Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by?
Answer choices:
A. 1/2
B. 2
C. 3
D.4
Answers
Given:
Endpoint of segment AB are A(0,2), B(2,3).
Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).
To find:
The scale factor of dilation.
Solution:
If a figure is dilated about the origin with factor k, then
[tex](x,y)\to (kx,ky)[/tex]
Using this rule, we get
[tex]A(0,2)\to A'(k(0),k(2))[/tex]
[tex]A(0,2)\to A'(0,2k)[/tex]
So, the image of A is A'(0,2k).
It is given that image of A is A'(0,4). So,
[tex]A'(0,2k)=A'(0,4)[/tex]
On comparing the y-coordinates from both sides, we get
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2 and the correct option is B.
Dilation involves changing the size of a line
The scale factor is 2.
From the graph, the coordinates of AB are:
[tex]\mathbf{A = (0,2)}[/tex]
[tex]\mathbf{B = (2,3)}[/tex]
The coordinates of AB are:
[tex]\mathbf{A' = (0,4)}[/tex]
[tex]\mathbf{B' = (4,6)}[/tex]
Divide A' by A or B' by B to calculate the scale ratio (k)
[tex]\mathbf{k = \frac{A'}{A}}[/tex]
So, we have:
[tex]\mathbf{k = \frac{(0,4)}{(0,2)}}[/tex]
Expand
[tex]\mathbf{k = \frac{2(0,2)}{(0,2)}}\\[/tex]
Divide
[tex]\mathbf{k = 2}\\\\\\\\[/tex]
Hence, the scale factor is 2.
Read more about scale factors at:
https://brainly.com/question/16713785
Related Questions
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find the
time that the rocket will hit the ground, to the nearest 100th of second.
y = -16x^2 + 232x + 134
Answers
Answer:
15.06 seconds.
Step-by-step explanation:
Hit Ground→Height=0
−16x^2 +232x + 134=0
PLS HELP TIMED QUESTION!!!
A quantity with an initial value of 9800 decays exponentially at a rate such that the quantity cuts in half every 6 days. What is the value of the quantity after 138 hours, to the nearest hundredth?
Answers
Answer:
About 5043.58
Step-by-step explanation:
The standard form for an exponential decay after t time is:
[tex]\displaystyle f(t)=a(r)^{t/d}[/tex]
Where a is the initial value, r is the rate decay, t is the time that has passed, and d is the amount of time it takes for 1 cycle.
The initial value is 9800. So a = 9800.
The quantity cuts in half. So, r = 1/2.
And it cuts in half every 6 days. For this question, we will convert this to hours. 6 days = 144 hours. So, we can let d = 144, where t will be in hours.
Therefore, our function is:
[tex]\displaystyle f(t)=9800\Big(\frac{1}{2}\Big)^{t/144}[/tex]
Where t is the amount of time that has passed, in hours.
Then the quantity left after 138 hours will be:
[tex]\displaystyle f(138)=9800\Big(\frac{1}{2}\Big)^{138/144}\approx 5043.58[/tex]
find the number n of hours you need to study on Saturday so that mean number of hours you study per day is 1.5
Days Hours
Sunday 0
Monday 1.5
Tuesday 2.5
Wednesday 2.5
Thursday 3
Friday 0
Sunday N
Answers
Answer:
1 hour
Step-by-step explanation:
We are given that
Day Hours
Sunday 0
Monday 1.5
Tuesday 2.5
Wednesday 2.5
Thursday 3
Friday 0
Saturday n
Mean number of hours of study per day=1.5
Mean=[tex]\frac{sum\;of\;data\;}{total\;number\;of\;data\;points}[/tex]
Total number of days=7
Using the formula
[tex]1.5=\frac{0+1.5+2.5+2.5+3+0+n}{7}[/tex]
[tex]1.5\times 7=9.5+n[/tex]
[tex]10.5-9.5=n[/tex]
[tex]n=1[/tex]
Hence, number of hours you need to study on Saturday=n=1
Geometry A. In unit 2, you learned three different criteria for proving triangle congruence: ASA, SAS, and SSS. Can you give me the summarize each of them for me? 100 POINTS
Answers
Answer:
we use the ASA when a triangle is conguerent by angle,side,angle.
