A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
PLEASE ANSWER
Answers
Answer:The answer is B !
Step-by-step explanation:
A translation is a rigid translation that changes the location of a figure without a net reflection or rotation
The option that gives the correct image of the preimage DEFG, which is D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3), is; The second diagram
Please find attached a diagram showing the preimage and the image
The reason why the selected option is correct is given as follows
The given translation is T₍₋₁, ₂₎(x, y)
Coordinates of the pre-image are D(-1, 3), E(4, 3), F(4, 1), and G(-1, 1)
Required:
To find the image formed following the translation
Solution:
To translate a preimage given the measure of the translation of the x and y-values, in the form T₍₋₁, ₂₎(x, y), '-1' is added to the x-values, and '2' is added to the y-values, as follows
D(-1, 3) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] D'(-1 - 1, 3 + 2) = D'(-2, 5)E(4, 3) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] E'(4 - 1, 3 + 2) = E'3, 5)F(4, 1) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] F'(4 - 1, 1 + 2) = F'(3, 3)G(-1, 1) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] G'(-1 - 1, 1 + 2) = G'(-2, 3)The coordinates of the vertices of the image are D'(-2, 5), E'(3, 5), F'(3, 3), and G'(-2, 3)
The image of DEFG is the second diagram, D'E'F'G'.
Please find attached the diagram of the image of the preimage DEFG constructed with dashes
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Related Questions
Find the range of each function for the domain {-4, -2, 0, 1.5, 4}. f(x) = 5x^2 + 4
Answers
f(x) = 5x² + 4
Substitute with the domain of -4
f(x) = 5x² + 4
f(-4) = 5(-4)² + 4
f(-4) = 5(16) + 4
f(-4) = 80 + 4
f(-4) = 84
Substitute with the domain of -2
f(x) = 5x² + 4
f(-2) = 5(-2)² + 4
f(-2) = 5(4) + 4
f(-2) = 20 + 4
f(-2) = 24
Substitute with the domain of 0
f(x) = 5x² + 4
f(0) = 5(0)² + 4
f(0) = 5(0) + 4
f(0) = 0 + 4
f(0) = 4
Substitute with the domain of 1.5
f(x) = 5x² + 4
f(1.5) = 5(1.5)² + 4
f(1.5) = 5(2.25) + 4
f(1.5) = 11.25 + 4
f(1.5) = 15.25
Substitute with the domain of 4
f(x) = 5x² + 4
f(4) = 5(4)² + 4
f(4) = 5(16) + 4
f(4) = 80 + 4
f(4) = 84
The range of the function for those domain is {4, 24, 15.25, 84}
To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, evaluate the function for each value in the domain and find the minimum and maximum outputs. The range of the function is {4, 84}.
Explanation:To find the range of the function f(x) = 5x^2 + 4 for the given domain {-4, -2, 0, 1.5, 4}, we need to evaluate the function for each value in the domain and find the minimum and maximum outputs.
Substitute -4 into the function: f(-4) = 5(-4)^2 + 4 = 84Substitute -2 into the function: f(-2) = 5(-2)^2 + 4 = 24Substitute 0 into the function: f(0) = 5(0)^2 + 4 = 4Substitute 1.5 into the function: f(1.5) = 5(1.5)^2 + 4 = 16.75Substitute 4 into the function: f(4) = 5(4)^2 + 4 = 84The range of the function is the set of all possible outputs. In this case, the minimum output is 4 and the maximum output is 84. Therefore, the range of the function is {4, 84}.
Today's newspaper contains a 20%-off coupon at Old Army. The $100 jacket that you want was already reduced by 40%. What as the final price that you paid for the jacket
Answers
60-20%=48
$48.00 is the final price you pay.
The final price that is paid for the jacket is:
$ 48
Step-by-step explanation:The actual cost of jacket was: $ 100
The cost of the jacket was reduced by 40%
This means that the after reduction of 40% the jacket will cost:
[tex]100-\dfrac{40}{100}\times 100\\\\\\=100-40\\\\=60[/tex]
This means that the cost of jacket after 40% reduction is: $ 60
Also, there was a coupon that contains 20% off.
