<h3>

is the simplified expression</h3>
<em><u>Solution:</u></em>
Given that,
We have to simplify

We can simplify the above expression by combining the like terms
Like terms are terms that has same variable with same exponent and same or different coefficient
From given,

Group the like terms

Thus the given expression is simplified
Answer: the length of the angle bisector of angle ∠A is 6 ft
Step-by-step explanation:
The diagram of the right angle triangle ABC is shown in the attached photo
Looking at triangle ABC,
cos θ = adjacent side/hypotenuse side
cos θ = 5/13 = 0.3846
θ = 67.38 degrees
The bisector of an angle divides it into two equal halves. The bisector is represented by line AD.
θ/2 = 67.38/2 = 33.69 degrees
Therefore,
Cos 33.69 = 5/AD
AD × Cos 33.69 = 5
AD = 5/Cos 33.69 = 5/0.832
AD = 6 ft
Answer:
y = 0.80
Step-by-step explanation:
Given:
- The expected rate of return for risky portfolio E(r_p) = 0.18
- The T-bill rate is r_f = 0.08
Find:
Investing proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%.
What is the proportion y?
Solution:
- The proportion y is a fraction of expected risky portfolio and the left-over for the T-bill compliance. Usually we see a major proportion is for risky portfolio as follows:
E(r_c) = y*E(r_p) + (1 - y)*r_f
y*E(r_p) + (1 - y)*r_f = 0.16
- Re-arrange for proportion y:
y = ( 0.16 - r_f ) / (E(r_p) - r_f)
- Plug in values:
y = ( 0.16 - 0.08 ) / (0.18 - 0.08)
y = 0.80
- Hence, we see that 80% of the total investment budget becomes a part of risky portfolio returns.
Answer:
L/k
Step-by-step explanation:
If Tim has a wire that is L inches long and each piece is k inches long, then you would divide the total length by the length of each individual to get the number of pieces.
So,
L/k
Answer:
The lines representing these equations intercept at the point (-4,2) on the plane.
Step-by-step explanation:
When we want to find were both lines intercept, we are trying to find a pair of values (x,y) that belongs to both equations, which means that it satisfies both equations at the same time.
Therefore, we can use the second equation that gives us the value of y in terms of x, to substitute for y in the first equation. Then we end up with an equation with a unique unknown, for which we can solve:

Next we use this value we obtained for x (-4) in the same equation we use for substitution in order to find which y value corresponds to this:

Then we have the pair (x,y) that satisfies both equations (-4,2), which is therefore the point on the plane where both lines intercept.