Answer:
The answer to your question is:
Step-by-step explanation:
Q1. They are vertical angles, so they measure the same
[2(x + 10)] = (3x - 30)
2x + 20 = 3x -30
2x - 3x = -30 - 20
- x = - 50
x = 50
Q2. They are also vertical angles, so they measure the same.
[6(x - 2)] = 3x + 30
6x - 12 = 3x + 30
6x - 3x = 30 + 12
3x = 42
x = 42/3
x = 14
∠DHG = 6(14 - 2)
∠DHG = 6(12)
∠DHG = 72
To find the product of (4x-5y)^2,
we can rewrite the problem as:
(4x-5y)(4x-5y) (two times because it is squared)
Now, time to use that old method we learned in middle school:
FOIL. (Firsts, Outers, Inners, and Lasts)
FOIL can help us greatly in this scenario.
Let's start by multiplying the 'Firsts' together:
4x * 4x = <em>16x^2</em>
Now, lets to the 'Outers':
4x * -5y = <em>-20xy</em>
Next, we can multiply the 'Inners':
-5y * 4x = <em>-20xy</em>
Finally, let's do the 'Lasts':
-5y * -5y = <em>25y</em>^2
Now, we can take the products of these equations from FOIL and combine like terms. We have: 16x^2, -20xy, -20xy, and 25y^2.
-20xy and -20xy make -40xy.
The final equation (product of (4x-5y)^2) is:
16x^2 - 40xy + 25y^2
Hope I helped! If any of my math is wrong, please report and let me know!
Have a good one.
Answer:
Stated Below:
Step-by-step explanation:
x + y = 90 because the 2 angles add up to 90
.
Now, m < x = five times m < y, so x = 5y or y = x/5
So the last choice is the correct one.
The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Answer:
1.8
Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1)
(86-32)/(30-0)
54/30
1.8