This means that the jacket will actually cost:
[tex]60-\dfrac{20}{100}\times 60\\\\\\=60-12\\\\\\=48[/tex]
The final price of jacket is:
$ 48
128,96,72,54,...find the common ratio
Answers
To find the common ratio of the given sequence, divide each term by the previous term. The common ratio is 0.75.
Explanation:The given sequence is: 128, 96, 72, 54, ...
To find the common ratio, we need to determine the ratio between consecutive terms. We can do this by dividing each term by the previous term.
Ratio between the 2nd and 1st terms: 96/128 = 0.75
Ratio between the 3rd and 2nd terms: 72/96 = 0.75
Ratio between the 4th and 3rd terms: 54/72 = 0.75
Since the ratio is the same for all consecutive terms, we can conclude that the common ratio of this geometric sequence is 0.75.
The correct common ratio for the given sequence is [tex]\(\frac{3}{4}\) or 0.75.[/tex]
To find the common ratio of the sequence, we divide each term by the previous term and look for a consistent value:
1. For the second term, \(96\), divided by the first term, [tex]\(128\)[/tex], we get:
[tex]\[ \frac{96}{128} = \frac{3}{4} = 0.75 \][/tex]
2. For the third term, [tex]\(72\),[/tex] divided by the second term, [tex]\(96\),[/tex] we get:
[tex]\[ \frac{72}{96} = \frac{3}{4} = 0.75 \][/tex]
3. For the fourth term, [tex]\(54\),[/tex] divided by the third term, [tex]\(72\)[/tex], we get:
[tex]\[ \frac{54}{72} = \frac{3}{4} = 0.75 \][/tex]
Rodney bought a 25-pound bag of dog food.His dog at 10 2/5 pounds of food in the first month and 10 4/5 pounds of the food in the second month.How much dog food,in pounds, was remaining in the bag at the end of the two months
Answers
25- 20 1/5 = 4 4/5 pounds of dog food is left.
Take 25 and subtract it by 21 1/5 you would get 3 4/5
which would be 3.8 pounds
A group of 500 transistors is known to contain one defective unit. What is the probability that a transistor selected at random from the lot is the bad one?
Answers
The answer is 1/500 because it will always be the probability of the event occurring/total events
which numerical expression would provide the solutions to the equation 7x^2 + 4x - 8 = 14
Answers
7x^2 + 4x - 8 = 14-----------------> 7x²+4x-22=0
Step 1
Solving a second degree equation
x1=[-b+√(b²-4ac)]/2a
x2=[-b-√(b²-4ac)]/2a
a=7
b=4
c=-22
then
x1=[-4+√(4²-4*7*(-22))]/(2*7)-----------> [-4+√(632)]/(14)
x1=-(-4+25.14)/14=1.51
x2=[-4-√(4²-4*7*(-22))]/(2*7)-----------> [-4-√(632)]/(14)
x2=-(-4-25.14)/14=-2.08
the solutions of the system is
x1=1.51
x2=-2.08
to check the result
using a graph tool
see the attached figure
the answer is
the numerical expressions is
x1=[-b+√(b²-4ac)]/2a
x2=[-b-√(b²-4ac)]/2a
The quadratic equation 7x^2 + 4x - 8 = 14 does not have any real solutions.
Explanation:The given equation is a quadratic equation of the form at² + bt + c = 0, where a = 7, b = 4, and c = -22. To find the solutions, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values, we get:
x = (-4 ± √(4² - 4(7)(-22))) / (2(7))
Simplifying further, we get:
x = (-4 ± √(16 - 616)) / 14
x = (-4 ± √(-600)) / 14
The expression inside the square root is negative, which means there are no real solutions to the equation.
In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be .7008. what is the apparent interest rate?
