Graph the polygon and its image after a dilation centered at C(1,1)
with scale factor k=0.5
.
J(3,1), K(5,−3), L(5,5), M(3,7)
Answers
Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.
DIlations are defined by the follwing operation:
[tex]P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation.[tex]k[/tex] - Dilation factor.[tex]P(x,y)[/tex] - Original point of the polygon.[tex]P'(x,y)[/tex] - Dilated point of the polygon.If we know that [tex]O(x,y) = (1,1)[/tex], [tex]k = 0.5[/tex], [tex]J(x,y) = (3,1)[/tex], [tex]K(x,y) = (5, -3)[/tex], [tex]L(x,y) = (5,5)[/tex] and [tex]M(x,y) = (3,7)[/tex], then the coordinates of the new polygon are:
[tex]J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)][/tex]
[tex]J'(x,y) = (1,1)+0.5\cdot (2,0)[/tex]
[tex]J'(x,y) = (1,1) +(1,0)[/tex]
[tex]J'(x,y) = (2,1)[/tex]
[tex]K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)][/tex]
[tex]K'(x,y) = (1,1) +0.5\cdot (4,-4)[/tex]
[tex]K'(x,y) = (1,1) +(2,-2)[/tex]
[tex]K'(x,y) = (3,-1)[/tex]
[tex]L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)][/tex]
[tex]L'(x,y) = (1,1) + 0.5\cdot (4,4)[/tex]
[tex]L'(x,y) = (1,1) + (2,2)[/tex]
[tex]L'(x,y) = (3,3)[/tex]
[tex]M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)][/tex]
[tex]M'(x,y) = (1,1) +0.5\cdot (2,6)[/tex]
[tex]M'(x,y) = (1,1) +(1,3)[/tex]
[tex]M'(x,y) = (2,4)[/tex]
Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.
We kindly invite to check this question on dilations: https://brainly.com/question/13176891
Related Questions
The sum of the ages of a woman and her
son is 64 years. In 4 years time the woman
will be three and half times as old as her
son. How old were they three years ago?
Answers
Step-by-step explanation:
sorry for my ugly handwriting, hope it helps
Please help ASAP!! I am in desperate need and please don’t just do this for points
Answers
Answer:
[tex]106 yd^2[/tex]
Step-by-step explanation:
Answer is attached. Let me know if you would like another explanation that would yield the same solution.
the ratio of adult to children in the spot club is 5:3 There are 120 people in the club. how many children are there
Answers
Answer:
5:3=8
3/8 x 120
3/1 x 15
3 x 15=45
Step-by-step explanation:
hope this helps
sorry
3x+5x=120
Then combine like terms
8x=120
Divide 8 by both sides
x=15
Now that we have that we can figure out how many children and adults there are
Children: 3x15=45 children
Adults: 5x15=75 adults
Also, you can type this in your calculator for a faster method
Children : 120 x(3/8) =45
because eight is the sum of the ratio 5+3
And Adults : 120 x(5/8)=75
So the answer to your question is 45 children.
Hope this helps!!!
Are the ratios 2:3 and 8:12 equivalent? Justify you answer.
Answers
Answer:Yes
Step-by-step explanation:You are multiplying the ratios by 4
Which figure in the drawing best represents a dilation of figure A with a scale factor of 1.5?
A.r
b.q
c.s
d.t
Answers
please help!!
solve for x
Answers
Answer:
4
Step-by-step explanation:
These both angles are vertically opposite angles. And, vertically opposite angles are equal. So,
→ 5x ― 6 = 3x + 2
→ 5x ― 3x = 2 + 6
→ 2x = 8
→ x = 8/2
→ x = 4
Therefore, the value of x is 4.
What is 968.1 as a fraction
Answers
I believe it is 9681/10.
Answer:
the answer is 9681/10
Step-by-step explanation:
9681/10
Which of the following is not an advantage of renting? a. Ease of mobility b. Fewer responsibilities c. Lower initial costs d. Restricted lifestyle Please select the best answer from the choices provided A B C D.
Answers
A restricted lifestyle is not an advantage of renting.
Option D is the correct answer.
What is renting?Renting a property has several advantages, such as ease of mobility, fewer responsibilities, and lower initial costs.
We have,
Ease of mobility is an advantage because it is easier for renters to move to a new location since they are not tied down to a specific property.
Fewer responsibilities are another advantage because the landlord is usually responsible for maintaining the property, making repairs, and paying for utilities.
This means that renters do not have to worry about these tasks or expenses.
Lower initial costs are also an advantage because renters do not have to pay for a down payment or closing costs, which can be a significant expense when purchasing a property.
A restricted lifestyle is not an advantage of renting.
This is because renters may be limited in terms of decorating, making changes to the property, or having pets.
Renters may also have to abide by certain rules set by the landlord or property management company.
This can limit their freedom and personalization of the space.
