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## Chemistry, Physics, SAT Math, and Calculus Tutor; CU Chemical Engineer

### Brooklyn, NY (11209)

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# John's Responses in WyzAnt Answers

#### One leg of a right triangle has a length of 7 centimeters. The other sides have lengths that are consecutive integers.find these lengths.

right triangles

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Asked by Marysa from Nampa, ID
00

You know by the Pythagorean theorem that a2 +b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse or longest side. When they say the other two legs are consecutive integers, that means that x = x+1 or in this case c = b+1. By substituting c = b+1 and 7cm into the Pythagorean theorem, you will get:

72 + b2 = (b+1)2

FOIL the b+1 and get all the b's on one side (b2 will cancel since you have +1b2 on both sides). You should be able to solve for b. Then, use that value to get c since you know c = b+1. Check it by plugging your values back into the Pythagorean theorem.

#### Identify the solution(s) of the system of equations, if any. 2x+5y=10 and y=2-x

Identify the solutions of the system of equations, if any

2x+5y=10

y=2-x

a. (-2,0)

b. (2,0)

c. (0,-2)

d. (0,2)

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Asked by Latoya from Copperas Cove, TX
00

This is a classic two equations with two unknowns type problem.  The goal in the first step is to eliminate one of the variables by making an equivalent statement in terms of one variable. In order to get rid of one of the variables, substitute either

y = 2-x    or  x = 2 - y    (These equations say the same thing)

into the first equation. (It is usually easier to substitute the smaller equation into the bigger one)

Now you should have one equation with one unknown(x or y). Solve for that unknown.

Next, use that value you just got to find the other value by substituting it into either equation. If you have done everything right, both equations will give you the same answer but the smaller one will be quicker.

The solution is (x,y) as you are looking for the x and y that satisfy your two equations.

#### How would you simplify this:(x + 3y - 5z) - (x - 2y + 6z)I need assistance on solving

How would I simplify this equation, where do I start?

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Asked by Harolyn from Chicago, IL
00

By the order of operations, multiplication comes before addition. The (x-2y+6z) is being mulitplied by -1, so distribute that through first. Then remember that addition is commutative and you can add/subtract like terms together, for example  3y + 4y = 7y.

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## Background Check Status for John Z.

John Z. passed a background check on 2/21/2013. You may run an updated background check on John once you send an email.