SAS se when atriangle is conguerent by side,angle,side
sss when the triangle is conguerent by side,side,side
Answer:
ASA- The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
SAS- is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
SSS- If two triangles are congruent it means that all corresponding angle pairs and all corresponding sides are congruent. The SSS criterion for triangle congruence states that if two triangles have three pairs of congruent sides, then the triangles are congruent
Step-by-step explanation:
Ira bought a t-shirt that was discounted 50%. He used a coupon for 50% off at the cash register. Why was he charged $6.50 instead of $0?
Answers
50% off makes the new price half of the original, then another 50 % would be half off the discounted price, so they actually end up paying 25 % of the original price:
50 % x 50 % = 25 %
Answer:
she was charged for 50% of the 50% off
Step-by-step explanation:
Lets say the original price was 100$ The store discounted it by 50% so it is now 50$ but the coupon take 50% off of that 50 so it would be 25$
Write an equation that is parallel to y=3x+5 and passes through the point (-4,-13).
Answers
Answer:
y = 3x - 1
Step-by-step explanation:
Please let me know if you want me to add an explanation.
y = 3x + 5
m = 3 but its parallel so m =-¹/₃
y-y₁ = m (x-x₁)
y - (-13) = -¹/₃ (x-(-4) )
y + 13 = -¹/₃ (x+4)
y + 13 = -¹/₃x - ⁴/₃
y = -¹/₃x - ⁴/₃ -13
y =-¹/₃x - ⁴³/₃
what is the area of a rectangle that is 4 inches long and 1 3/4 inches wide
Answers
Answer: 7 inches
Step-by-step explanation:
4 times 1 3/4 is 7
Help ASAP!!! Very confused
Answers
Take 155-39 as 155 is the whole diagram angle, but 39 is the MKL angle. So, you subtract 39 and that gives you JKM.
Answer:
Angle JKM = ANGLE JKL - MKL
= 155 - 39
= 116
find the logarism of 6395
Answers
Answer:
this is clear that answer
can anyone give me the formula to this or how to solve it? thanks
Answers
Multiply L x h and get 86.25
Divid that number by 258 and 3/4
BOOM
The width is 3.
A rectangular prism is 3d. This means that there are three dimensions being multiplied by each other to obtain the overall volume. We can use the equation V = lwh to solve this equation, with V being volume, and the following, length, width, height. Substituting in the values (and changing the mixed numbers to improper fractions for simplicity):
1035/4 = (15/2)(23/2)(w)
w = (1035/4)(2/15)(2/23)
w = 3
2. The water rate for Charlotte, North Carolina, is $1.33 per 748 gallons of water used.
a. What is the water bill if 30,000 gallons of water are used?
b. How many gallons of water can be used for the water bill to be $150.
Answers
Answer:
I'm only here cause of the pfp haha
Step-by-step explanation:
you look good if that's you
Answer:
a) $53.34
b) 84,360.9 gallons
Step-by-step explanation:
let 'x' = cost of bill for 30,000 gallons
a) i set up a proportion as follows:
$1.33/748g = x/30,000
i cross-multiplied and got $53.34
b) i set up a proportion as follows:
let 'y' = how many gallons $150 can buy
$1.33/748g = 150/y
i cross-multiplied and got 84,360.9 gallons
Without making any calculations, which distribution of data has the largest standard deviation?
1, 1, 1, 1, 4, 4, 7, 7, 7, 7
1, 1, 1, 4, 4, 4, 4, 7, 7, 7
1, 1, 4, 4, 4, 4, 4, 4, 7, 7
1, 4, 4, 4, 4, 4, 4, 4, 4, 7
Answers
Answer:
#4 it makes the most sense.