Thus,
A restricted lifestyle is not an advantage of renting.
Learn more about renting here:
https://brainly.com/question/26268428
#SPJ5
plz help me 3x+87 i really need help
Answers
Answer:
3 ( x + 29 )
Step-by-step explanation:
The best I can do is factor them, hope it helps!
Help please I’m going to be in big trouble
Answers
Assessment started: undefined.
Item 1
Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21?
Select each correct answer.
(−1, −6)
(−3, 3)
(11, 3)
(7, 0)
Answers
On a trip, you see a large, sphere-shaped house. The volume of the house was 3,367,575 cubic feet. What is the radius? Use 3.14 to approximate pi. Round your answer to the nearest whole number.
Answers
Answer:
r≈93
Step-by-step explanation:
V=4/3πr³
3,367,575=4/3(3.14)r³
3,367,575=314/75r³
multiply both sides by 75/314
804357 27/314=r³
∛804357 27/314=∛r³
r≈93
The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean Mu and standard deviation Sigma. According to the Empirical Rule, what percentage of the bags will have weights within 3 standard deviations of the mean? 47. 5% 68% 95% 99. 7%.
Answers
Evaluate the expressions. Show your thinking.
10/25 x 10
Answers
Answer:
4
Step-by-step explanation:
[tex]\frac{10}{25}[/tex] × 10
[tex]\frac{100}{25}[/tex]
4
Some spiders, dragonflies, and houseflies are kept in three separate enclosures. They have a total of 20 heads, 136 legs, and 19 pairs of wings.
Given that...
a spider has 8 legs and 0 pairs of wings
a dragonfly has 6 legs and 2 pairs of wings
a housefly has 6 legs and 1 pair of wings
Find the number of spiders, the number of dragonflies, and the number of houseflies.
Answers
Answer:
Number of Spiders: 8
Number of Dragonflies: 7
Number of Houseflies: 5
Step-by-step explanation:
s= spider
d= dragonfly
h= housefly
Heads:
20= s+d+h
Legs:
136= 8s+6d+6h
Wings:
19= 0s+2d+1h
Solve with substitution.
Divide the second equation by 2.
136= 8s+6d+6h
68= 3d+3h+4s
Set the last equation in terms of d.
19= 0s+2d+1h
d= [tex]\frac{19}{2} -\frac{1}{2}h[/tex]
Substitute what we just found (d) into the first and our new second equation. Simplify.
20= s+d+h
20= s+[tex]\frac{19}{2} -\frac{1}{2}h[/tex]+h
h+2s=21
68= 3d+3h+4s
68= 3([tex]\frac{19}{2} -\frac{1}{2}h[/tex])+3h+4s
3h+8s=79
Take both simplified equations and solve with elimination. Do this by multiplying the top equation by negative 3.
h+2s=21
3h+8s=79
-3h-6s=-63
3h+8s=79
2s=16
s=8
Plug in s=8 into the other equation.
h+2s=21
h+2(8)=21
h=5
Plug in h=5 into the last equation we rewritten.
[tex]d= \frac{19}{2} -\frac{1}{2} h[/tex]
[tex]d=\frac{19}{2} -\frac{1}{2}(5)[/tex]
d=7
(d,h,s)= (7,5,8)
Select the correct answer.
Which expression is equivalent to 27x^4/x^2? Assume that the denominator does not equal zero.
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The equivalent expression is ~
[tex] \boxed{27 {x}^{2} }[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve ~
[tex] \dfrac{27 {x}^{4} }{ {x}^{2} } [/tex][tex] \dfrac{27 \times x \times x \times x \times x}{x \times x} [/tex][tex]{27 \times x \times x}[/tex][tex]27 {x}^{2} [/tex]Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem. A ball is thrown upward from a height of 1.2 m at an initial speed of 58 m/sec. Acceleration resulting from gravity is -9.8 m/sec^2. Find the following:
v(t)= _________
h(t)= ________
Answers
If v(t) and h(t) denote the ball's velocity and height at time t, respectively, then we have h(0) = 1.2 m and v(0) = 58 m/s.
