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V125BC [204]
3 years ago
11

Need help with number 10 please

Mathematics
1 answer:
Naddika [18.5K]3 years ago
3 0

Answer:

  Pilar is correct. Both systems have solution (-2, 4).

Step-by-step explanation:

Graphing, or any other means of solving these systems of equations reveals both systems have the same solution: (x, y) = (-2, 4).

_____

By Cramer's rule, the solution to the first set is ...

  x = (2(6)-4(2))/(2(5)-4(3)) = 4/-2 = -2

  y = (2(5)-6(3))/-2 = -8/-2 = 4

(x, y) = (-2, 4) is the solution to the first system

__

Since the first equation of the second system is the same as the first equation of the first system, we know the above solution satisfies that equation. We only need to check to see if the same point satisfies the second equation of the second system:

  11(-2) +8(4) = -22 +32 = 10 . . . . . yes,

(-2, 4) is the solution of the second system

Pilar is correct that both systems have the same solution.

_____

Cramer's Rule tells you the solution to

  • ax +by = c
  • dx +ey = g

is ...

  • x = (bg -ec)/(bd -ea)
  • y = (cd -ga)/(bd -ea) . . . . same denominator as for x

I like to use Cramer's Rule when the solution is needed without a lot of steps. Here, we could use the Elimination method to eliminate the y-variable and solve for x. Then more steps are needed to find y. The writing out and explanation are tedious, so it is much simpler just to use a formula that gives the answer.

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m dot n would equal 8, or 8 = 2*2+3*y.  Then 8 = 4 + 3y, and 4 = 3y, and y =3/4.

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7 0
3 years ago
F(x) = -322 Find f(-2)​
serg [7]

Answer:

f ( - 2 ) =  - 12

Step-by-step explanation:

f ( - 2 ) = - 3 ( -2 )^2

then you do the exponent first so

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8 0
2 years ago
3x^2 - 4x = -2<br> Solve
amid [387]

Answer:

x =   \bigg \{\frac{ 2   - \sqrt{2} \: i }{3}, \:  \: \frac{ 2    +  \sqrt{2} \: i }{3} \bigg \}

Step-by-step explanation:

3 {x}^{2}  - 4x =  - 2 \\ 3 {x}^{2}  - 4x + 2 = 0 \\ equating \: it \: with  \\ a {x}^{2}  + bx + c = 0 \\ a = 3 \:  \: b =  - 4 \:  \: c = 2 \\  {b}^{2}  - 4ac \\  =  {( - 4)}^{2}  - 4 \times 3 \times 2 \\  = 16 - 24 \\  =  - 8  \\  \ {b}^{2}  - 4ac < 0  \\  \therefore \: given \: quadratic \: equation \: have \:  \\ imaginary \: solutios. \\  \\ x =  \frac{ - b \pm \sqrt{{b}^{2}  - 4ac } }{2a}  \\ =  \frac{ - ( - 4) \pm \sqrt{ - 8} }{2 \times 3} \\ =  \frac{ 4 \pm 2\sqrt{2} \: i }{2 \times 3}  \\  =  \frac{ 2 \pm \sqrt{2} \: i }{3} \\  \therefore \: x  = \frac{ 2   - \sqrt{2} \: i }{3}  \: or \: x  = \frac{ 2   +  \sqrt{2} \: i }{3} \:  \\  \\ x =   \bigg \{\frac{ 2   - \sqrt{2} \: i }{3}, \:  \: \frac{ 2    +  \sqrt{2} \: i }{3} \bigg \}

7 0
3 years ago
6. Give the slope of each line. Also, state if the lines are parallel (yes or no). Hint: rewrite to slope-intercept form. AB: 2y
Dmitriy789 [7]

Answer:

gvc TV h r the g4vt22cynukbh5nj66n

8 0
3 years ago
What is the linear function equation represented by the graph?<br><br><br> f(x)=______________
Katen [24]

The linear function equation represented by the graph is \boxed{y =  - \frac{1}{2}x + 1}.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

\boxed{y = mx + c}

The formula for slope of line with points \left( {{x_1},{y_1}} \right) and \left( {{x_2},{y_2}} \right) can be expressed as,

\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}

Given:

Explanation:

From the graph it has been observed that the line passes through the points \left( {0,1} \right) and \left( {2,0} \right).

The line intersect y-axis at \left( {0,1} \right).

Therefore, the y-intercept is 1.

The line the line passes through the points \left( {0,1} \right) and \left( {2,0} \right).

The slope can be obtained as follows,

\begin{aligned}m&=\frac{{0 - 1}}{{2 - 0}}\\&= \frac{{ - 1}}{2}\\\end{aligned}

The slope of the line is - \dfrac{1}{2}.

Substitute - \dfrac{1}{2} for m and 1 for c in equation y = mx + c to obtain the equation of the line.

y = - \dfrac{1}{2}x + 1

The linear function equation represented by the graph is \boxed{y =  - \frac{1}{2}x + 1}.

Learn more:

  1. Learn more about inverse of the function brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: graph function, numbers, slope, slope intercept, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

6 0
3 years ago
Read 2 more answers
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