ChowMein

a) 
Distance is 195 miles.
Speed or rate is 50 mph

1) Use the distance formula.
d=rt; where d=distance, r=rate or speed, t=time
You have d and r, solve for t.
195=50t
t=195/50=3.9 hours
 

2) Tack on that time to the time it leaves. 

Leaves at 3:30

Add the whole amount of hours (3)
Becomes 6:30
Turn the 0.9 hours to minutes by multiplying by 60
0.9*60=54 minutes
Add 54 minutes to 6:30, you get the arrival time which is:
7:24

b) Since the coach has a lower average speed in other words, it's slower, the arrival time will be later than the calculated time of 7:24.

Probability of taking a red sweet = 3/8
eats it so amount of reds in the bag drops to 2, total amount of sweets in bag drops to 7.
Probability of taking the 2nd red sweet = 2/7

P(R,R) = 3/8(2/7) = 6/56

\(\frac{5}{24}+|x-\frac{11}{48}|<\frac{5}{16}\)

1) Isolate the absolute value part
\(|x-\frac{11}{48}|<\frac{5}{48}\)

2) For absolute value inequalities, split the inequality into two parts, then solve.

For one of the parts, just drop the absolute value and solve.
For the second part, drop the absolute value, flip the inequality sign and make the other side negative. 
\(x-\frac{11}{48}<\frac{5}{48}\\ x<\frac{16}{48}\\ x<\frac{1}{3}\) and  \(x-\frac{11}{48}>-\frac{5}{48}\\ x>\frac{6}{48}\\ x>\frac{1}{8}\)
3) Turn that into interval notation.

(1/8)

\((\frac{1}{8},\frac{1}{3})\)

(f•g)(x) --> f(g(x))
Basically, where there is an x, replace it with g(x), in this case x²+2

f(x)=x³-4x+2

f(x²+2)=(x²+2)³-4(x²+2)+2
           =x⁶+6x⁴+12x²+8-4x²-8+2
           =x⁶+6x⁴+8x²+2

Find the slope of the line going through (-5,1) and (1,1) using the slope formula:
m=(y₂-y₁)/(x₂-x₁₎
m=(1-1)/(1--5)
m=0/6

m=0

Parallel lines have the same slope, so the slope of the parallel line is 0.
Plug in (3,3) to y=mx+b as (x,y)
3=0(3)+b
b=3

line is y=3


 

Vertex form of a parabola is:
y=a(x-h)²+k; where (h,k) is the vertex

Vertex is given, plug them in.
y=a(x-10)²-7
 

Now we need to find the value of a.
Graph goes through (5,168), so plug those into x and y to solve for a.

168=a(5-10)²-7
175=a(-5)²

175=25a

a=7

With that, we now have the function of the parabola.
f(x)=7(x-10)²-7

make a 2-way table

Steps to finding the directrix given the equation of the parabola:
1) Find p-value
2) Find vertex
3) Sketch a diagram and label it (optional, but helpful)
steps 1 and 2 can be done in any order

x=-b/2a is the formula used to find the axis of symmetry of parabolas
Refer to this for more info on the axis of symmetry and what it is: https://mathbitsnotebook.com/Algebra1/Quadratics/QDGraphInfo.html

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