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2 is the scale factor of the dilation of figure ABCD
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
The scale factor of a dilation is a number that represents how much a figure's size alters following a dilation. It is the ratio of similar sides' lengths in the original and dilated figures.
A figure is stretched or extended if the scale factor is larger than 1, and lowered or shrunk if it is less than 1. If the scale factor is 1, the dilation has no effect on the figure; if it is less than 1, the figure is reflected beyond the line of dilation.
The scale factor is represented by the symbol k, and its value may be determined using the formula below:
k = Length of the corresponding side in the dilated figure / Length of the corresponding side in the original figure.
On the given figure,
Before dilation the measurement of the side AD = 1 unit.
After dilation the measurement of the same side = 2 units
Thus, from the formula
k = 2/1
k=2
Therefore, The scale factor of the dilation of Figure ABCD is 2.
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Related Questions
which transformations are needed to change the parent some function to the sine function below?
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Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Solution:
the function y = sin x, which would have range from -1 to 1 and period of 2pi:
So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2
Greg has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs on it. What is \text{P(not a rap song})P(not a rap song)P, left parenthesis, n, o, t, space, a, space, r, a, p, space, s, o, n, g, right parenthesis?
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We have been given that Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs.
Therefore, total number of songs are
[tex]666+777+999\\ =2442[/tex]
The formula for probability is given by
[tex]P(E)=\frac{n(E)}{n(s)}[/tex]
Let us first find the probability for rap song
[tex]P(\text{rap song})= \frac{999}{2442} \\ P(\text{rap song})= \frac{9}{22}[/tex]\\
Therefore, we have
[tex]P(\text{ not rap song})=1- P(\text{rap song})\\ \\ P(\text{ not rap song})=1-\frac{9}{22} \\ \\ P(\text{ not rap song})=\frac{13}{22} =0.59[/tex]
Hence, we have
P(not rap song)=0.59
y = x3 - 3x On which intervals is this function increasing?
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x ∈ (-∞, -1) ∪ (1, ∞)
What is the similarity ratio of the smaller to the larger similar pyramids? Enter your answer as a:b
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Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
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Factor \2x^2-11x+5=0
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2x² - x - 10x + 5
x(2x - 1) - 5(2x - 1)
(2x - 1)(x- 5) is your answer.
The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.
Explanation:The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.
We rewrite the middle term using these two numbers and then group the terms to factor by grouping:
[tex]2x^2[/tex]- 10x - x + 5 = 0([tex]2x^2[/tex]- 10x) - (x - 5) = 0
2x(x - 5) - 1(x - 5) = 0
(2x - 1)(x - 5) = 0
The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.
fresh raspberry contain 80% water.Dried raspberry contain only 20%.how many pounds do you get from 36lb fresh berries
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1 % water = 36 ÷ 80 = 0.45 lb
20% water = 0.45 x 20 = 9 lbs
Answer: You will get 9 lbs of raspberry.
The amount of fresh berries that contain 80% water is 7.2 pounds.
Amount of water in fresh raspberry = 80%
It means the amount of raspberry only in a fresh raspberry =20%
Amount of water in dry raspberry =20%
What is a percentage?A percentage is a value per hundred.
So, the amount of raspberry only in 36 lbs fresh berries = 20% of 36
20% of 36 = (20/100)*36 = 7.2 lbs
So, the amount of raspberry only in 36 lbs of fresh berries = 7.2 lbs
Therefore, we get 7.2 lbs from 36lb fresh berries.
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In the number 7,777.777, how does the 7 in the hundreds place compare to the 7 in the place to its left?
A.
The 7 in the hundreds place represents of what the 7 to its left represents.
B.
The 7 in the hundreds place represents 10 times what the 7 to its left represents.
C.
The 7 in the hundreds place represents of what the 7 to its left represents.
D.
The 7 in the hundreds place represents 100 times what the 7 to its left represents.
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hgfgjdhsghdfg
After a comparison of the number 7 which is at hundreds of places to the number 7 left off it, it is 10 times of what the 7 to its left represents. Hence, option B is correct
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data provided in the question,
The given number is 7,777.777
Now, we have to compare the number 7 which is at the hundreds place with the 7 in the place left to it.
