Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
[tex](x,y)\to (kx,ky)[/tex] ...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
[tex]G(2,-2)\to G'(k(2),k(-2))[/tex]
[tex]G(2,-2)\to G'(2k,-2k)[/tex]
The image of G after dilation is G'(5,-5). So,
[tex](2k,-2k)=(5,-5)[/tex]
On comparing both sides, we get
[tex]2k=5[/tex]
[tex]k=\dfrac{5}{2}[/tex]
So, the scale factor is [tex]k=\dfrac{5}{2}[/tex].
Substituting [tex]k=\dfrac{5}{2}[/tex] in (i), we get
[tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex]
Therefore, the required algebraic representation to represents this dilation is [tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex].
Short Answer Note: Your teacher will grade your responses to questions 4-8 to ensure you receive proper credit for your answers. 4. Find the value of k. The diagram is not to scale. (I point) I need the answer as soon as possible
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon ABCD is a parallelogram, and m-ABC = 127º. The length of BC is 10 units, and the length of AB is 5 units.
1271
D
units, and m_BCD is
The perimeter of the parallelogram is
Answer:
Perimeter = 30 units
m<BCD = 53°
Step-by-step explanation:
Recall: in any parallelogram, consecutive angles are supplementary. Also, the pairs of parallel sides are equal in length.
We would use this knowledge to solve the problem given.
m<ABC = 127° (given)
BC = 10 units
AB = 5 units
✔️Perimeter of the parallelogram = AB + BC + CD + AD
AB = CD = 5 units (pair of parallel sides)
BC = AD = 10 units (pair of parallel sides)
Perimeter = 5 + 10 + 5 + 10
Perimeter = 30 units
✔️m<BCD = 180° - m<ABC (consecutive angles are supplementary)
m<BCD = 180° - 127° (Substitution)
m<BCD = 53°
What is the surface area of a sphere with a diameter of 6 cm?
A jazz concert brought in $167,000 on the sale of 8,200 tickets. If the tickets sold for $15 and $25 each, how many of each type of ticket were sold?
Answer:
x=3800, y=4400
Step-by-step explanation:
X+y=8200 equation 1
15x+25y=167000 equation 2
x=8200-y isolate x in equation 1
15(8200-y)+25y=167000 substitute value of x from equation 1 into equation 2
123000-15y+25y=167000
10y=44000
y=4400
solve for x by inserting y value into either equation.
x+y=8200
x+4400=8200
x=3800
Check answer:
15x+25y=167000
15(3800)+25(4400)=167000
57000+110000
167000=167000
When the hour hand moves from 3 pm to 6 pm, through how many degrees does it move?
A. 3⁰
B. 90⁰
C. 18⁰
D. 36⁰
Find the center and raduis of the circle
Answer:
B
Step-by-step explanation:
Because the equation can be written in the form (x-p)^2+(y-q)^2. So it represents a circle with the radius r=3 and the center of (5,0).
Answer:
C
Step-by-step explanation:
The circle equation (x-a)²+(y-b)²=r² has a radius of r and a center of (a,b).
You can expand your equation from (x-5)²+y²=9 to (x-5)²+(y-0)²=3².
Using this information, you can see that a=5, b=0, and r=3.
Therefore the center is (5,0) and the radius is 3.
**This question involves circle equations, which you may want to revise. I'm always happy to help!
Nala and lily are playing a dice game where they score points. After one round, the ratio of nala point to lily's point is 7 to 9. If nala has 14 more points than lily, determine how many points lily has.
Answer:
Lily has 63 points and Nala has 49.
Step-by-step explanation:
Since Nala and Lily are playing a dice game where they score points, and after one round, the ratio of Nala's points to Lily's points is 7 to 9, if Nala has 14 more points than Lily, to determine how many points Lily has se you must perform the following calculation:
9 - 7 = 2
14/2 = 7
7 x 7 = 49
7 x 9 = 63
63 - 49 = 14
Therefore, Lily has 63 points and Nala has 49.
