If the y-intercepts are the same, the two equations represent the same line and there are INFINITELY MANY SOLUTIONS
Answer: 0.8413
Step-by-step explanation:
Given : Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution.
Mean :
Standard deviation : 
Let x be the random variable that represents the typing speeds for the students.
The z-score :-

For x= 51

Using the standard normal distribution table ,the probability that a randomly selected student has a typing speed of less than 51 words per minute :-

Hence, the probability that a randomly selected student has a typing speed of less than 51 words per minute = 0.8413
Θ
=
arcsin
(
.7
4.2
)
≈
10
∘
Explanation:
We view the ramp as a right triangle. The hypotenuse is 4.2 and the vertical side .7, which is opposite the angle
θ
we seek.
sin
θ
=
.7
4.2
=
1
6
I'm going to finish the problem but I'll note if we were actually building the ramp we don't need to know the angle; this sine is sufficient.
θ
=
arcsin
(
1
6
)
θ
≈
10
∘
which I think is a pretty steep ramp for a wheelchair.
There will be another inverse sine that is the supplementary angle, around
170
∘
, but we can rule that out as a value for a ramp wedge angle.
Answer:
2m
Step-by-step explanation:
(m+3) (m-1)
We need to FOIL
first m*m = m^2
outer -1*m = -m
inner = 3m
last 3*-1 = -3
Add these together
m^2 -m +3m -3
m^2 +2m -3
Alright remember, if any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
k+1=0
k-5=0
Set the first factor equal to 0 and solve
k=-1
Set the next factor equal to 0 and solve
k=5
The final solution is all the values that make (k+1)(k-5)=0 true.
k=-1, 5
Hope this helped you out :)