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3 years ago

What is the value for Z in the solution of the system?

Mathematics

1 answer:

ss7ja [257]3 years ago

3 0

3x-4y+2z=20
x+y-z=-4
6x-y+2z=23

x=2
y=-1
z=5

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What is x if n≠m? Please help!

lorasvet [3.4K]

Answer: $x = \frac{mn(q - p)}{n-m}\\\\$

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Work Shown:

Part 1

$\frac{x-m}{m} + p = \frac{x-n}{n} + q\\\\\frac{x-m}{m} - \frac{x-n}{n} = q - p\\\\\frac{n(x-m)}{mn} - \frac{m(x-n)}{mn} = q - p\\\\\frac{xn-mn}{mn} - \frac{xm-mn}{mn} = q - p\\\\\frac{xn-mn-(xm-mn)}{mn} = q - p\\\\$

Part 2

$\frac{xn-mn-xm+mn}{mn} = q - p\\\\\frac{xn-xm}{mn} = q - p\\\\\frac{x(n-m)}{mn} = q - p\\\\x(n-m) = mn(q - p)\\\\x = \frac{mn(q - p)}{n-m} \\\\$

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Explanations:

There are quite a bit of steps. I decided to break things into two parts.
The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
Afterward, I gave each fraction the LCD mn. I multiplied top and bottom of the first fraction by n/n. I did a similar operation to the second fraction, but with m instead.
From there, we distribute and simplify. The mn terms cancel on the left side numerator (second step of part 2).
The n≠m is there to prevent the denominator (n-m) from being zero. We cannot divide by zero.
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3 years ago

How do I solve this? Person to help gets brainliest.

REY [17]

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I believe its C?

Step-by-step explanation:

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In the figure, AB║CD and ∠EIA is congruent to ∠GJB Complete the following statements to prove that ∠IKL is congruent to ∠DLH.

REY [17]

Here it is given that AB || CD

< EIA = <GJB

Now

∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)

∠EIA ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)

∠IKL + ∠IKC 180° and ∠DLH + ∠JLD =180° (Linear Pair Theorem)

m∠IKL + m∠IKC = 180° ....(1)

But ∠IKC ≅ ∠JLD

m∠IKC = m∠JLD (SUBTRACTION PROPERTY OF CONGRUENCY)

So we have

m∠IKL + m∠JLD = 180°

∠IKL and ∠JLD are supplementary angles.

But ∠DLH and ∠JLD are supplementary angles.

∠IKL ≅ ∠DLH (CONGRUENT SUPPLEMENTS THEOREM)

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It should be the first one

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since positive ten would represent going further up and negative ten going further down, the diver would be within ten feet of her current position

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