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katrin [286]
2 years ago
13

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

t to y from the second equation is substituted into the first equation.
2x − 7y = 4
3x + y = −17

A) 2(3x − 17) − 7y = 4
B) 2(−3x − 17) − 7y = 4
C) 2x − 7(3x − 17) = 4
D) 2x − 7(−3x − 17) = 4
Mathematics
1 answer:
adell [148]2 years ago
3 0

Answer:

option D

2x − 7(−3x − 17) = 4

Step-by-step explanation:

Given in the question two equations

<h3>Equation 1</h3>

2x - 7y = 4

<h3>Equation 2</h3>

3x + y = -17

Rearranging equation 2 in terms of y

3x + y = -17

y = -17 - 3x

Put this value of y in Equation 1

2x - 7y = 4

2x - 7(-17 - 3x) = 4

So,

If you use the substitution method to solve the following system, new equation will be

<h3>2x - 7(- 3x - 17) = 4 </h3>

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What two numbers multiply to 54 and add up to 7
k0ka [10]
Xy = 54
x + y = 7

xy = 54
\frac{xy}{x} = \frac{54}{x}
y = \frac{54}{x}

x + y = 7
x + \frac{54}{x} = 7
\frac{x^{2}}{x} + \frac{54}{x} = 7
\frac{x^{2} + 54}{x} = 7
x^{2} + 54 = 7x
x^{2} - 7x + 54 = 0
x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}
x = \frac{7 \± \sqrt{49 - 216}}{2}
x = \frac{7 \± \sqrt{-167}}{2}
x = \frac{7 \± i\sqrt{167}}{2}
x = \frac{7 \± 12.9i}{2}
x = 3.5 \± 6.45i
x = 3.5 + 6.45i    or    3.5 - 6.45i

                  x + y = 7
   3.5 + 6.45i + y = 7
- (3.5 + 6.45i)       - (3.5 + 6.45i)
                        y = 3.5 - 6.45i
                  (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)

                          or

                  x + y = 7
   3.5 - 6.45i + y = 7
- (3.5 - 6.45i)     - (3.5 - 6.45i)
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                 (x, y) = (3.5 - 6.45i, 3.5 + 6.45i)

The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.
5 0
3 years ago
Anna said that the product of 78·112=72. How can you tell that her answer is wrong?
Andreyy89
Her answer is wrong because the product of 78.112 = 8736.
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3 years ago
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A sequence is defined by the following: an = 4n – 1 What is a1?
Alexandra [31]

an = 4n – 1

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a1 = 4(1) -1

a1 = 4-1

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Answer: 3

6 0
3 years ago
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The American Bankers Association reported that, in a sample of 120 consumer purchases in France, 48 were made with cash, compare
tatuchka [14]

Answer:

Step-by-step explanation:

Hello!

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n₂= 55 consumer purchases

x₂= 24 cash purchases

p'₂= 24/55= 0.4364

You need to construct a 90% CI for the difference of proportions p₁-p₂

Using the central limit theorem you can approximate the distribution of both sample proportions p'₁ and p'₂ to normal, so the statistic to use to estimate the difference of proportions is an approximate standard normal:

[(p'₁-p'₂) ± Z_{1-\alpha /2} * \sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }]

Z_{0.95}= 1.648

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[-0.1689;0.0961]

The interval has a negative bond, it is ok, keep in mind that even tough proportions take values between 0 and 1, in this case, the confidence interval estimates the difference between the two proportions. It is valid for one of the bonds or the two bonds of the CI for the difference between population proportions to be negative.

I hope this helps!

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Whitepunk [10]

Answer: 30

Step-by-step explanation:

5+5 = 10

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