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Brut [27]
3 years ago
8

Which ordered pair (a, b) is the solution to the following system of equations?

Mathematics
1 answer:
Kamila [148]3 years ago
8 0

Answer:

  (-13, -4)

Step-by-step explanation:

It is about as easy to try the solutions as it is to find them from scratch.

__

However, we can determine which one it is by adding twice the second equation to the first.

  (-2a +3b) +2(a -4b) = (14) +2(3)

  -5b = 20

  b = -4 . . . . . . matches the first choice

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the measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147 and 130. if the two remaining angles are equal
mars1129 [50]
A polygon is any figure sided with three sides and above such that triangle (3) is the smallest polygon. A nonagon is a polygon with 9 sides. To get the sum of interior angles of a polygon we use the formula;
(n-2) 180 or (n-4)90 where n is the number of sides.
Therefore, for a nonagon the sum of interior angles = (9-2) 180 = 1260 degrees
If we add all the angles we should get 1260, considering the remaining angles to be each x
Thus 138+154 +145 +132 +128 +147 +130 + x +x =1260
                             = 974 + 2x = 1260
                             = 2x = 286
                             = 143
 therefore, each of the other angles was 143 
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3 years ago
A garden has an area of 18 square meters. Which measurement is closest to the length of each side of the garden?
Katena32 [7]

9m is is the closest length of each side of the garden
3 0
3 years ago
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RSB [31]
Change in temperature = final - initial
= 22 - (-13)
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ch4aika [34]

Answer:

m∠3 = 73°

Step-by-step explanation:

Vertical angles are equivalent in measure. Complement angles add up to 90°, so subtract 17° from 90° to get your answer.

6 0
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without building the graph, find the coordinates of the point of intersection of the lines given by the equation y=3x-1 and 3x+y
DaniilM [7]
<h2><u>1. Determining the value of x and y:</u></h2>

Given equation(s):

  • y = 3x - 1
  • 3x + y = -7

To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.

<h3 /><h3><u>Method-1: Substitution method</u></h3>

Given value of the y-variable: 3x - 1

Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.

\implies 3x + y = -7

\implies3x + (3x - 1) = -7

\implies3x + 3x - 1 = -7

Combine like terms as needed;

\implies 3x + 3x - 1 = -7

\implies 6x - 1 = -7

Add 1 to both sides of the equation;

\implies 6x - 1 + 1 = -7 + 1

\implies 6x = -6

Divide 6 to both sides of the equation;

\implies \dfrac{6x}{6}  = \dfrac{-6}{6}

\implies x = -1

Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.

\implies y = 3(-1) - 1

\implies     \ \ = -3 - 1

\implies     = -4

Therefore, the value(s) of the x-variable and the y-variable are;

\boxed{x = -1}   \boxed{y = -4}

<h3 /><h3><u>Method 2: System of equations</u></h3>

Convert the equations into slope intercept form;

\implies\left \{ {{y = 3x - 1} \atop {3x + y = -7}} \right.

\implies \left \{ {{y = 3x - 1} \atop {y = -3x - 7}} \right.

Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.

\implies \left \{ {{y = 3x - 1 } \atop {- (y = -3x - 7)}} \right.

\implies \left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.

Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.

\implies\left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.

\implies 0 = (6x) + (6)

\implies0 = 6x + 6

This problem is now an algebraic problem. Isolate "x" to determine its value.

\implies 0 - 6 = 6x + 6 - 6

\implies -6 = 6x

\implies -1 = x

Like done in method 1, substitute the value of x into the first equation to determine the value of y.

\implies y = 3(-1) - 1

\implies y = -3 - 1

\implies y = -4

Therefore, the value(s) of the x-variable and the y-variable are;

\boxed{x = -1}   \boxed{y = -4}

<h2><u>2. Determining the intersection point;</u></h2>

The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.

⇒ (x, y) ⇒ (-1, -4)

Therefore, the point of intersection is (-1, -4).

<h3>Graph:</h3>

5 0
1 year ago
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