Answer:
x = y = 22
Step-by-step explanation:
It would help to know your math course. Do you know any calculus? I'll assume not.
Equations
x + y = 44
Max = xy
Solution
y = 44 - x
Max = x (44 - x) Remove the brackets
Max = 44x - x^2 Use the distributive property to take out - 1 on the right.
Max = - (x^2 - 44x ) Complete the square inside the brackets.
Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.
Max = -(x - 22)^2 + 484
The maximum occurs when x = 22. That's because - (x - 22) becomes 0.
If it is not zero it will be minus and that will subtract from 484
x + y = 44
xy = 484
When you solve this, you find that x = y = 22 If you need more detail, let me know.
Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L = 
cos ∠L = 
∠L = cos⁻¹ 
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6
Answer:
If Dominic buys 2 points (2% of the loan value) he will get a better rate and hence less payment. The question is asking how long will it take him to save the initial investment of 2% of the loan value due to a smaller payment. The monthly payment at 5.45% is $1,146.43, the monthly payment for 5.2% is $1,118.66. This is a difference of $27.77 per month. The 2 points will cost him $3,752.00. The question is asking how long will it take Dominic to re-coup his $3,752.00 if he saves $27.77 per month. Just divide the 2 numbers and you get 135.10 months. If you divide that by 12 you get 11.26 years, which is roughly 11 years, 4 months.
Step-by-step explanation:
Here is what the question is asking. If Dominic buys 2 points (2% of the loan value) he will get a better rate and hence less payment. The question is asking how long will it take him to save the initial investment of 2% of the loan value due to a smaller payment. The monthly payment at 5.45% is $1,146.43, the monthly payment for 5.2% is $1,118.66. This is a difference of $27.77 per month. The 2 points will cost him $3,752.00. The question is asking how long will it take Dominic to re-coup his $3,752.00 if he saves $27.77 per month. Just divide the 2 numbers and you get 135.10 months. If you divide that by 12 you get 11.26 years, which is roughly 11 years, 4 months.
Answer:
Step-by-step explanation:
a)
the sum of all angles in a quadrilateral must be 360º
y+88+25+35 = 360
y = 360=88-25-35
y = 212º
b)
the sum of all angles in an octagon must be 1080º
45+45+140+140+6y = 1080
6y = 1080-90-280
6y = 710
y = 710/6
y=~ 118,3º
The answer is 84 because of process priority
