Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').
The dilation is therefore:
(x,y) ............> (x',y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.
Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.
Hope this helps :)
Answer:
First you have to find the ordered pairs for the shapes. Then figure out how much the pre-image was multiplied by. The number it was multiplied by is your scale value.
Step-by-step explanation:
I took the assessment. :)
A new car is purchased for 17600 dollars. The value of the car depreciates at 11.75%
per year. What will the value of the car be, to the nearest cent, after 11 years?
Answer:
The value of the car will be
4450.15
Step-by-step explanation:
we know that
11.75%=11.75/100=0.1175
so Let
x-----> the value of the car after 11 years
X=17600(1-0.1175)11=4450.15
Step-by-step explanation:
Tyrone ran the 100-meter race 3 times. His fastest time was 10.84 seconds. His slowest time was 13.52 seconds. If Tyrone's average time was 12.0 seconds, what was his time for the third race? *
Answer:
The third time = 11.64 seconds
Step-by-step explanation:
Let the average time be x
The average of a set of numbers is the sum of the numbers divided by the number of terms. In this case:
Average = (10.84 + 13.52 + x) ÷ 3 = 12.0
[tex]\frac{10.84\ + 13.52\ + x}{3}= 12.0\\\frac{24.36\ +\ x}{3} = 12.0\\cross-multiplying\\24.36\ +\ x = 3 \times 12.0\\24.36\ +\ x = 36\\x = 36 - 24.36\\x = 11.64\ seconds[/tex]
prime factorisation of 27,45 and 54
Answer:
27= [tex]3\sqrt{3}[/tex] (3 x 3 x 3)
45= [tex]3\sqrt{5}[/tex] (3 x 3 x 5)
54= [tex]3\sqrt{6}[/tex] (3 x 3 x 3 x 2)
Step-by-step explanation:
Answer:
We found the factors and prime factorization of 27 and 45. The biggest common factor number is the GCF number. So the greatest common factor 27 and 45 is 9.
Solve for the quotient 8498 / 70
Answer:
121.4 is the answer ❣️
Answer:
The answer I got is 121.4
Hi! Is there anyone good with finding the surface area of something? If so, please comment. If you do help me, I will give you 5 star every time you help.
how do i find a slope
Answer:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points
Answer:
To the find slope in slope-intercept form (y=mx+b) you just find the m of the equation for example: y=4x+8 the 4 is the slope since it is replacing the m
To find the slope in two points (x1,y1) (x2,y2) follow this formula
y2-y1/x2-x1
For example: Find the slope of (4,9) and (9,19)
19-9/9-4 Which is 10/5 simplify: 2
The slope is 2
Step-by-step explanation:
f (x) = 13[tex]\sqrt[3]{x}[/tex] power function yes or no
if yes where is k and p
Answer:
f =
x = 13 = x
k = x
p = x
Step-by-step explanation:
I really need help please :))))))
Answer:
If there were 25% fewer sunny days this year, then the answer would be 75%. This is because there are(100-25)% of the sunny days this year compared to last year.
Let me know if this helps!
Write an algebraic expression for the verbal expression
the quotient for 45 and r
Answer:
45/r
Step-by-step explanation:
You're just doing 45 divided by r.
Loan: Ross borrows $5625 to buy a car. He pays back $125 each month. The equation y = 5625 - 125x represents that amount Ross owes y after x months.
A. Find the x and y-intercepts and interpret their meaning in the context of the situation.
The x-intercept is _____. This means that after ____ months, Ross will owe $____. The y-intercept is _____. This means that Ross initially owed $_____.
B. Graph the equation using the intercepts.
Answer:
Ross initially owed 5625. the y intercept is 0,3500. Part of the answer.
There are x and y-intercepts that would be 5625 and 45 respectively for the given equation.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Ross borrows $5625 to buy a car. He pays back $125 each month which is given in the question.
The equation y = 5625 - 125x represents the amount Ross owes y after x months
⇒ y = 5625 - 125x
To determine the y-intercepts of the equation,
We have to substitute x = 0 in the equation
⇒ y = 5625 - 125(0)
⇒ y = 5625
To determine the x-intercepts of the equation,
We have to substitute y = 0 in the equation
⇒ 0 = 5625 - 125x
⇒ 125x = 5625
⇒ x = 45
Hence, there are x and y-intercepts that would be 5625 and 45 respectively for the given equation.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ2
Pllssss helppppp thank u
Which sentence states the author’s point of view of microloans?
A.They help people, not communities.
B.They can change people’s lives for the better.
C.They need to be changed in order to work correctly.
D.They should be paid back quickly to make a difference
Answer:
B
Step-by-step explanation:
It is right
Can someone explain me how to do this? No answers, just explanation how to solve. Click on the picture to see the question.
Answer:
800 cm
Step-by-step explanation:
x = height of lamp post
set up a proportion:
90/160 = 450/x
cross-multiply:
90x = 72000
x = 800
Answer:
Since you did not want the answer the things you need to solve this question are below.
Step-by-step explanation:
In order to solve this, you will need to read about the scale factor. Here is a picture telling about it briefly.
You would like to start your own business in Hempstead. You borrow
$10,000 form the bank at a 9% rate for 5 years. How much interest
will you pay on this loan?
Answer:
$ 4,500.00
Step-by-step explanation:
I = $ 4,500.00
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 9%/100 = 0.09 per year,
then, solving our equation
I = 10000 × 0.09 × 5 = 4500
I = $ 4,500.00
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 9% per year
for 5 years is $ 4,500.00.
if cos theta + sin theta = root 2 cos thetha prove that cos theta - sin theta = root 2 sin theta
Answer:
We have:
If:
Cos(θ) + Sin(θ) = √2*cos(θ)
We want to prove that:
Cos(θ) - Sin(θ) = √2*Sin(θ)
Well, let's start with the first relation:
Cos(θ) + Sin(θ) = √2*cos(θ)
Now we can subtract 2*Sin(θ) and we will get:
Cos(θ) + Sin(θ) - 2*Sin(θ) = √2*cos(θ) - 2*sin(θ)
Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)
Now, we also can rewrite the first equation as:
Cos(θ) + Sin(θ) = √2*cos(θ)
Cos(θ) - √2*cos(θ) = - Sin(θ)
Cos(θ)*( 1 - √2) = -Sin(θ)
Cos(θ) = -Sin(θ)/( 1 - √2) = Sin(θ)/(- 1 + √2)
We can replace this in the right side of theequation:
Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)
Cos(θ) - Sin(θ) = √2* Sin(θ)/(- 1 + √2) - 2*sin(θ)
Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)
Now we have this:
√2/(- 1 + √2)) - 2 = a
if we multiply all by (-1 + √2) we get:
√2 - 2*(-1 + √2) = a*(-1 + √2)
√2 + 2 - 2*√2 = a*(-1 + √2)
2 - √2 = a*(-1 + √2)
√2*(√2 - 1) = a*(-1 + √2)
√2*(√2 - 1)/(-1 + √2) = a
√2 = a
Then:
√2/(- 1 + √2)) - 2 = √2
If we replace this in the equation:
Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)
We get:
Cos(θ) - Sin(θ) = √2*Sin(θ)
Which is the thing we wanted to get.
Please find attached herewith the solution of your question.
If you have any query, feel free to ask.
Graph quadrilateral abcd whose vertex matrix is shown below. Then graph the dilation of quadrilateral abcd with a scale factor of 3 on the same coordinated grid. Quadrilateral abcd with vertex matrix -1 5 5 -4
2 5 3 -1
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation is reflection, translation, rotation and dilation.
Dilation is the increase or decrease in size of an object.
Given the vertex matrix of quadrilateral ABCD as:
[tex]\left[\begin{array}{cccc}-1&5&5&-4\\2&5&3&-1\end{array}\right][/tex]
Therefore the vertex of quadrilateral ABCD is at A(-1, 2), B(5, 5), C(5, 3) and D(-4, -1).
Quadrilateral ABCD is dilated by a scale factor of 3 to produce quadrilateral A'B'C'D'.
Hence, the vertex matrix of quadrilateral A'B'C'D' is:
[tex]3\left[\begin{array}{cccc}-1&5&5&-4\\2&5&3&-1\end{array}\right]=\left[\begin{array}{cccc}-3&15&15&-20\\6&15&9&-3\end{array}\right][/tex]
Therefore the vertex of quadrilateral A'B'C'D' is at A'(-3, 6), B'(15, 15), C'(15, 9) and D'(-20, -3).
The correct option is figure A
what is the cheapest way to buy 48 cans of cola
Answer:
both the first one
Step-by-step explanation:
use unit rate
Work out the surface area of this cylinder radius 2cm and height 4cm pls help
Step-by-step explanation:
surface area of cylinder is
2×pi×r (h+r)
2×22/7×2 (4+2)
88/7 (4+2)
75.4 cm square
There is a line that includes the point (9, 1) and has a slope of -8. What is its equation in
point-slope form?
Answer:
y - 1 = -8(x -9)
Step-by-step explanation:
Point-slope form is y - y1 = m(x - x1) given a point (x1, y1) on the line and slope m. Plug all the values in and this is the answer.
The triangles are congruent by
1. AAS
2. ASA
3. SSS
Answer:
the triangles are congruent by ASA.
9 is 25% of what number
How many 0.8 liter glasses can be filled by a 6.8 liter pitcher?
Answer:
8.5 glasses
Step-by-step explanation:
6.8L / 0.8L = 8.5 glasses
Answer:
8 glasses
Step-by-step explanation:
You divide [tex]6.8/0.8[/tex]
This gives you 8.5 glasses
since 9 glasses is too much, at 7.2 liters. The maximum glasses possible is 8 assuming you're not filling a half of the glass which would be 8.5 glasses.
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer:
816 square feet
Step-by-step explanation:
13(16+20+12) + 16(12) = 816
students plan to decorate the schools flagpole with strings of lights. one end of each string of lights will be attached to the top of the flagpole, and the other end will be attached to the ground.
which measurement is closest to the length of one string of lights in feet?
Answer: D
Step-by-step explanation:
♡ The Question/Task ♡
-What is the mean absolute deviation of her quiz scores?
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
-I believe the answer should be, 17!
I apologize in advance if this is incorrect! ♡
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
-No Explanation/Step-By-Step Provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-No Tips Provided!
I need help with this fast i apericiatte it
Answer:
13/12
Step-by-step explanation:
Answer:
12/13
Step-by-step explanation:
remember it's adj/hyp so it would be 36/39. When simplified it becomes 12/13.
Please help, I would appreciate it thank you :)
Answer:
HERE IS YOUR ANSWER FRIEND,HOPE IT HELPED YOU,PLEASE MARK ME AS BRAINLISTheight (inches) 8 2 02 0.4 0.6 0.8 time (seconds) The graph represents the height of a frog's jump as a function of time. What is the average rate of change across the interval 0.4x
Answer:
x-2y = 8
-2y = -x + 8
y = x/2 - 4
y intercept: (0, -4)
slope: 1/2
3x-2y = 12
-2y = -3x + 12
y = 3x/2 - 6
y intercept: (0, -6)
slope: 3/2
I assume I would graph with the following points (0,-4) and (4,0) for the second one I assumed I would graph the following points (0,-6) (6,0). I think I have confused the actual points in which I am to graph. Could you please tell me if I am graphing the correct points? I do not have the ISBN for this book becasue it is an online class. Thanks and have a great day!!
Step-by-step explanation:
Simplify each expression by combining like terms
a). x + 2x
b). 3m + 4n - 6n
Answer:
1) 3x
2) 3m - 2n
Answer:
below
Step-by-step explanation:
3x, 3 m − 2 n
aNoThEr qUeStiOn tO bRiNg mY gRaDeS uP // Ill mark brainliest ^^
Answer:
[tex]\boxed {\boxed {\sf b=60 \ meters}}[/tex]
Step-by-step explanation:
This is a right triangle because of the small square in the corner representing a 90 degree angle.
Therefore, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
80 and b are the legs, because they form the right angle. 100 is the hypotenuse because it is opposite the right angle.
[tex]a=80 \\b=b \\c=100[/tex]
[tex](80)^2+b^2=(100)^2[/tex]
Solve the exponents.
(80)²=80*80= 6400 (100)²= 100*100= 10000[tex]6400+b^2=10000[/tex]
Solve for the unknown by isolating the variable. First, subtract 6400 from both sides.
[tex]6400-6400+b^2=10000-6400\\b^2=3600[/tex]
Take the square root of both sides.
[tex]\sqrt {b^2}= \sqrt {3600}\\b=60 \\b= 60 \ m[/tex]
The missing leg is 60 meters.
Irina has 6 tubs yogurt. She wants to scoop it all into bowls. Each bowls holds 1/4 tub of yogurt. Which division equation can be used to find b, number of bowls she needs.
Answer:
6 divided by 1/4 = b
Step-by-step explanation:
Answer:
b = 6 ÷ 1/4
i did it before lol