Use the solution of the equation to solve the following problem: 7.5/x=0.25 4.5/x=9 54-x=24 13+x=28.5 35-x=12

Use the solution of the equation to solve the following problem: 7.5/x=0.25 4.5/x=9 54-x=24 13+x=28.5 35-x=12

7.5/x=0.25
x=7.5/0.25
x=50
4.5/x=9
x=4.5/9
x=0.5
54-x=24
x=54-24
x=30
13+x=28.5
x=28.5-13
x=15.5
35-x=12
x=35-12
x=23
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There are 105 more books on the upper shelf than on the lower shelf. After 25 books are taken from the upper shelf and put into the lower shelf, the upper shelf is 1.25 times as large as the lower shelf. How many books are there on the upper shelf?

Let x original books on the upper shelf (x-25) * 4 / 5 = x-105 + 254x / 5-20 = x-80x / 5 = 60x = 300. There are 300 original books on the upper shelf. You can also do this: 1. When the upper shelf takes 25 books to the lower shelf, the number of books on the upper shelf is 105-25-25 = 55 more than that on the lower shelf. 2. If the number of books on the lower shelf is 4 / 5, the number of books on the upper shelf is 1 / 4 more than that on the lower shelf

1.8*4*2+(5X-4)*3+(3x-4)*3=32.4
The final answer is seven fourths

Original formula = 14.4 + 15x-12 + 9x-12 = 32.4
2.4+24x=32.4
24x=30
X = 1.25 (five fourths) how about seven fourths?

1 / r = 1 / r2 + 1 / R1, using the fraction of r1r2 to express R, there are many ways

1/r=(r1+r2)/r1*r2
r=r1*r2/(r1+r2)

In the binomial expansion of (a + b) ^ n, the maximum value of binomial coefficient is

1.n=2m
Maximum = C (n, m)
2.n=2m＋1
Maximum = C (n, m) = C (n, M + 1)

If a * a + AB + B = 24, a + AB + b * b = 18, find the value of a + B

a*a+ab+b=24,a+ab+b*b=18
a²+ab+a+a+ab+b²=42
a²+2ab+b²+a+b-42=0
(a+b)²+(a+b)-42=0
(a+b+7)(a+b-6)=0
a+b+7=0 a+b-6=0
A + B = - 7 or a + B = 6

It is known that the difference of 4 times the square of x minus 1 is equal to the sum of the difference of a times x minus 1 plus B times x plus 1, then a =? B =?

Firstly, the right formula is divided into two parts: right formula = a (x + 1) / (x-1) + B (x-1) / (x + 1) = [a (x + 1) + B (x-1)] / (x ^ 2-1) = [(a + b) x + (a-b)] / (x ^ 2-1). Then, the left formula = 4 / (x ^ 2-1), we can get the equations: a + B = 0; A-B = 4, we can get the equations: a = 2, B = - 2

3.6x-x = 5.2 solution equation

Let A1 and A2 be n-dimensional column vectors and a be n-order orthogonal matrix. It is proved that [Aa1, aa2] = [A1, A2]

Because a is an orthogonal matrix
So a ^ TA = E
therefore
[Aa1,Aa2] = (Aa1)^T(Aa2) = a1^TA^TAa2 = a1^Ta2 = [a1,a2]

Given the square of x-3x-5, find the value of the third power of x-14x + 5
That's x minus 3x minus 5, finding the third power of x minus 14x plus 5

Let x ^ 2 - 3x - 5 = ax ^ 3 - 14x + 5 = B, then 3x ^ 2 - 9x + 5 = ax - b3a + 20 = ax - BXA = B + 20 + 3A (B + 20 + 3a) ^ 2 - 3A ((B + 20 + 3a) - 5A ^ 2 = a ^ 3B ^ 2 + (40 + 3a) B + 20 (20 + 3a) - 5A ^ 2 - A ^ 3 = 0 Δ = (40 + 3a) ^ 2 -