Answer:
( x + 5 )² + ( y - 8 )² = 25
Step-by-step explanation:
Standard form for the equation of a circle - ( x - h )² + ( y - k )² = r²
Where r = radius and Center is located at ( h , k )
We are given that the center is at ( -5 , 8 )
Thus, h = -5 and k = 8
We are also given that the radius = 5
Thus, r = 5
Now we just plug all of the given values into the standard form equation
( x - (-5))² + ( y - 8 )² = 5²
*simplify*
in - ( - 5 ) the two negative sign cancel out and it turns into + 5
5² = 25
Thus, the equation is ( x + 5 )² + ( y - 8 )² = 25
36-x squared i don’t know if it’s right sorry
<h2>
Answer:</h2>
↓∴↓∴↓∴↓∴
<h3>
Step-by-step explanation:</h3>
Definition:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.
Answer:
We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
Please check the attached graph.
Step-by-step explanation:
Given the parent function
y = x²
Given the transformed function
y = (x - 12)²
Horizontal Translation:
The horizontal translation of y = x² is of the form
f(x-h)
so y = y = (x - 12)² means y = x² is shifted 12 right.
Vertical Translation:
y = x²
Then y = x² + b is a vertical translation of y = x²
if b > 0, then y = x² + b is the graph of y = x² 'b' units up.
if b < 0, then y = x² + b is the graph of y = x² 'b' units down.
Thus, y = x² + 3 means the graph y = x² is vertically shifted up by 2 units.
Please check the attached graph.
-
The blue graph is representing the graph of y = x².
- The red graph is representing the graph of y = (x - 12)²+3
Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.
Hence, option D is true.
Answer:97/125
Step-by-step explanation:
“As illustrated in the Venn diagram,
We let
U=[The total number of people at the sport center]
This implies that,
n(U)=125
G=[Those who use the gym]
This implies that,
n(G)=59
P=[Those who use the pool]
This implies that,
n(P)=70
T=[Those who use the track]
This implies that,
n(T)=55
a=[Those who use the gym only]
This implies that,
n(a)=59-(6+11+19)=59-36=23
b=[Those who use the pool only]
This implies that,
n(b)=70-(6+19+24)=70-49=21
c=[Those who use the track only]
This implies that,
n(c)=55-(6+24+11)=55-31=14
Also, number of people who use gym and track=11+23+19+6+14+24=97”
