X minus two thirds x equals two and a quarter

X minus two thirds x equals two and a quarter

X-2 / 3x = 2 and 1 / 4
（1-2/3）x=9/4
1/3x=9/4
x=27/4

One third of X is equal to 560 minus x, which is solved by difference multiplied by one fourth

x/3=(560-x)*(1/4)
So x * (1 / 3 + 1 / 4) = 140
So x * (7 / 12) = 140
x=240

It is known that the solution of the equation KX = 4-x about X is a positive integer

The original equation is transformed into KX + x = 4, that is, (K + 1) x = 4, the solution of the equation KX = 4-x about X is a positive integer, and the product of K + 1 and X is 4, then K + 1 = 4 or K + 1 = 2 or K + 1 = 1 can be obtained, and the solution is k = 3 or K = 1 or K = 0. Therefore, the integer solution of K can be obtained as 0, 1, 3

A semicircular flower bed is 20.56 meters in circumference, and its area is () square meters

Radius: 20.56 ÷ (3.14 + 2) = 4m
Area: 3.14 × 4 & # 178; △ 2 = 25.12 square meters

How can 37 * 21 be operated easily?

=37*(20+1)
=37*20+37*1
=740+37
=777

As shown in the figure, BP and CP are bisectors of ∠ ABC and ∠ ACB respectively. If ∠ a = 40 °, then ∠ BPC =; if ∠ BPC = 120 °, then ∠ a ==

∵ BP and CP are bisectors of ∠ ABC and ∠ ACB respectively ≠ PBC = 1 / 2 ∠ ABC ∠ PCB = 1 / 2 ∠ ACB ≠ BPC = 180 ° - (∠ PBC + ∠ PCB) = 180 ° - 1 / 2 (∠ ABC + ∠ ACB) = 180 ° - 1 / 2 (180 ° - a) = 90 ° + ∠ A / 2 = 90 ° + 40 ° / 2 = 110 ° 2, ∠ BPC = 90 ° + - A / 2 ≠ 120 ° = 90 ° + ∠ A /

It is known that B1, B2, A1, A2 are three-dimensional column vectors. If the determinant | a | = | A1, A2, B1 | = - 4, | B | = | A2, A1, B2 | = 1, then the row and column are
|a1+a2,-2a1+a2,b1-2b2|=?

The title is not complete
|a1+a2,-2a1+a2,b1-2b2|
= |3a1,-2a1+a2,b1-2b2| --c1-c2
=3 | A1, - 2A1 + A2, b1-2b2 | -- column 1 proposes 3
= 3|a1,a2,b1-2b2| --c2+2c1
=3 (| A1, A2, B1 | + | A1, A2, - 2B2 |) - split by column 3
= 3(|a1,a2,b1|+2|a2,a1,b2|)
= 3(|A|+2|B|)
= 3(-4+2)
= -6.

The area of trapezoid (composed of two triangles) is 34.5 square centimeters, the upper bottom is 3.5, and the lower bottom is 8. Find the area of the shadow part (one of the triangles)
╱ ╲ ╱ ━━━━━━━━━━╲
Please, great Xia, I'm really in a hurry

Trapezoid height = 2 * 34.5 / (3.5 + 8) = 6cm
Area of a triangle = 1 / 2 * 6 * 3.5 = 10.5 square centimeter
The area of the other triangle = 1 / 2 * 6 * 8 = 24 square centimeters
I don't know which triangle your shadow is

Given function f (x) = LG (AX ^ 2 + 2x + 1)
If the range of F (x) is r, find the range of real number a

The range is r
Then the true number should be able to get all positive numbers
If a = 0
Then the true number = 2x + 1
When x > - 1 / 2, all positive numbers can be obtained
If a is not equal to 0
Then the real number is a quadratic function
To get all the positive numbers, open up
a>0
And the minimum value cannot be greater than 0
Otherwise, the positive number between 0 and the minimum value cannot be obtained
So the discriminant is greater than or equal to 0
4-4a>=0,a

A granary is a cone on the top and a cylinder with the same bottom as the cone on the bottom. The circumference of the bottom is known to be 6.28 meters, and the height of the cylinder is 3 meters and 5 meters
Each cubic meter of grain weighs 200 kg. How many kg of grain can this granary hold?

Radius = 6.24 △ 3.14 △ 2 = 1m
Cylinder volume = 3.14 × 1 × 1 × 3 = 9.42 cubic meters
Cone volume = 1 / 3 × 3.14 × 1 × 1.5 = 1.57 M3
(9.42 + 1.57) × 200 = 2198kg