So, the 7 which is left to the 7 at the hundredth place will be 10 times it. Also, the 7 which is the second left to the 7 at the hundredth place is 100 times and so on it will increase like this.
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Terry uses 3 cups of pumpkin seeds to decorate the tops of 12 loaves if bread. She puts an equal amount of seeds on each loaf. How many cups of pumpkin seeds does she put on each loaf of bread?
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please help! i dont understand this.
a 25 gram sample substance that's used for drug research has a k-value of 0.1229. find the substances half-life, in days using the exponential decay formula. round your answer to the nearest tenth
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With a k-value of 0.1229, the half-life is approximately 5.6 days.
The exponential decay formula is given by:
amount remaining = initial amount × e^-(k × t)
For a substance's half-life, the amount remaining is half of the initial amount. The formula to find the half-life (t1/2) is:
t1/2 = ln(2) / k
Here, ln(2) is approximately 0.693 and k is given as 0.1229. Substituting these values in:
t1/2 = 0.693 / 0.1229 ≈ 5.64 days
Rounding to the nearest tenth, the half-life of the substance is 5.6 days.
fully expand the logarithm: log(x^3/z^5)
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Log(A/B) = logA - LogB and Alogx=log(x∧A)
Log (x³/z∧5) = log (x³) - log z∧5
=3log x - 5log z
1) Quotient Rule of Logs:
Log(A/B) = Log A - Log B
2) Power Rule of Logs:
[tex]Log(a)^{b}=b*Log(a) [/tex]
[tex]log( \frac{ x^{3} }{ z^{5} } ) \\ \\ =log( x^{3})-log( z^{5}) \\ \\ =3logx-5logz[/tex]
Q # 15 in the diagrams a || b a. Use the fiagrama o answer the question(diagrama not to scale.)
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because ∠7 + ∠4 = 180°
The correct choice is number 1
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Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is , and the probability that he goes 3 days is .
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1-.1=.9
He needs more time at 3 days so:
3 days > 2 days
The equality has to be bigger on three so It can be .46 or bigger. Yet we want concise, clear answers:
.1 (zero), .23 (two) .67 ( three)
function that has the same domain as y=2√x
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A.y= [tex] \sqrt{2x} [/tex]
B.y=[tex] \sqrt[3]{ x^{2} } [/tex]
C.y=[tex] \sqrt{x-2} [/tex]
D.y=[tex] \sqrt[3]{x-2} [/tex]
====================================================
We are given the function
y = 2 √x
The domain for the given function is this
{ x | x ≥ 0 }
The answer is A. y = √2x
In general any function that has a domain of x that is equal to or greater than 0. Some examples:
f(x) = √x - 2
f(x) = 5 √x
Answer:
The answer is A. y = √2x
Step-by-step explanation:
To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?
Answers
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We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.
The formula for the combination is given by
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be
[tex]^{50}C_6[/tex]
Using the above formula, the number of different selections are
[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]
Therefore, 15890700 different selections are possible.
graph of this ellipse
x^2 + y^2 =1
_ _
4 16
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on a game show that are 10 keys in the bag and three of the key start a car and contest in randomly choosing the key it doesn't not start the car she returned to the bag the host mixed up the back she randomly selects another key this key does not start the car either what is the probability of this no start no start outcome
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Instructions:Select the correct answer from each drop-down menu. The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is
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2x - 5< 7
2x <12
x < 6
Solve for the second inequality:
4x +10 > 6
4x > -4
x > -1
Graph these two inequalities on a number line to see that their union is the complete number line. Note that for any number of x can either be greater than negative 1 or less than 6 and can be both.
so the answer is:
range of negative infinity to infinity. required to use parenthesis
(-∞, ∞)
The net asset value of stock in a mutual fund had increased by $20 per share when an investor decided to redeem them. The investor had purchased 100 shares of the stock for $2,316 and redeemed them for $4,301. What can you conclude about the fund? a. The fund is a no-load fund. b. The offer price of the fund was $0.15 less than the net asset value when purchased. c. The offer price of the fund was $0.15 more than the net asset value when purchased. d. The offer price of the fund was $0.15 more than the net asset value when sold.
