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Natalka [10]
3 years ago
13

5^2xyz×5^4x^3y^-10z^-12

Mathematics
1 answer:
Leviafan [203]3 years ago
5 0
There is so solution to this problem
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Prove the following statements: (a) For every integer x, if x is even, then for every integer y, xy is even. (b) For every integ
Murrr4er [49]

Answer and Step-by-step explanation:

(a) Given that x and y is even, we want to prove that xy is also even.

For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.

(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:

Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.

(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.

3 0
3 years ago
What are the solutions of 4x2 + x = -3? (5 points) and <br> x2 - 7x = -12 (5 points)
Yuki888 [10]
4x^2 + x + 3 = 0

x =  [-1 +/- sqrt (1^2 - 4 * 4 * 3)]  / 8 =  - 1 +/- sqrt ( --47) / 8

=  ( - 1 +/- sqrt47i) / 8  =  -0.125 + 0.857i ,  -0.125 - 0.857i
7 0
3 years ago
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Find the inverse of the following functions algebraically
Inessa05 [86]
The answer is g^-1= x^2/2 + 1/2
4 0
3 years ago
What’s the answer? Please!!
gogolik [260]

Answer:

1

Step-by-step explanation:

:)

8 0
3 years ago
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The line graphed by the equation, y=5/6x +1/2, has a slope of 1/2 and a y-intercept of 5/6 true or false?
vazorg [7]
False. It has a slope of 5/6 and y intercept of 1/2.
8 0
3 years ago
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