The ball is in free fall after being tossed, so its acceleration is constant at any time t :
[tex]a(t) = -9.8 \dfrac{\rm m}{\mathrm s^2}[/tex]
By the fundamental theorem of calculus, the velocity function is given by
[tex]\displaystyle v(t) = v(0) + \int_0^t a(u) \, du[/tex]
Compute the integral:
[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) \int_0^t du[/tex]
[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t - 0)[/tex]
[tex]\displaystyle \boxed{v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t}[/tex]
Similarly, the height function is given by
[tex]\displaystyle h(t) = h(0) + \int_0^t v(u) \, du[/tex]
[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \int_0^t \left(58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t\right) \, du[/tex]
[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) (t - 0) - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t^2 - 0^2)[/tex]
[tex]\displaystyle \boxed{h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) t - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t^2}[/tex]
Answer:
V(t) = 58-9.8t
h(t)=1.2+58t-4.9[tex]t^{2}[/tex]
Step-by-step explanation:
Using the standard formula
a=V f-Vi/t --rearrange
at=V f-Vi
V f=V i + a t
therefore
V(t)=58-9.8t
same with height
H= Hi+Vit+1/2at^2
therefore
h(t)=1.2+58t-4.9t^2
What is 20 dived by 5 +19-6
Answers
Answer:
17
Step-by-step explanation:
20 divided by 5 + 19 - 6
20 divided by 5 = 4
4 + 19 = 23
23 - 6 = 17
the person who answes my question can u stay because i have more thankyou
Answers
Answer:
c. 60 mins
Step-by-step explanation:
12 * 5 = 60
15 * 4 = 60
100 POINTS PLEASE
PLEASE BRAINLIEST
Answers
Here
NB||NAShow sum of interior angles is 180°
[tex]\\ \sf\longmapsto <NBA+<NAB=180[/tex]
[tex]\\ \sf\longmapsto <NAB+103=180[/tex]
[tex]\\ \sf\longmapsto <NAB=180-103[/tex]
[tex]\\ \sf\longmapsto <NAB=77°[/tex]
Vertical angles are supplementary
We need m<NAB
180-m<NBA180-10377°Katrice wrote the numbers 137 and 174. Which sentence is true about the digit 7 in each number?
The 7 in 137 represents ten times the 7 in 174.
The 7 in 174 represents ten times the 7 in 137.
The 7 in 137 represents one hundred times the 7 in 174.
The 7 in 174 represents one hundred times the 7 in 137.
Answers
Answer:
The 7 in 137 represents ten times the 7 in 137 (the second option)
Step-by-step explanation:
The seven in 137 equals 7
The seven in 174 equals 70
7 times 10 = 70
I hope this helped!
What does Point P on the number line represent? (Use the hyphen for negative numbers, such as −9) Number line from negative 8 to positive 8 in increments of 1 is shown. Only the even numbers are labeled. A point labeled P is placed at the seventh tick mark to the left of 0. Numerical Answers Expected!
Answers
Answer:
-7
Step-by-step explanation:
there are 16 increments in total, and half are labeled
so the answer is -7 because if the increments are 1 and it is left of zero, so do 7*-1 because it is to the left
Answer:
-7
Step-by-step explanation:
Please help I do not understand
Answers
Answer:
-3/7
Step-by-step explanation:
Hi,
First of all, we know that the slope is not undefine because both the x-coordinates are not the same.
To find the slope, do change in y/change in x. Here, it would be ((2/7)-(5/7))/(2-1) or (-3/7)/1. Hence, the slope is -3/7.
i need help in this math
Answers
Answer:
2
Step-by-step explanation:
Plug in 3 for the a's and -2 for the b's:
[tex]-2^{2} -(-2 + 3(3)) + 3 = ?[/tex]
Then simplify:
[tex]4 - (-2 + 9) + 3 = ?[/tex]
remember to add 1 as a placeholder if the sign before the parenthesis is a minus:
[tex]4 + 4 - 9 + 3 = ?[/tex]
Solve:
[tex]4 +4 -9+3=2[/tex]
slope = -5/2,y-int=2
Answers
Answer:
Step-by-step explanation:
The equation of this line is:
y = -5/2 x + 2.
I'M CONFUSED can anyone explain how to solve/do this ?
Answers
Answer:
The pantograph is spring-loaded and pushes a contact shoe up against the underside of the contact wire to draw the current needed to run the train. As the train moves, the contact shoe slides along the wire and can set up standing waves in the wires which break the contact and degrade current collection.
Step-by-step explanation:
Can someone help me solve this integral plsss?
integral of (2xˆ3+3xˆ2+x)/(xˆ2+1) dx
Answers
PLEASE HELP IT’S DUE TMR!!
Answers
Answer:
see below
Step-by-step explanation:
just reduce to 3 digits before the decimal place and count how many are behind the decimal for what power the 10 is, not including numbers that were already behind the decimal
a. 107.92*10^2
b. 376.932*10^0
c. 998.461*10^3
Answer:
When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.
Step-by-step explanation:
(a) 10792 ≈ 10800
(b) 376.932 ≈ 377
(c) 998461 ≈ 998000
Why is all the answers on this website saying my work is wrong.
Answers
Answer:
you're wrong
Step-by-step explanation:
should have been "Why are all the answers on this website saying my work is wrong?"
Please show work, I have no idea how to do this
Answers
Answer:
161 Remainder 4
Step-by-step explanation:
trust me on this
Answer:
_
161.2 BUT if with remainder it is 161 with a remainder of 4
Step-by-step explanation:
By the way the 2 is a repeating number so make sure to add that line at the top.