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Formula for calculating NAV:
Net Asset Value (NAV) = (Assets - Debts) / (Number of Outstanding Units)
The Net Asset Value (NAV) is the price in which you pay to buy a unit of mutual fund scheme when you invest.
hey can you please help me posted picture of question
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It has its vertex at origin and opens upwards.
The given graph is obtained by shifting the graph of x² 2 units vertically down. This vertically translation can be expressed by subtracting 2 from the parent function.
So,
F(x) = G(x) - 2
F(x) = x² - 2
Thus the correct option is A
What is the number of social security credits a worker needs to earn over his or her working lifetime to collect Social security benefits?
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The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?
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After transformation the vertex becomes at (-3,-2)
Apply axes transformation from (0,0) to (h,k)
So, the transformation rule is (x,y) → (x-h, y-k)
(h,k) will be equal (-3,-2)
∴ y=|x| ⇒ (y-(-2)) = |x-(-3)|
∴(y+2) = |x+3|
∴ y = |x+3|-2
So, the correct answer is option 2
we have that
the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]
The transformed function has the vertex at point [tex](-3,-2)[/tex]
so
the rule of the translation is equal to
[tex](x,y)------> (x-3,y-2)[/tex]
That means
The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down
therefore
the answer is
the transformed function is [tex]y=\left|x+3\right|-2[/tex]
Two thirds of the families in smithville own their own homes. The total number of home owning families there is 480. How many families live in smithville?
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(2/3)x - the number of home owning families.
At the same time, the number of home owning families is 480.
(2/3)x=480
x=480*3/2=720.
720 families live in Smithville.
The circle belowis centered at the point (-2 ,1) and has a radiusof length 3
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Answer:
Option A, (x + 2)² + (y - 1) = 9
Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.
From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9
The equation for the given circle is (x + 2)² + (y - 1)² = 9
Given the least squares regression equation, = 1202 + 1,133x, when x = 4, what does equal?
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This can be done by substituting the value of x for 4 and multiplying it by 1,133 which will eventually give you the answer of 4532.
After this step, all you have to do it add 1202 to 4532, resulting in an answer of 5734.
A line has a slope of 2 and a y intercept of (0,-4) what is the value of y when x=6
Answers
y = 2x -4
next plug in 6 for x.
y = (2x6) - 4
y = 12 - 4
And this will give us the value of y: 8.
The question is about finding the y-value of a line when the x-value is given, knowing the slope and the y-intercept. By plugging the given slope, y-intercept and the provided x-value into the formula y = mx + b, we find that y equals 8 when x equals 6.
Explanation:If we know the slope (m) of a line and the y-intercept (b), we can use the formula y = mx + b to calculate the y-value for any x-value. In the given question, the slope (m) is 2 and the y-intercept (b) is -4. If we want to find the y-value when x = 6, we can substitute these values into the formula:
y = 2*6 - 4
So, y = 12 - 4 = 8. Therefore, when x = 6, the value of y is 8.
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What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)
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Answer: (5, -9)
What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?
This is incredibly frustrating. PLEASE HELP ME
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Explanation:
Given expression:
[tex]\sum_{i=1}^{25} 2^{2i}[/tex]
When i = 1: The answer is [tex]2^{2*1}[/tex] = 4
When i = 2: The answer is [tex]2^{2*2}[/tex] = 16
When i = 3: The answer is [tex]2^{2*3}[/tex] = 64
.
.
When i = 25: The answer is [tex]2^{2*25}[/tex] = [tex]2^{50}[/tex]
Which is the series mentioned in Option C
What is the equivalent of pi over 3 radians in degrees?
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A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height? 1 s; 54 ft 2 s; 6 ft 2 s; 22 ft 1 s; 22 ft
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h = -16t2 + 32t + 6
Deriving we have:
h '= -32t + 32
Equaling to zero:
-32t + 32 = 0
We clear the time:
t = 32/32
t = 1 s
We are now looking for the maximum height:
h (1) = -16 * (1) ^ 2 + 32 * (1) + 6
h (1) = 22 feet
Answer:
The ball reaches its maximum height in:
t = 1 s
The ball's maximum height is:
h (1) = 22 feet
option: 22 ft, 1 s
Answer: 22 ft, 1 s
Step-by-step explanation: