Hey there! I'm happy to help!
First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).
Let's convert this below
A: (1,1)⇒(-1,-1)
B: (5,4)⇒(-5,-4)
C: (7,1)⇒(-7,-1)
D: (3,-2)⇒(-3,2)
Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.
A: (-1,-1)⇒(4,-2)
B: (-5,-4)⇒(0,-5)
C: (-7,-1)⇒(-2,-2)
D: (-3,2)⇒(2,1)
Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)
Now you know how to find the coordinates of translated figures! Have a wonderful day! :D
Answer:
1. 14/15
2. 5 7/8
3. 81.25%
Step-by-step explanation:
1. (fraction) 7/9 divided by 5/6 (fraction)
7/9 ÷ 5/6 =
= 7/9 * 6/5
= (7 * 6)/(9 * 5)
= 42/45
= 14/15
2.
1 3/8 + 4 1/2 =
= 1 + 3/8 + 4 + 1/2
= 1 + 4 + 3/8 + 4/8
= 5 + 7/8
= 5 7/8
3.
percent = part divide by whole times 100
13/16 * 100 =
= 81.25%
Since ![[0,4]=[0,1]\cup(1,4]](https://tex.z-dn.net/?f=%5B0%2C4%5D%3D%5B0%2C1%5D%5Ccup%281%2C4%5D)
, we can rewrite the integral as
Now there is no ambiguity about the definition of f(t), because in each integral we are integrating a single part of its piecewise definition:
Both integrals are quite immediate: you only need to use the power rule
to get
![\displaystyle \int_0^11-3t^2\;dt = \left[t-t^3\right]_0^1,\quad \int_1^4 2t\; dt = \left[t^2\right]_1^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E11-3t%5E2%5C%3Bdt%20%3D%20%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%2C%5Cquad%20%5Cint_1%5E4%202t%5C%3B%20dt%20%3D%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4)
Now we only need to evaluate the antiderivatives:
![\left[t-t^3\right]_0^1 = 1-1^3=0,\quad \left[t^2\right]_1^4 = 4^2-1^2=15](https://tex.z-dn.net/?f=%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%20%3D%201-1%5E3%3D0%2C%5Cquad%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4%20%3D%204%5E2-1%5E2%3D15)
So, the final answer is 15.
Answer:
Number of children, x= 400
Number of adults, y = 100
Step-by-step explanation:
Let the number of children be x
Let the number of adults be y
Given : Total number of people, x + y = 500 --------(1)
Total amount collected, 5x + 10y = 3000 ---------(2)
(1) => y = 500 - x
Substitute y in (2) : 5x + 10(500 - x) = 3000
5x + 5000 - 10x = 3000
-5x = 3000 - 5000
-5x = -2000
x = 400
Substitute x in (1) : 400 + y = 500
y = 500 - 400
y = 100
Answer:
Kims savings will be $60.
Step-by-step explanation:
120 * .50 = 60
