Answer:
I'm assuming it's 1 lemon piece among 5 other pieces, if so then 1 out of 6.
Step-by-step explanation:
Answer:
<u>2,365,200,000 times</u>
Step-by-step explanation:
<u>Given</u> :
- Average heartbeat rate = 60 times/minute
- Avg. human lifespan = 75 years
<u>To Find</u> :
- Number of heartbeats in lifetime of 75 years
<u>Solving</u> :
- Let the number we require be n
- n = average heartbeat rate x 60 x 24 x 365 x 75
- n = 60 x 60 x 24 x 365 x 75
- n = 3600 x 24 x 365 x 75
- n = 86400 x 365 x 75
- n = 31536000 x 75
- n = <u>2,365,200,000 times</u>
<span>1) y = -f(x) (This is the reflection about the x-axis of the graph y = f(x).) That is for every point (x, y) there is a point (x, -y).
</span><span>2) y = |f(x)| means that the entire graph will be above the x-axis. Why? (The absolute value is always positive, that's why!!)<span> To graph the absolute value graph, graph the function y = f(x). Anything above the x-axis, stays above it, anything below the x-axis is reflected above the x-axis and anything on the x-axis, stays on the x-axis.
</span></span><span>3) y = f(-x) (This is reflection about the y-axis of the graph y = f(x)) For every point on the right of the y-axis, there is a point equidistant to the left of the y-axis. That is for every point (x, y), there is a point (-x, y).
</span><span>4) Reflections about the line y = x is accomplished by interchanging the x and the y-values. Thus for y = f(x) the reflection about the line y = x is accomplished by x = f(y). Thus the reflection about the line y = x for y = x2 is the equation x = y2. </span>
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
Slope formula : y2 - y1 / x2 - x1
( 34 , 12 ) and ( 32 , 48 )
48 - 12 / 32 - 34
36 / - 2
slope = - 18
