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natima [27]
3 years ago
10

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider this s

ystem of equations: x + 2y = -13 12x + 5y = -4 The solution of this system of equations is ( , ).
Mathematics
1 answer:
Brut [27]3 years ago
8 0

Answer:

<u>The solution of this system of equation is ( 3, - 8)</u>

Step-by-step explanation:

1. Let's solve the system of equations:

First equation:

x + 2y = - 13

x = - 13 - 2y

Second equation:

12x + 5y = -4

12 * (- 13 - 2y) + 5y = - 4 (Replacing x with - 13 - 2y)

-156 -24y + 5y = - 4

-24y + 5y = - 4 + 156 (Like terms)

-19y = 152

y = - 152/19

<u>y = -8</u> (Dividing by 19)

Solving x

x + 2y = -13

x + 2 (- 8 ) = - 13

x - 16 = - 13

x = - 13 + 16

<u>x = 3</u>

2. Proving that x = 3 and y = - 8 are correct:

12x + 5y = -4

12 * 3 + 5 * -8 = -4

36 - 40 = - 4

- 4 = - 4

<u>We proved that x = 3 and y = - 8 are correct</u>

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babunello [35]

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8 0
2 years ago
Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3
kirill115 [55]

Answer:

f(x) = x^{4} + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + \sqrt{2} is a zero then - 1 - \sqrt{2} is also a zero

\sqrt{3} is a zero then - \sqrt{3} is also a zero

Thus the corresponding factors are

(x - (- 1 + \sqrt{2}) ), (x - (- 1 - \sqrt{2}) ), (x - \sqrt{3}), (x - (- \sqrt{3})), that is

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The polynomial is then the product of the roots

f(x) = (x + 1 - \sqrt{2})(x + 1 + \sqrt{2})(x - \sqrt{3})(x + \sqrt{3})

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     = (x² + 2x + 1 - 2)(x² - 3)

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3 0
3 years ago
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What’s the length of the new fence?
natulia [17]
We apply the Pythagorean theorem twice and obtain:
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