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avanturin [10]
3 years ago
8

What is the solution to y=5x-7 -3x-2y=-12

Mathematics
2 answers:
poizon [28]3 years ago
7 0
Since <span>−3x</span><span> does not contain the </span>variable<span> to solve for, move it to the right-hand side of the </span>equation<span> by adding </span><span>3x</span><span> to both sides.
</span><span>y=5x−7</span> 
<span>−2y=3x−12

</span>Divide<span> each </span>term<span> in the </span>equation<span> by </span><span><span>−2</span>.
</span><span>y=5x−7</span> 
<span>y=−<span><span>3x/</span>2</span>+6

</span>Create a graph<span> to locate the </span>intersection<span> of the </span>equations<span>. The </span>intersection<span> of the </span><span>system of equations</span><span> is the </span>solution<span>.
</span>
<span>(2,3)
</span>

likoan [24]3 years ago
4 0
y=5x-7 \\&#10;-3x-2y=-12 \\ \\&#10;\hbox{substitute 5x-7 for y in the 2nd equation:} \\&#10;-3x-2(5x-7)=-12 \\&#10;-3x-10x+14=-12 \\&#10;-13x+14=-12 \ \ \ |-14 \\&#10;-13x=-26 \ \ \ |\div (-13) \\&#10;x=2 \\ \\&#10;y=5x-7=5 \times 2-7=10-7=3 \\ \\&#10;\boxed{(x,y)=(2,3)}
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Given the polynomial 2x3 18x2 − 18x − 162, what is the value of the constant 'k' in the factored form? 2x3 18x2 − 18x − 162 = 2(
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The value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

<h3>What is polynomial equation?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

2x^3 +18x^2 - 18x - 162

The factor of the polynomial equation are given as,

2(x+ k)(x - k)(x +9)

First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 2, which can divide each term of the above equation (2, 18, -18, -162). Thus,

2(x+ k)(x - k)(x +9)=2(x^3 +9x^2 - 9x - 81)

Take out the highest common factor to make the groups as,

2(x+ k)(x - k)(x +9)=2(x^2( x+9) - 9(x + 9))\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 9)\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 3^2)

Use the property of difference of the square for the (x²-3²) term as,

2(x+ k)(x - k)(x +9)=2( x+9) (x+3)(x-3)\\2(x+ k)(x - k)(x +9)=2 (x+3)(x-3)( x+9)

On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

Learn more about factor of polynomial here;

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Solve the inequality for x<br> 3^(6x+18)&lt;27^(3x)
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Answer:

\displaystyle x > 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
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  4. Multiplication
  5. Division
  6. Addition
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Equality Properties

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<u>Algebra I</u>

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<u>Algebra II</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle 3^{6x + 18} < 27^{3x}<em />

<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Rewrite:                                                                                                             \displaystyle 3^{6x + 18} < 3^{3(3x)}
  2. Set:                                                                                                                     \displaystyle 6x + 18 < 3(3x)
  3. Factor:                                                                                                               \displaystyle 3(2x + 6) < 3(3x)
  4. [Division Property of Equality] Divide 3 on both sides:                                  \displaystyle 2x + 6 < 3x
  5. [Subtraction Property of Equality] Subtract 3x on both sides:                       \displaystyle -x + 6 < 0
  6. [Subtraction Property of Equality] Subtract 6 on both sides:                        \displaystyle -x < -6
  7. [Division Property of Equality] Divide -1 on both sides:                                 \displaystyle x > 6
8 0
3 years ago
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