Answers
from the present value table, the percentage corresponding to discount factor of 0.7008 in 5 years is 7%
therefore using the formula:
FV=PV(1+r/100)^n
where:
FV=$1000
PV=?
r=7%
hence:
1000=PV(1+7/100)^5
PV=1000/(1+7/100)^5
PV=712.986
Find a second-degree polynomial p such that p(1) = 5, p'(1) = 7, and p''(1) = 10.
Answers
p'(x) = 2ax +b
p''(x) = 2a
You require
.. 2a = 10
.. 2a +b = 7
.. a + b + c = 5
Thus a=5, b=-3, c=3, and
.. p(x) = 5x^2 -3x +3
The given conditions suggest a second-degree polynomial of form p(x) = ax^2 + bx + c. By solving the given conditions a = 5, b = -3, and c = 3, yielding the polynomial p(x) = 5x^2 - 3x + 3.
Explanation:The question is asking for a second-degree polynomial, which can generally be written in the form p(x) = ax^2 + bx + c. Given that p(1) = 5, that means a + b + c = 5. The derivative of p(x), p'(x) = 2ax + b, and p'(1) = 7, so 2a + b = 7. The second derivative, p''(x) = 2a, and p''(1) = 10, so 2a = 10 or a = 5. We can substitute a = 5 into the first two equations to find the values of b and c. So, b = -3 and c = 3. Therefore, the original function is p(x) = 5x^2 - 3x + 3.
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The graph shows the amount of money the Phillips family spent each month on groceries.
When did the greatest month-to-month increase in spending occur?
July–August
April–May
June–July
May–June
Answers
Answer:
Option A. July-August.
Step-by-step explanation:
Phillips family spent each month on groceries. The amount of money in each month is shown in a graph.
Approximate amount in each month was spent :
March : $450
April : $400
May : $400
June : $500
July : $300
August : $ 500
Sep. : $480
Oct. : $420
From the graph given, there is a greatest month to month increase in spending occur in July to August (from $300 to $500).
So Option a. July-August is the correct answer.
ABE Software creates customized software that sells for $3,816,981.10 total. ABE Software’s cost is $1,723,000.00 and overhead expenses are estimated at 47% of the selling price. What is ABE Software’s net profit to the nearest dollar?
Answers
Net profit, rounded to the nearest dollar, is $300,000.
What is the area of the polygon
Answers
Formula:
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 22 x 9
Area of triangle = 99 square units
I don't get it x/5 + x+4/3 = 4
Answers
[tex] \dfrac{x}{5} \times \dfrac{3}{3} + \dfrac{x + 4}{3} \times \dfrac{5}{5} = 4 [/tex]
[tex] \dfrac{3x}{15} + \dfrac{5x + 20}{15} = 4 [/tex]
[tex] \dfrac{8x + 20}{15} = 4 [/tex]
[tex] 8x + 20 = 60 [/tex]
[tex] 8x = 40 [/tex]
[tex] x = 5 [/tex]
What is 5/8 ± 2/5? Please Help easy points
Answers
In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.
Answers
See attached image.
For this case what you should see is that you have two similar triangles.
We then have the following relationship:
((AB) / (BX)) = ((CD) / (DX))
We cleared CD:
CD = ((AB) / (BX)) * (DX)
Substituting the values:
CD = ((12) / (5)) * (2.5)
CD = 6
Answer:
CD = 6
A Hummingbird moves its wings at a rate of 5520 wingsbeats a minute. Write this rate in wingbeats per second?
Answers
The required rate of wingbeats per second is 92.
A Hummingbird moves its wings at a rate of 5520 wingsbeats a minute. Write this rate in wingbeats per second?
Rate of change is defined as the change in value with rest to the time is called rate of change.
given rate = 5520 wingsbeats a minute.
now to convert it in seconds divide it by 60
= 5520/60
= 92 wingsbeats a second
Thus, The required rate wingbeats per second is 92.
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Answers please???????
Answers
.. A = b*h
.. 10*h = 9.8*5.6
.. h = 9.8*5.6/10
.. h = 5.488
On a trip, you had to change your money from dollars to British pounds. You got 560 pounds for 800 dollars. How many pounds will you get for 300 dollars?
