The first one is the correct answer, enjoy!
Answer:
3) (2,-9)
4) (0,-5)
5) (1,-8)
Step-by-step explanation:
3)
The vertex will occur between you x-intercepts.
You already found that happens at x=2.
To find the corresponding y-coordinate, replace x in
f(x)=(x+1)(x-5) with 2:
f(2)=(2+1)(2-5)
f(2)=(3)(-3)
f(2)=-9
So the vertex is (2,-9).
4)
The y-intercept is when x=0.
So in f(x)=(x+1)(x-5) replace x with 0:
f(0)=(0+1)(0-5)
f(0)=(1)(-5)
f(0)=-5
So the y-intercept is (0,-5).
5)
To find another point just plug in anything besides any x already used.
We preferably want to use a value of x that will keep us on their grid however far up,down,left, or right their grid goes out. So I'm going to choose something close to the vertex which is at x=2. Let's go with x=1.
So replace x in f(x)=(x+1)(x-5) with x=1:
f(1)=(1+1)(1-5)
f(1)=(2)(-4)
f(1)=-8
So another point to graph is (1,-8).
Answer: 2 19/24 hours was spent in practising.
Step-by-step explanation:
During the first hour, they practiced for 5/8 of an hour. During the second hour, they practiced for 2/3 of an hour. This means that the total time for which they practiced in the first 2 hours would be
5/8 + 2/3 = 31/24 hours
During the last two hours, they first practiced for 3/5 of an hour, took a 1/2 hour break and then practiced the rest of the time. This means that the rest of the time for which they practiced is
2 - (3/5 + 1/2) = 2 - 11/10 = 9/10
Therefore, the time they spent practicing in total would be
31/24 + 3/5 + 9/10 = 67/24 =
2 19/24 hours
Answer:
x=4.5
Step-by-step explanation:
Using sohcahtoa we know tangent is equal to (length of side opposite to the angle ) / (lenth of side adjacent to the angle)
therefore: tan (theta) = (x-3) / (x) = 1 / 3
now cross multiply
3(x-3) = x
now solve for x
3x - 9 = x
-9= -2x
x= 4.5
To solve this problem, start by plugging in your given n value.
This results in:
k = 100 - 4(60)
Next, simplify the parentheses by multiplying the -4 and the 60 together.
This leaves you with:
k = 100 - 240
To simplify for k, subtract 240 from 100 to get:
k = -140
So your final answer is k = -140 when n = 60