Step-by-step explanation:
Sorry if i'm wrong
Answer:
It's the first one, A
Step-by-step explanation:
Plugged each one into a SD calculator, the first one is the largest
7 1/3 : 2 4/9= what does it equal?
Answers
Answer:
3/1 or 3
Step-by-step explanation:
7 1/3 = 7x3 + 1/3 =21 + 1/3 =22/3
7x3/3 = 21/3
-------------------------------------------------
2 4/9 2x9 + 4/9 = 18 + 4 /9= 22/9
2x9/9 = 18/9
Divide: 22/3 : 22/9 =22/3 x9/22 =
22/3 x 9/22 = 198/66 66/66 x 3/1 = 3
Find the curved surface area of a cylinder if it's base circumference is 36 cm and it's height is 4 cm
Answers
Answer:
CSA of a cylinder = 144cm²
Step-by-step explanation:
Given the following data;
Base circumference = 36cm
Height = 4cm
To find the curved surface area (CSA) of the cylinder;
CSA of a cylinder = 2πr * h
But 2πr = 36cm
Substituting the values into the equation, we have;
CSA of a cylinder = 36 * 4
CSA of a cylinder = 144cm²
can someone please solve this?
I'm stuck and I don't know how
Answers
Answer:
D
Step-by-step explanation:
If im inncorect you can check this with "Mathaway"
Answer: D
Hope this helps!
PLEASE HELP ME WITH GEOMETRY. I need help with this problem but I don't just want the answer, I want to know how to do it. Thank you.
Answers
Answer:
Pythagorean theorm
Step-by-step explanation:
A^2+B^2=C^2
c is the long line, a and b are the outside lines
1. The average police office writes 40 tickets each week (with a standard deviation of 12). If the number of tickets a police officer writes in a week is normally distributed, what is the probability that an officer writes more than 60 tickets in a week?
Answers
Answer:
3/5
Step-by-step explanation:
A 12-m ladder is leaning against a wall.
The foot of the ladder is 3 m from the base of
the building. How far up the wall is the top
of the ladder?
Answers
Answer:
Step-by-step explanation:
Use Pythagorean's Theorem for a right triangle. Your best bet when learning/visualizing word problems is to draw a picture, then learn how to visualize in your head over time.
[tex]3^2+x^2=12^2\\9+x^2=144\\x=\sqrt{135}[/tex]
The radical can be further simplified because 135 is the product of 9 and 15. 9 has a perfect root of 3.
[tex]x=3\sqrt{15}[/tex] meters or 11.62 meters
Kyla sold her laptop to Fely in a condition that Fely should give he a downpayment of Php8,000 and Fely will pay her Php1,000 every month for 1 year .if the money ears 0.5% compound monthly what is the market value of Fely's offer?
Answers
Find the third term of a proportional if the first, second and fourth terms are 24, 36, 126, pls help me :(
Answers
Answer:
84
Step-by-step explanation:
Let the third term be x.
So, the numbers will be:
24, 36, x, 126
Since, all the four terms are in proportion.
Therefore,
[tex] \frac{24}{36} = \frac{x}{126} \\ \\ x = \frac{24 \times 126}{36} \\ \\ x = \frac{3,024}{36} \\ \\ x = 84[/tex]
1. The average attendance at a local high school this year was 950
students. Each year the attendance decreases at a rate of 0.5% per year.
What will the average attendance be in three years? *
Answers
100% - 0.5% = 99.5% or 0.995
One year: 950 x 0.995 = 945.25 or 945 students
Two years: 945 x 0.995 = 940.5 or 941 students
Three years: 941 x 0.995 = 935.8 or 936 students :)
A set of 6 number cards contain the numbers 2, 5, 7, 8, 9, and 11. Which ratio is less than the ratio of odd number cards to total cards in this set?
Answers
Answer:
[tex]Ratio = 2:3[/tex]
Step-by-step explanation:
Given
[tex]Cards = \{2,5,7,8,9,11\}[/tex]
Required
Ratio of odd numbers to total
First, list out the odd numbers
[tex]Odd = \{5,7,9,11\}[/tex]
The card has 4 odd numbers out of a total of 6.
