The system of quadratic equations of two variables: Y / 3 - (x + 1) / 6 = 31, 2 (X-Y / 2) = 3 (x + Y / 18) 2

The system of quadratic equations of two variables: Y / 3 - (x + 1) / 6 = 31, 2 (X-Y / 2) = 3 (x + Y / 18) 2

y/3-(x+1)/6=3
2(x-y/2)=3(x+y/18)
After simplification
y = 9+(x+1)/2
0 = 6x+7y
therefore
x= -7
y=6

Simplification: 2sin50 ° + sin100 ° (1 + radical 3 * tan370 °) / radical 1 + cos10 °
Try to be as detailed as possible
I have a headache

{2sin50°+ sin100°[1 + (√3)tan370°]}/√(1 + cos10°)
= {2sin50°+ cos10°[1 + (√3)tan10°]}/√(1 + cos10°)
= {2sin50°+ [cos10°+ (√3)sin10°]}/√(1 + cos10°)
= {2sin50°+ 2[½cos10°+ ½(√3)sin10°]}/√(1 + cos10°)
= {2sin50°+ 2[sin30°cos10°+ cos30°sin10°]}/√(1 + cos10°)
= {2sin50°+ 2sin40°}/(√2)cos5°
= (√2){sin50°+ sin40°}/cos5°
= (√2)[2sin45°cos5°]/cos5°
= (√2)2sin45°
= (√2)2×(√2)/2
= 2
[the answer is safe]

The number that is more than 80% of a number is 13. Find this number

Let this number be X
0.8x+9=13
0.8x=13-9
0.8x=4
x=4/0.8
x=5
A: the number is 5

Recursive equation 5 / 6-3 / 4 + 1 / 3 11 / 12 - (1 / 6-1 / 8) 7 / 12 - (3 / 4-1 / 2) 1 / 2 - (3 / 4-3 / 8)

5/6－3/4+1/3
=10/12-9/12+4/12
=5/12
11/12－(1/6－1/8)
=22/24-4/24+3/24
=21/24
=7/8
7/12－(3/4－1/2)
=7/12-1/4
=1/3
1/2－(3/4－3/8）
=1/2-3/8
=1/8
If you don't understand this question, you can ask,

As shown in Figure 1, in the plane rectangular coordinate system, a (- 2,0) translates the line AB right 5 units along the X axis to the line PQ, which intersects the X and Y axes with C and D respectively
(2) If the equation of D (0,2) line PQ is ax + by = C (the coordinates of point C and D satisfy the equation of line PQ), find the value of 6A + B + C / 3a-b + 2C (C ≠ 0)
(3) As shown in Figure 2, am bisects NAC, DM bisects PDB, AE ⊥ DM at point E. when point B moves on the negative half axis of y-axis, calculate the degree of EAM

(2) If the equation of D (0,2) line PQ is ax + by = C (the coordinates of point C and D satisfy the equation of line PQ), the value of 6A + B + C / 3a-b + 2C (C ≠ 0) can be obtained, and the answer is 6 / 5
What about the third picture

How many hours is 36 minutes

36 divided by 60 = 0.6 hours

Find the equation of the line L which is perpendicular to the line L: 3x-4y + 7 = 0 and whose intercept sum on the two coordinate axes is 1
High 2 mathematics. Write the solution steps

3x-4y+7=0
The slope is 3 / 4
So the slope of the line is - 4 / 3
So 4x + 3Y + a = 0
x=0,y=-a/3
y=0,x=-a/4
So the sum of intercept = - A / 3-A / 4 = 1
a=12/7
4x+3y+12/7=0
That is 28x + 21y + 12 = 0

Given the function f (x) = SiNx + cosx, find the period and monotone decreasing interval of function f (x)

F (x) = SiNx + cosx = √ 2 [SiNx * (√ 2 / 2) + cosx * (√ 2 / 2)] = √ 2 [SiNx * cos (π / 4) + cosxsin (π / 4)] = √ 2Sin (x + π / 4) (1) t = 2 π (2) minus interval 2K π + π / 2 ≤ x + π / 4 ≤ 2K π + 3 π / 22K π + π / 4 ≤ x ≤ 2K π + 5 π / 4 minus interval [2K π + π / 4,2k π + 5 π / 4], K ∈

It is known that the line L passes through point P (3,2) and intersects with the positive half axis of X axis and Y axis at two points a and B respectively. As shown in the figure, the minimum area of △ ABO and the equation of the line L at this time are obtained

Let the linear equation be XA + Yb = 1 (a ＞ 0, B ＞ 0), 3A + 2B = 1. From the basic inequality, 3A + 2B ≥ 23a · 2B, that is, ab ≥ 24 (if and only if 3A = 2B, that is, a = 6, B = 4), and S = 12a · B ≥ 12 × 24 = 12, then the linear equation is X6 + Y4 = 1, that is, 2x + 3y-12 = 0

The definition field of function f (x) = 2x-1 / 3x + 2 is_______________ , the range is________ .
Explain as much as you can,
f(x)=2x-1/(3x+2)

Domain of definition: X ∈ (- ∞, 0) ∪ (0, + ∞). Because when x = 0, 1 / 3x is meaningless
Range: F (x) '= 2 - (1 / 3) × (- 1 / x ^ 2) = 2 + 1 / 3x ^ 2 ＞ 0. Therefore, this function is monotonically increasing, except that x = 0 cannot be obtained, its range is (- ∞, + ∞)