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).
Simplify the ration expression

start by seeing if anything in the numerator or denominator can be factored,
you should notice that you can factor out a 3 from 3x-6 in the numerator
when you do so, the result is

now, since there is an x-2 in the numerator and denominator, they "cancel" out since

however, only when

since

when you cancel out the x-2, you're left with 3
hence, your answer is C
Answer: 2x
^4
+7x−4x
^2
−4
Step-by-step explanation:
2x
^4
−x*3−4x
^2
+10x−4
2x
^4
−3x−4x
^2
+10x−4
2x
^4
+(−3x+10x)−4x
^2
−4
2x
^4
+7x−4x
^2
−4
Answer:
there are 3.3399 moles in 318 grams! ✔️
Step-by-step explanation:
So we know that 100 grams MgCl2 to mol = 1.0503 mol.
Therefore, to find the number of moles in 318g of the compound, we use the rule of three:
if 1.0503 mol -------------> 100 grams
X <------------- 318 grams
The solution is: X = (318*1.0503)/100 = 3.3399 mol.
Summarizing, there are 3.3399 moles in 318 grams! ✔️