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Is 7 to the power of 5 minus 12 to the power divisible by 240?

Since the end of 25 5 is 5, it is not divisible by 2, so: 25 5 120 is not divisible by 2 120, i.e., 25 to the power of 7 minus 5 to the power of 12 [cannot be] divisible by 240.

The product of 4 consecutive natural numbers plus 1 is equal to the square of the sum of the first and last two numbers and the sum of 1.

n-2）（n-1）n（n+1）

n²-n-1）²

n-2）(n+1)+1】²

1.Solution: 25 to the power of 7 = 5 to the power of 14, so the original formula = 5 to the 14th power - 5 to the 12th power.

Mention that the 12th power of 5 = the 12th power of 5 x (25-1) = the 12th power of 5 x 24 is obviously not divisible by 240, because the 12th power of 5 is not divisible by 102Solution: The law is = the product of the middle two terms minus 1 squared.

e.g. 2x3-1; Such as 3x4-1

proof of mathematical methods;

Let the sequence be (a-1)xax(a+1)x(a+2)+1, then the original formula = a(a+1)(a 2+a-2)+1a(a+1)(a(a+1)-2)+1

a(a+1))^2-2a(a+1)+1

According to the sum of squares formula, then the original formula = (a(a(a+1)+1) 2

Question 1: The 12th power of 5 is the 6th power of 25, so: the 7th power of 25 minus the 12th power of 5 = the 6th power of 25 (25-1).

25 to the 6th power *24, about 24, the question is that the 6th power converted to 25 is divisible by 10? No, the mantissa to the 6th power of 25 is 5 and is not divisible by 10.

Question 2: The square of n(n+1)(n+2)(n+3)=[n(n+3)+1].

12 to the power = 25 to the 6th power. 25 to the power of 7 minus 25 to the power of 6 is equal to 25 to the power of 6 times (25-1) = 25 to the power of 25 to the power of 24, because the power of 25 to the power of 6 is not divisible by 10, so the original formula is not divisible by 240.

The rule is that the number in parentheses is equal to the product of the numbers on both sides of the multiplication plus 1 is equal to the product of the middle two numbers minus 1.

Square Difference Formula. Move 1 to the right, which is equal to () 2-1=[()1][(1]Example: 155 2-1=154*156=11*14*12*13

The sum of ten integers is equal to 101, if the number can be several equal, there are many kinds of this situation, from the meaning of the question it can be seen that the maximum number does not exceed twice the smallest, and to make the maximum number in this case, only the other nine numbers are equal or the closest, is the smallest number, a number is the largest, the largest number is not more than twice the other nine numbers. Suppose the other nine numbers are x, and the maximum number is 2x, from 9x+2x=11x=101, x=, 2x=, rounded to 18, and the sum of the other nine numbers is 101-18=83, that is, 7 9s, two 10s. The maximum number is 18.

2x=19 cannot be taken as the maximum, so that the other numbers nine add up to 82, eight nines, and a 10, and 19 is twice as big as 9.

The formula for calculating the yield is principal * 1 + interest rate to the power of time = sum of principal and interest.

Two years after the elder brother, m*(1+n%) 2

The younger brother two years later m*(1-n%) 2

Using the elder brother to subtract the difference between the younger brother is a matter of how much more. The result is 4n%*m

Brother; m*(1+n/100)^2 (1)

Brother; m*(1-n/100)^2 (2)

1)-(2) means that the elder brother has more than the younger brother.

m(1+n) squared - m(1-n) squared.

2m n squared.

Two years after the elder brother, m*(1+n%) 2

The younger brother two years later m*(1-n%) 2

The elder brother is more than the younger brother: m(1+n%) 2-m(1-n%) 2=4*m*n% should be like this.

The * sign represents an operation.

b/a)*(a/b)

b/a)²×a/b)

b aIf you don't understand it, you can look at the following substitution.

Let a=b a, b=a b

then (b a) * (a b).

The square of a*ba is multiplied by b....The definition above = the square of (b a) multiplied by (a b).Bring in a=b a, b=a b

b/a

Simplifying the equation a*b=a 2*b, a=0, a=1, because a cannot be equal to 0 here, so only a=1 is selected, and the answer is calculated as "1".

Because: a*b=a*b

So: b=0 or a=a

a=0 or a=1

Because: b a*a b

So: a≠0, b≠0

That is: a=1 original = b*1 b=1

The result is 1

Although it is known that a=1 can be obtained, and then the result is equal to 1 by returning to the formula, it seems that b a*a b can be calculated to be equal to 1

288 (Yuan) suspicious Changcha.

18 (yuan) lost 18 yuan.

80x+120x=450+50

200x=500

x= Let car B x m s, carat x + 5 m s8 (x + x + 5) = 148 + 180

16x+40=328

16x=288

x=18x+5=23

Car B is 18 m Xun, and car A is 23 m s

5. The loss is 18 yuan.

6 hours. B Che shouted: (Collapsed.)

A car training nuclear circle:

Let the total workload be 1

Tractor A work takes 21 days to complete.

Tractor A worked 1 21 of the total workload per day

Tractor B work takes 18 days to complete.

Tractor B worked 1 18 of the total workload per day

It took six days for the three tractors to work together.

Let the daily workload of the C tractor be x

1/21+1/18+x)×6=1

x=4/63

c Total workload per day 4 63

So it takes 63 4 days for a person to work.

Let c take x days to complete this work.

1/x+1/21+1/18=1/6

1/x=1/6-1/18-1/21

1/x=4/63

x=63/4

1/6-1/21-1/18=4/63

That is to say, the efficiency of C should be greater than 4 63, and C should not go it alone for more than 15 days to be completed together in 6 days.

2+ 3+ 4=100° and 1= 2

1 + 3 + 4 = 100° Equation 1

Again 1 + 2 + 3 = 80° Equation 2

Eq. 1-Eq. 2 yields: , 4- 2 = 20°, i.e. 4 = 2 + 2 + 2 + 2 + 20 ° = 100°

The conditions are insufficient to calculate the results.

Depending on your criteria, there is no one answer. There should still be a condition missing.

First, the four points of ABCD satisfy the parabolic equation, and Y2=4 can be found Second, because of AD BC, the slope of the two straight lines of AD and BC is the same, that is, (Y4-Y1) (X4-2)=(Y3-Y2) (-2), and D is on the left side of C (that is, the abscissa of D is negative, which you can see by drawing a diagram).

By substituting y1, y2, y3, and y4 with a, b, and x4 into the above equation, we can get the equation x4 2+2*x4-8=0, and solve x4=2 (rounded) or x=-4

Finally, the area of the triangle = |y2|*|x4|/2=4*4/2=8

Junior high school math, slope, in order to remember this problem, I want to study it.