So, the ratio is:
[tex]Ratio = Odd : Total[/tex]
[tex]Ratio = 4:6[/tex]
Divide by 2
[tex]Ratio = 2:3[/tex]
Hence, the ratio of odd to total is 2 to 3
I need some help with this and with the other 6 question! Help this girl in need
Answers
Answer:
i think it is y=15x-6
Step-by-step explanation:
if it is correct plz plz mark as brainliest
thank you
19NBoli
Answer:
y = 2x-6
Step-by-step explanation:
Slope intercept form:
y = mx+b
m = slope
In this case the slope is 2/1 or 2.b = The point where the line crosses the y-axis
In this case -6 is the exact point the line crosses the y-axisSo if you put it all together you get the answer of:
y = 2x-6
I hope this helped!
P.S. I am so sorry I couldn't respond earlier :(
Sincerely,
Rekifromsk8theinfinity
:D
Choose the graph of the inequality x> -2
Choose 1 answer. HELPPPP
Answers
Step-by-step explanation:
step 1. x > -2 means numbers greater than -2 but not including -2.
step 2. you graph a single variable on a number line.
step 3. the graph would include an open circle above -2 (not equal to -2)
step 4. the line would go right of the open circle (greater than) and have an arrow at the end.
step 5. the answer is b.
A motor cyclist completes a journey at an average speed of 65 mph in 3½ hours. Calculate the distance travelled.
Answers
Answer:
227.5
Step-by-step explanation:
65 mhp
after 3.5 h
Just multiply
65 x 3.5 = 227.5
Answer:
227.5
Step-by-step explanation:
multiply 65 mph to 3 1/2 [3.5 (estimated)] to calculate the distanbce travelled
Explain the differences between properties of equality
and properties of inequality when solving equations and
inequalities.
Answers
Step-by-step explanation:
step 1. properties of equality have an "=" in the equation.
step 2. properties of inequality have a <, <=, >=, or a >.
The median household income in the US grew linearly from approximately $30, 000 in 1990 to $48, 000 in 2006. Let x be the number of years since 1990. Express the median income as a function of x. Use this function to approximate the median income in 2030. What is the significance of the slope of this function
Answers
Answer:
[tex]y = 1125x+30000[/tex] --- The equation
The median income in 2030 is $75000
Step-by-step explanation:
Given
Represent years since 1990 with x and the income with y.
So, we have:
[tex](x_1,y_1) = (0,30000)[/tex] --- In 1990
[tex](x_2,y_2) = (16,48000)[/tex] --- In 2006
Solving (a): Express as a function.
First, we calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{48000-30000}{16-0}[/tex]
[tex]m = \frac{18000}{16}[/tex]
[tex]m = 1125[/tex]
The equation is then calculated as:
[tex]y = m(x-x_1)+y_1[/tex]
This gives:
[tex]y = 1125(x-0)+30000[/tex]
Open bracket
[tex]y = 1125x-0+30000[/tex]
[tex]y = 1125x+30000[/tex]
Solving (b): Income in 2030.
In 2030, x = 40.
Substitute 40 for x in [tex]y = 1125x+30000[/tex]
[tex]y = 1125*40 +30000[/tex]
[tex]y = 45000 +30000[/tex]
[tex]y = 75000[/tex]
Solving (c): The significance of the slope.
In (a), the slope is calculated as 1125.
This implies that the yearly rate is $1125
0.3 - 0.04 = i need it ASAP
Answers
Can you explain to me how to solve this?
Answers
Can someone help on this please?
Answers
Answer:
The mean is 8.4
Step-by-step explanation:
First you find the class centers.
3-6 = 4.5
7-10 = 8.5
11-14 = 12.5
15-18 = 16.5
The sum of all the scores = 4.5 * 7 + 8.5 * 10 + 12.5 * 6 + 16.5 + 2 = 210
The sum of the number of scores = 7 + 10 + 6 + 2 = 25
The mean = 210/25 = 42/5 = 8.4