Answers
According to the Rational Root Theorem, which statement about f(x) = 12x3 – 5x2 + 6x + 9 is true? Any rational root of f(x) is a multiple of 12 divided by a multiple of 9. Any rational root of f(x) is a multiple of 9 divided by a multiple of 12. Any rational root of f(x) is a factor of 12 divided by a factor of 9. Any rational root of f(x) is a factor of 9 divided by a factor of 12.
Answers
Answer:
Any rational root of f(x) is a factor of 9 divided by a factor of 12.
Step-by-step explanation:
Given:
f(x) = 12x³– 5x² + 6x + 9
Required; Rational root of f(x)
The rational root theorem states that: each rational solution
x = p⁄q, written in lowest terms so that p and q are relatively prime
Where
p = factors of the constant
q = factors of the lead coefficient.
Given that
f(x) = 12x³– 5x² + 6x + 9
The constant is 9
And the lead coefficient is 12
The factor of these two are
9; ±1 , ±3, ±9
12: ±1, ±2, ±3, ±4, ±6, ±12
Then the rational root of f(x) is
factor of 9 divided by a factor of 12.
Possible Rational Roots
= (±1 , ±3, ±9) / (±1, ±2, ±3, ±4, ±6, ±12)
The correct statement according to the rational root theorem is
The rational root of f(x) is
factor of 9 divided by a factor of 12
Help please !!!!!!!!!!!!!!!!!???!?
Answers
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The idea is to go through each answer choice and see if that value is in the range. To do so, draw a horizontal line from that value at the y axis and see if it crosses the graph.
So for example, for choice A, we draw a horizontal line through -2 on the y axis. You'll see that the horizontal line crosses the green part of the piecewise function graph. So y = -2 is in the range. Similar situations will happen for B and C as well.
The only time that this doesn't happen is when y = 5. Draw a horizontal line through 5 on the y axis. This horizontal line is too high to cross through any part of the piecewise function. So y = 5 is not in the range.
Which is why the answer is choice D
Find the value of y for which line a is parallel to line b
38
52
76
142
Answers
1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
2. "D" and "x" are congruents, because they are Alternate Interior angles, so x=38º.
3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
76º+38º+B=180º
B=180º-76º-38º
B=66º
4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
The opposite angles are: 76º and 66ª. Then, we obtain:
y=76º+66º
y=142º
Therefore, the answer is: The value of y is 142º.
Cody graphed a quadratic equations, y = -(x+3)^2 + 1. What were cody's mistakes?
Answers
The vertex of cody's graph was ploted in x = 3, where it should be x = -3
This changes the position of the parabola
Answer:
the answer is d
Step-by-step explanation:
The vertex and the axis of symmetry are graphed incorrectly.
The digits 8,7,6,5,4,3,2,1 are written in a pattern over and over again. what will be the 5479th digit
Answers
The 5479th digit is 2.
What is Division?One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation can be used to quickly and easily fix such issues. In this case, we must divide 30 by 5.
given:
8 digits written in that same order ( 8,7,6,5,4,3,2,1 ) over and over again
So, we have to find 5479th digit
= 5479/8
= 684 7/8
Now, The 684 quotient tells us how many complete times the sequence goes through the cycle of 8,7,6,5,4,3,2,1, and the 7 remainder tells us which member of the cycle is the 5479 digit.
Since the 7th member of the cycle is 2.
Hence, the 5479th digit is 2.
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How to find common difference of arithmetic sequence given first and last term?
Answers
Find the common difference of an arithmetic progression whose first term Is 1 and last term is 1023...
First term = T¹ =a
Last term = Tn = a + (n-1)d
Since your given the values of the first and the last term... You can substitute
Tn = 1 + (1023-1)d
1023 = 1 + 1022d
1022d = 1023 - 1
1022d = 1022
common difference = 1...
So there is a way....
You can get the common difference using the two terms given...
Hope this helped...
To find the common difference, subtract the first term from the last term and divide by the number of terms minus 1.
Explanation:To find the common difference of an arithmetic sequence given the first and last term, you can use the formula: common difference = (last term - first term) / (number of terms - 1). First, subtract the first term from the last term. Then, subtract 1 from the number of terms. Finally, divide the result of the subtraction by the number of terms minus 1 to find the common difference.
how many bricks 3.75 in wide times wide x 8 in long are required to cover a patio 13 ft. 6 in wide by 18. 9 ft long
Answers
13 x 12 = 156
156+6 = 162
18.9 x 12 = 226.8
226.8 x 162 = 36741.6 in (patio size)
36741.6 / 30 = 1224.72
You need 1224.72 bricks
(or round to 1225)
Anybody have a correct answer?
Answers
The formula for the Lateral Area of Square-based Pyramid
L.A = [tex] \frac{1}{2} [/tex] (Perimeter of the base) x Apothem
Given:
Apothem = 10 in
Side length = 5 in
Perimeter of Square = 4 x side = 4 x 5 = 20 in
L.A = [tex] \frac{1}{2} [/tex] (20)(10)
= [tex] \frac{1}{2} [/tex] (200)
= 100 in²
Answer:
100
Step-by-step explanation:
Please HELP NEEDED ASAP APPRECIATED !! Brainlestwill be given
Answers
sqrt(x) = x^(1/2) so
(x^(1/2) )^5 = x^(5/2)
The answer closest to the bottom of the page <<<<===== answer.
A local store buys used video games. For each game bought, they will pay $18 less than the original price paid for the game. Which expressions represent the total amount Jordan will receive if he sells “n” games that originally cost “d” dollars each? Check all that apply.
Answers
Answer:
B. [tex]n(d-18)[/tex]
D. [tex]dn-18n[/tex]
Step-by-step explanation:
Let d represent the original price paid for the game.
We have been given that a local buys used video games. For each game bought, they will pay $18 less than the original price paid for the game.
The price of used video game would be original price minus 18. We can represent this information in an expression as:
[tex]d-18[/tex]
We have been given that Jordan sold n games, so the cost of n used games would be [tex]n(d-18)[/tex].
Using distributive property we will get,
[tex]n(d-18)=dn-18n[/tex]
Therefore, option B and D are correct choices.
HELP FAST PLEASE
A six-feet-tall man looks off the roof of a five-story hotel. He sees a statue that is 75 ft. away from the hotel. If he is looking at the base of the statue, what angle does his sight line form with the side of the hotel? Assume that each complete story of the hotel is 12 ft. tall.
32.6 degrees
43.9 degrees
48.7 degrees
54.2 degrees
Answers
Answer: 48.7 degrees
Step-by-step explanation:
Let [tex]\theta[/tex] is the angle between the his sight line form with the side of the hotel,
Since, the building is of 5-story and a men having height 6 feet is in the fifth-story.
Thus, the total length from the eyes of the man and foot of the building = 6 + 12 × 5 = 6 + 60 = 66 feet
Also, the distance of the statue from the foot of the building = 75 feet.
Then by the below diagram,
[tex]tan\theta = \frac{75}{60+6}[/tex]
[tex]tan\theta = \frac{75}{66}[/tex]
[tex]\theta=48.6522227803\approx 48.7\text{ degree}[/tex]
BRAINLIESTTT ASAP!!!!
Answers
The 1st selection is appropriate.
Ciara solved the exponential equation 3x+1 = 15 and her work is shown below. What is the first step she did incorrectly? (3 points) Step 1: log 3x+1 = log15 Step 2: (x + 1)log 3 = log15 Step 3: log3 = log 15 over x plus 1 Step 4: 0.477121 = 1.176091 over x plus 1 Step 5: 0.477121(x + 1) = 1.176091 Step 6: x + 1 = 1.176091 over 0.477121 Step 7: x + 1 = 2.464975 Step 8: x = 1.464975
Answers
Answer:
The Answer is Step 3. I took the test :)