In △ ABC, ∠ BAC = 105 °, EF and Mn are the vertical lines of AB and AC respectively, then ∠ fan=_____ °

In △ ABC, ∠ BAC = 105 °, EF and Mn are the vertical lines of AB and AC respectively, then ∠ fan=_____ °

thirty
reason:
Because it is a vertical line, B = FAE, C = Nam
And because B + C = 75
So fan = BAC - (B + C) = 30
(PS: the superscript of the angle is missing)

The greatest common divisor of 12 and 14 is 2, and the least common multiple is 42
The divisor of 12 is 12 6 4 3 2 1
The divisors of 14 are: 14721
Greatest common divisor: among these divisors, only 2 and 1 are both divisors of 12 and 14, so 2 and 1 are common divisors. Take the greatest common divisor 2
Least common multiple: if there are more than two items in a column, take a 2, if there are more than one items in a column, take a 1, 3 and 7. If you want to take all the prime factors, there will be a least common multiple: 2 × 7 × 3 × 1 = 42, say 84, say 42. Which is accurate? Please explain the basic principle and formula. Thank you

The least common multiple is 84, the greatest common divisor is 2.12 and 14 can be about 2 together, and the remainder is 6 and 7 respectively. 6 and 7 can't be reduced any more, so multiply the greatest common divisor by the remainder (2 * 6 * 7) to get 84. Conversely, you can divide 84 by 12 and 14, and there is no remainder, but if you divide by 42, there is a remainder, which is incorrect! The content of a long time ago is actually the feeling of division operation~

If the slope of the line is 0, what is the inclination angle of the line? If the slope of the line is - 1, what is the inclination angle of the line

If the slope of the line is 0, then the inclination angle of the line is 0 degree
If the slope of the line is - 1, the inclination angle of the line is 135 degrees

Banana are my favorite

What's your favorite fruit?

The parabola y = - x square + 2mx-m square - M + 3 is known
When m is 1, there are two intersections between the parabola and the x-axis
2. If the parabola and X-axis intersect at two points m and N, if / OM / * / on / = 3, and / OM / does not = / on /, find the analytical formula of the parabola

1.
There are two intersections
So (2m) ^ 2 + 4 (- m ^ 2-m + 3) = - 4m + 12 > 0
m

Given that f (x) = 12x2 + 4lnx-5x, f ′ (x) is the derivative of F (x). (I) find the extremum of y = f (x); (II) find the interval where f ′ (x) and f (x) have the same monotonicity

(I) ∵ f (x) = 12x2 + 4lnx-5x, ∵ f '(x) = x + 4x-5 = (x-1) (x-4) x (x > 0), from F' (x) > 0, 0 < x < 1 or x > 4, from F '(x) < 0, 1 < x < 4. When x changes, f' (x), f (x) changes as follows: ⊙ ⊙ x ⊙ x ⊙ 1 ⊙ (1,4) ⊙ (4, + ∞) ⊙ f '(x) ⊙ + ⊙ 0 ⊙ + ⊙ f (x) ⊙ ↗ ⊙ maximum value ⊙ ↘ ⊙ minimum ⊙ ↗ The maximum of F (x) = f (1) = - 92, the minimum of F (x) = f (4) = 8ln2-12 6 points (Ⅱ) Let G (x) = x + 4x-5 (x ＞ 0), G '(x) = (x + 2) (X-2) x, from G' (x) ＞ 0, X ＞ 2, G (x) is an increasing function, from G '(x) ＜ 0, 0 ＜ x ＜ 2, G (x) is a decreasing function 12 points

The following parametric equation is reduced to the ordinary equation x = 1-3T, y = 4T

y=(1-x)*4/3

In the original algorithm of rational number, we define the new operation "⊕" as follows:
When a ≥ B, a ⊕ B = B & # 178; when a < B, a ⊕ B = a, using this definition to calculate: [1 ⊕ - 2] ⊕ 5-4 × [(- 3) ⊕ 2],

When a ≥ B, a ♁ B = B & # 178; when a < B, a ♁ B = a,
[1♁(-2)]♁5-4×[(-3)♁2]
=（-2）²♁5-4×(-3)
=4♁5-4×(-3)
=4-（-12）
=4+12
=16
For your reference

Point C is a point in the first quadrant of y = x, y = 2x + 1 is translated by 4 units along the OC direction of the ray, and the analytical expression after translation is obtained

The OC direction is 45 degrees to the upper right, and the translation 4 to the upper right is 2 √ 2 to the right, and then 2 √ 2 to the upper right. First, translate 2 √ 2 to the right, and compare the function after translation with the function before translation. When y values are equal, X is larger than 2 √ 2, that is, y = 2 (X-2 √ 2) + 1, so y is the same. Now (X-2 √ 2) of the function is equal to X of the original function

Given the equation 4x & # 178; - 7x-3 = 0, the two roots are x1, X2, - find x1-x2

（x1-x2）²
=x1²+x2²-2x1x2
=（x1+x2）²-4x1x2
=（7/4）²-4*（-3/4）
=49/16+3=
97/16
x1-x2=±√97/4