (Example: 12 hours)
Question 4 options:
Spell check
Answers
You get his by dividing 768 by 12.
If correct brainliest please.
Thank you.
A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 12 mugs mugs with coffee, how many quarts of coffee does she need?
Answers
16 is half of 32 so 1 quart fills 2 mugs meaning that she needs 6 quarts of coffee
in a certainin linear pair, one angle measures three less than twice as much as the other. choose the diagram that you would draw to represent this linear pair.
Answers
one angle - x°
other angle - (2x - 3)°
diagrams A and D are wrong as they show that the angles sum up to 90°, whereas in linear angles the adjacent angles should sum up to a straight line that's 180°
diagram C is wrong as they haven't depicted the angles correctly.
diagram B
x + 2x-3 = 180
3x = 183
x = 61
other angle 61*2 - 3 = 119
this is the correct diagram as the angles in the diagram look simiar to the angles calculated.
Edwin needs to buy a car, a truck, and a motorcycle for his shipping business. He wants the car to be red or yellow; the truck to be black, white, or silver; and the motorcycle to be green, blue, or orange.
How many different combinations of vehicles does Edwin have to choose from?
Answers
Car: Red, Yellow
Truck: Black, White, Silver
Motorcycle: Green, Blue, Orange
We have 2 options with a car, 3 options with a truck, and 3 options with a motorcycle. Since he wants one of each, we will multiply all of the color options together:
2 x 3 x 3
= 18
Edwin has 18 different combination of vehicles to choose from.
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate
The store donates __ basketballs
Answers
what does this mean? and can gove answer
Answers
These are exponents. Here, lets try #1.
100+6^2-9
First and foremost, you ALWAYS want to simplify the exponents. So our expoennt here is 6^2. Basically its 6*6.
Whats 6*6? 36!
Now, you plug that in. Lets see.
100+36-9= ? Solve
Lets do this little by little. Whats 100+36? 136. Now subtract that by 9.
Your answer is 127! Now try number 2,3,4 and tell me what you got and Ill check with you (:
#1 would be 6*6 is 36, then plugging into the problem it's 100+36-9. Then you would add 100 to 36, getting 136. Finally, you would subtract 9 from 136, making it 127.
100 + 6^2 -9
100 + 36 - 9
136 -9
127
Derek uses a $50 gift card to purchase 3 books for $12 each and a calendar for $9.What is the amount left on the card ?
Answers
Vote for the best representation of 7 95/125 what’s the answer ??
Answers
simplified is 194/25
and for a decimal 7.76
hope it helps
Given is a mixed number i.e. [tex] 7\frac{95}{125} [/tex].
We can solve it as given below :-
[tex] 7\frac{95}{125} \\\\
=\frac{(125*7)+95}{125} \\\\
=\frac{875+95}{125} \\\\
=\frac{970}{125} \\\\
=\frac{194}{25} \\\\
=7\frac{19}{25} \;\;or\;\; 7.76 [/tex]
Hence, [tex] \frac{194}{25} \;or\; 7\frac{19}{25} \;or\; 7.76 [/tex] would be better representation of given mixed number i.e. [tex] 7\frac{95}{125} [/tex].
Hope, this helps! :)