In four digit ABCA, two digit AB is a prime number, BC and Ca are both a complete square number. Find this number

In four digit ABCA, two digit AB is a prime number, BC and Ca are both a complete square number. Find this number

In four digit ABCA, two digit AB is a prime number, BC and Ca are both a complete square number. Finding this number AB is a prime number, which means that B is odd and can't be 5, only 1,3,7,9bc is a complete square number, which means that B can't be 5,7,9bc is a complete square number, so B is 1 or 3, BC is a complete square number 16 or 36, C is 6, CA is a complete square number

It is known that ABCA is a four digit number. If two digit AB is a prime number, BC is a complete square number, and Ca is the product of a prime number and a complete square number that is not 1, then what are all the four digits that satisfy the condition?

It is known that ABCA is a four digit number. If two digit AB is a prime number, BC is a complete square number, and Ca is the product of a prime number and a complete square number which is not 1, then all four digits satisfying the condition are:
three thousand one hundred and sixty-three
eight thousand three hundred and sixty-eight

(1) Try to find the four digit number XXYY, so that it is a complete square number (2). The sum of the square of a prime number and a positive odd number is equal to 125. Find the product of the two numbers
By 5 p.m

1. From the characteristics of the number XXYY, we can see that the number can be divided by 11, and it is a complete square number, so it can be divided by the square 121 of 11. It is a 4-digit and complete square number, so it should be one of the products of 121 and 9162536496481. Through calculation, we can see that the number should be the product of 121 and 64, which is 7744
2.125 is odd. A positive odd number and another number add up to 125, which is odd, so the other number is even. The even number is the square of a prime number, so the prime number is even. Among all prime numbers, the even number is only 2, so the two numbers are 2 and 121. So the product of the two numbers is 242

Given a (- 2,4), B (3, - 1), and vector cm = vector 3CA, vector CN = vector 2CB, find the coordinates of M, N and vector Mn
Process thank you

Note: you may have written o as C
Vector om = vector 3oa = (- 6,12)
Vector on = vector 2ob = (6, - 2)
So the coordinates of M (- 6,12) and n (6, - 2)
Vector Mn = (12, - 14) [coordinates of n-coordinates of M]

Given points m (2,4), n (- 1,1), point a is on line Mn, and vector Ma = 3, vector an, then the coordinate of point a is

Let a (x, y)
MA=(x-2,y-4)
AN=(-1-x,1-y)
Because Ma = 3an
therefore
x-2=3(-1-x)
y-4=3(1-y)
The solution is as follows
x=-1/4
y=7/4

If the ratio of the point M-component vector AB is - 4 / 1, and the ratio of the point N-component vector AB is 3, find the ratio of the A-component vector Mn

AM=-4MB => MB=-AM/4(1)
AN=3NB => NB=AN/3 (2)
(1)-(2)
=> MN=-AM/4-AN/3
=> MA+AN=-AM/4-AN/3
=> MA=-AN
=>The ratio is - 1

As shown in the figure, OQ bisects ∠ AOB, point P is the point on OQ, and points n and m are on OA and ob. If ∠ PNO + ∠ PMO = 180 °, the size relationship between PM and PN is ()
A.PM>PN B.PM

Connecting Mn
∵∠PNO+∠PMO=180°
The four points o, m, P and N are in the same circle
∴∠PMN=∠PON
∠PNM=∠POM
∵ OQ bisection ∠ AOB
∴∠QOA=∠QOB
That is ∠ POM = ∠ PON
∴∠PMN=∠PNM
A PMN is an isosceles triangle
∴PM=PN
Are you satisfied with the above answers?

It is known that in the same plane, OA is perpendicular to CD and ob is perpendicular to CD. What is the relationship between OA and ob and why

OA and ob parallel

As shown in the figure, the quadrilateral ABCD is a square, the diagonal AC and BD intersect at O, Mn ‖ AB, and intersect at M and N with AO and Bo respectively. The proof is: (1) BM = CN; (2) BM ⊥ CN

The following results are proved: (1) Mn ‖ AB, OM = on, am = oa-om = ob-on = BN. In △ ABM and △ BCN, ab = BC, mAb = NBCAM = BN, ABM ≌ BCN (SAS), BM = CN

It is known that P is a point in the angle AOB, Po = 24cm, angle AOB = 30 °, try to find two points c and D on OA and ob respectively, so as to minimize the perimeter of △ PCD and find the minimum perimeter

Make the axisymmetric points P / and P / / of point P with respect to the straight line where OA and ob are located, connect these two points, and the intersection point with OA and ob is the two points to minimize the perimeter of △ PCD. Because OP = op / = op / /, the length of P / P / / is the minimum perimeter, because the angle AOB = 30 °,
So the angle P / P / / = 60 degrees, so op / P / / is an equilateral triangle, so p / P / / = OP = 24cm