Lucas and Tony were trying to solve the equation: x^2=16x+25 Lucas said, "The x^2, squared term is isolated, so I"ll take the square root of both sides and solve." Tony said, "I'll solve using the quadratic formula with a=1,b=16, an c equals 25." Whose solution strategy would work? Choose 1 answer:
Answer:
Tony's solution strategy
Step-by-step explanation:
Given the equation that Lucas and Tony trying to solve expressed as: x^2=16x+25
This can be written in standard form as x^2 - 16x - 25 = 0
This can then be factorized using the general formula
x = -b±√b²-4ac/2a where a, b and c are constants
From the given expression;
a = 1, b = -16, c = -15
Hence the best strategy that would have worked based on the explanation is Tony's
Answer: Neither
Step-by-step explanation: got it right on khan
Pls help math coordinates of pt P
Answer:
( 3, - 2 )
Step-by-step explanation:
p is located at below 3
Please help me find the answers
For the mean median mode range mm max q1
Everything has been explained in there
Please help with math
Answer:
easy that thing needs help
x = 8 × Cos( 72 )
x = 8 × Cos( 90 - 18 )
x = 8 × Sin( 18 )
x = 8 × 0.309
x = 2.472
x = 2.470
x = 2.500
x = 2.5
Another not so difficult one, Giving Brainliest and 35 points
Answer:
[tex] 3^{-2}=\frac{1}{3²}=\frac{1}{9}[/tex]
Answer:
1/9
Step-by-step explanation:
cause it would the negative would got the 3 so it would be -3×-3 so it would be positive 9 with a 1 over it
Can u guys hurry up pleasee The manager of a local appliance store wants to conduct a customer satisfaction survey. Which population should the manager survey? A.Sales people in the store. B.People in charge of repairs at the store. C.People who bought a major appliance from the store. D.Prospective buyers who visit the store.
C. People who bought a major appliance from the store.
Step-by-step explanation:A customer satisfaction survey is a market survey carried out to analyze how satisfied users or customers are in using or consuming a particular product or service. Basically, it has to be carried out on the customers themselves. By costumers, we mean those that have bought and/or used the service or product.
For the local appliance store, the manager should survey people that have bought at least one major appliance from the store. Those are the right people that should make up the population to be surveyed. This is because;
i. They are the consumers of the product.
ii. They have bought and definitely used the product.
iii. They have some usable and useful experiences since they have handled the product.
can you answer this please
Answer:
C
Step-by-step explanation:
y=mx+b where m =slope and b= y intercept
m=y-y/x-x or 3-1/1-0 or 2
B is where the line crosses the x axis or 1
So y=2x+1
Please help me I will give you 16 points I don’t know what that do but I will
Answer:
40
Step-by-step explanation:
The serving sizes, [tex]x[/tex], of 20, 80, and 120 have a required amount of meat in pounds, [tex]y[/tex], of [tex]y=\frac{1}{10}x[/tex] (the number of pounds of meat is equal to 1/10th the serving size)
However, for the row with a serving size of 40, the number of pounds of meat is equal to [tex]\frac{6}{40}=\frac{3}{20}[/tex] the serving size. Therefore, the serving size of 40 has a different ratio of serving size to pounds of meat than the other ratios.
Can someone help me with this? i’m struggling urgent help please!!!!
Answer:
Similar by SAS
Step-by-step explanation:
If you multiply the two given sides by 3/2 you will get the sides for the large triangle
3/2 * 10 = 30 / 2 = 15
3/2 * 24 = 72 / 2 = 36
Therefore they are similar by SAS postulate for similarity. Notice that the right angle is between the legs of the triangle. That is the main qualification that allows you to use SAS for similarity.
Find the other two angles of both the triangles, if they were similar then the triangles are similar
A 5-pack of granola bars costs $3.55. What is the unit price?
Answer:
0.71 is the unit price
Step-by-step explanation:
all u gotta do is divide 3.55 by 5 to find out how much it cost each:)))
hope this helps!!!!
please mark brainiest<3
true or false : A triangle can have interior angles of 50 degrees, 70 degrees, and 68 degrees
Answer:
it is false as the sum of the degrees of the triangle should be 180 but here it is 188 so it is false
what is the area of parallelogram if base is 13 and the height 14
Answer:
A = 182
Step-by-step explanation:
14 x 13 = 182
So, 182 would be your answer.
With your bare feet, stand with one foot on a rug, and the other foot on a tile, linoleum, or wood floor. Which one feels colder? Which one is really colder? Explain what is going on in a paragraph
Answer:
The tile feels colder because it's a heat conductor and moves heat rapidly away from your skin which is much warmer than the air temperature. The rug is a heat insulator. The rug slows down the flow of the heat which makes it feel warmer.
Step-by-step explanation:
Suppose you have a bag with 50 letter tiles in it and 23 of the tiles are the letter Y. If
23
you pick a letter tile at random from the bag, the probability that it is the letter Y is Suppose
50
another bag has 200 letter tiles in it and 172 of the tiles are the letter Y. Write the probability of
picking a tile that is the letter Y as a fraction and as a percent. From which bag are you more likely
to pick a tile that is the letter Y?
Answer:
23
Step-by-step explanation:
234Suppose you have a bag with 50 letter tiles in it and 23 of the tiles are the letter Y. If
23
you pick a letter tile at random from the bag, the probability that it is the letter Y is Suppose
50
another bag has 200 letter tiles in it and 172 of the tiles are the letter Y. Write the probability of
picking a tile that is the letter Y as a fraction and as a percent. From which bag are you more likely
to pick a tile that is the letter Y?
The probability of picking the letter Y from bag of 50 letters is 23/50 or 0.46 or 46% and probability of picking the letter Y form bag of 200 letters is 172/200 or 0.86 or 86%. as the probability of getting the letter Y is more in second bag this it is better to pick the bag containing 200 letters.
