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otez555 [7]
3 years ago
9

System of linear equations. 2x + 4y =, 10 2x + 2y + 3z = 3 -3x + y + 2z = -3

Mathematics
1 answer:
Dimas [21]3 years ago
3 0

Answer:

x = 1, y = 2, z = -1

Step-by-step explanation:

2x + 4y = 10

2x = -4y + 10

x = -2y + 5

now sub -2y + 5 in for x, back into the other 2 equations

2x + 2y + 3z = 3                                   -3x + y + 2z = -3

2(-2y + 5) + 2y + 3z = 3                       -3(-2y + 5) + y + 2z = -3

-4y + 10 + 2y + 3z = 3                           6y - 15 + y + 2z = -3

-2y + 3z = 3 - 10                                    7y + 2z = - 3 + 15

-2y + 3z = - 7                                         7y + 2z = 12

-2y + 3z = -7....multiply by 2

7y + 2z = 12...multiply by -3

--------------------------

-4y + 6z = -14 (result of multiplying by 2)

-21y - 6z = -36 (result of multiplying by -3)

---------------------------add

-25y = - 50

y = -50/-25

y = 2 <===

2x + 4y = 10                        2x + 2y + 3z = 3

2x + 4(2) = 10                      2(1) + 2(2) + 3z = 3

2x + 8 = 10                          2 + 4 + 3z = 3

2x = 10 - 8                            6 + 3z = 3

2x = 2                                   3z = 3 - 6

x = 2/2                                 3z = -3

x = 1  <==                              z = -3/3

                                            z = -1 <===

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sergey [27]

Answer:

  4. 11/6, 121/36

  5. 5/8, 25/64

  6. 4/7, 16/49

  7. 14/9, 196/81

Step-by-step explanation:

The ratio of perimeters is the same as the ratio of corresponding legs:

  perimeter ratio = red leg/blue leg

The area ratio is the square of that:

  area ratio = (perimeter ratio)²

__

<h3>4.</h3>

perimeter ratio = 11/6

area ratio = (11/6)² = 121/36

__

<h3>5.</h3>

perimeter ratio = 5/8

area ratio = (5/8)² = 25/64

__

<h3>6.</h3>

perimeter ratio = 4/7

area ratio = (4/7)² = 16/49

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<h3>7.</h3>

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area ratio = (14/9)² = 196/81

3 0
2 years ago
Factor. w(squared)+18w+81
solong [7]

{w}^{2}  + 18w + 81 \\ (w + 9)(w + 9) \\ or \\ {(w + 9)}^{2}
7 0
3 years ago
Kate paid $118.65 for a jacket. the price includes a 5% sales tax. how much was the jacket before the tax?
Harman [31]

Let, the price of jacket before tax = x

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8 0
2 years ago
1. Mark Ford deposits $11,800 into Role Bank, which pays 8% interest that
borishaifa [10]

Answer:

The amount after 4 years = $ 16198.87

Step-by-step explanation:

Points to remember

Compound interest

A = P[1 + R/n]^nt

Were A - Amount

P - Principle

R - Rate of interest

t - Number of years

n - Number of times compounded

<u>To find the amount</u>

Here P = $11,800, R = 8% = 0.08, t = 4 years and n = 4 times

A = P[1 + R/n]^nt

 =  11800[1 + 0.08/4]^(4 * 4)

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Therefore amount after 4 years = $ 16198.87

5 0
3 years ago
Simplify the rational expression. State any restrictions on the variable.
natulia [17]

Answer:

t+4, t≠8

Step-by-step explanation:

\dfrac{t^2-4t-32}{t-8}=\dfrac{(t+4)(t-8)}{(t-8)}=t+4

The value of t must not be one that makes the denominator zero, hence must not be 8.

8 0
3 years ago
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