What is a probability?The probability explains the chances of happening a event. The probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event to happen and 1 indicates certainty of the event to happen.
From the question it is said that a bag of 50 letter contain 23 Y letters. Thus the probability of the letter Y picking is 23/50 i.e, number of times the letter Y can come out if we pick the letters 50 times. So, it is certain that 23 Y letters can come out.
23/50= 0.46 or 46%
And if the bag contain 200 letters in which 172 are Y letters then the probability to pick Y is 172/200
172/100 =0.86 or 86%
As the chance to get Y letter is mor in bag containing 200 letters thus pick this bag.
thus the 1st bag probability is 46% and for 2nd bag is 86%. Hence choose 2nd bag
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Which polynomial is factored completely? g Superscript 5 Baseline minus g 4 g cubed + 18 g squared + 20 g 24 g squared minus 6 g Superscript 4 2 g squared + 5 g + 4
Answer:
It's D on Edge 2021
I did the assignment
The polynomial that is factored completely is one that can not be factored again is 2g² + 5g + 4. Therefore, option D is the correct answer.
What is the factorisation of a polynomial?Factorisation of a polynomial is the decomposition of a polynomial into smaller polynomials.
Thus, the polynomial that is factored in completely is the polynomial that can not be decomposed again.
Now,
g⁵ - g = g(g⁴ - 1) (it can be factored)
4g³ + 18g² + 20g = 2g(g + 2)(2g + 5)
24g² - 6g⁴ = 6g²(4g² + g²)
2g² + 5g + 4 cannot be factored again. It is already factored completely
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Which of these quadrilateral types must have all four sides congruent?
A. Rectangle, square
B. Parallelogram, rectangle, square, rhombus
C. Square, rhombus
D. Rectangle, square, rhombus
C. Square, a rhombus is the right answer.
What does it mean that all four sides are congruent?A rhombus is a parallelogram in which all four sides are congruent. Shaped like a diamond. A square is a parallelogram with four congruent sides and four right angles. In other words, squares are rectangles and diamonds.
Exactly all the shapes on the four sides are called squares. Each type of figure here is a square type. The lengths of the congruent sides are the same. If parallel sides are drawn as lines, they never intersect.
Two triangles are congruent If the corresponding sides have the same length and the corresponding angles are the same, then the two triangles are congruent.
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Brainliest help please
Answer:
The 7 is in the tenths place
Step-by-step explanation:
869.74
hundreds tens ones. tenths hundredths
8 6 9 7 4
The 7 is in the tenths place
Answer: The 7 is in the tenths place not the hundreds place.
Tenths Hundreds
0.1 0.01
Hope this helps...
Have a great day.
What is a cofunction? Give examples and explain the purpose.
If I had 3000 plums and I sold 100 how much money would I have plums would I have left.
Answer:
2,900 plums left
Step-by-step explanation:
3,000 plums - 100 sold plums = 2,900 plums left
Answer:
2900
Step-by-step explanation:
3000 (plums) - 100 (plums sold) = 2900 (plums left.)
You didn't say how much money you started out with by the plums.
Given
f (x) = x3 + 1
and
g(x) = x – 1
find the composition
f(g(x))
Answer:
(x-1)³+1
is correct option
Mariya is solving the quadratic equation by completing the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
Mariya is solving the quadratic equation by completing the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
What is the value of A?
-20
3
4
5
Answer:
4
Step-by-step explanation:
just 4 -_-
4x^2-20x
=4(x^2-5x)
so the value is 4
By solving the quadratic equation, the value of A is 4
Option (3) is correct.
What is a quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2}+bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
Given quadratic equation
[tex]4x^{2} -20x+3=0[/tex]
⇒ [tex]4x^{2} -20x=-3[/tex]
By taking 4 as common in [tex]4 x^{2}[/tex] and 20x
⇒ [tex]4(x^{2} -5x)=-3[/tex]...................(1)
According to the question by solving the quadratic equation. Mariya got, [tex]A(x^{2} -5x)=-3[/tex] .....................(2)
By comparing equation 1 and 2 we can clearly see that A = 4
Hence, by solving the quadratic equation, the value of A is 4
Option (3) is correct.
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A parking lot in the shape of a parallelogram has a length of
300 meters and a width of 150 meters. A scale drawing of the
Sarking lot has a length of 10 centimeters and a width of 5
centimeters
Answer:
C. 1 centimeter = 30 meters
[tex]10 \: cm = 300 \: m \\ 1 \: cm = ( \frac{1}{10} \times 300) \: m \\ = 30 \: m \\ \\ 5 \: cm = 150 \: m \\ 1 \: cm = 30 \: m[/tex]
PLEASE HELP. !!!!!!
the 4th option is “A translation 2 units left and 1 unit up
