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SVEN [57.7K]
3 years ago
10

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, 3) and (3, 4).

Everything above the line is shaded. The second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.
Which system of linear inequalities is represented by the graph?
Mathematics
2 answers:
11Alexandr11 [23.1K]3 years ago
8 0

Answer:

The first one

Step-by-step explanation:

Nastasia [14]3 years ago
4 0

Answer:

A. y≥\frac{1}{3\\}x+3, 3x-y>2

Step-by-step explanation:

The linear equations above match the lines in terms of slope and y-intercept.

I hope you found this helpful! If you did, I'd really appreciate if you'd mark my work as 'brainliest'. Please don't hesitate to ask any questions!

Have a great day!

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Answer:

For 3x^2+4x+4=0

Discriminant= = -32

The solutions are

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= -44

The solutions

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= -36

The solutions

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a= (1-√-1)/3

Step-by-step explanation:

Formula for the discriminant = b²-4ac

let the discriminant be = x for the equations

The solution of the equations

= (-b+√x)/2a and = (-b-√x)/2a

For 3x^2+4x+4=0

Discriminant= 4²-4(3)(4)

Discriminant= 16-48

Discriminant= = -32

The solutions

(-b+√x)/2a =( -4+√-32)/6

(-b+√x)/2a= (-4 +4√-2)/6

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a =( -4-√-32)/6

(-b-√x)/2a= (-4 -4√-2)/6

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= 2²-4(3)(4)

Discriminant= 4-48

Discriminant= -44

The solutions

(-b+√x)/2a =( -2+√-44)/6

(-b+√x)/2a= (-2 +2√-11)/6

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a =( -2-√-44)/6

(-b-√x)/2a= (-2 -2√-11)/6

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= (-6)²-4(9)(2)

Discriminant= 36 -72

Discriminant= -36

The solutions

(-b+√x)/2a =( 6+√-36)/18

(-b+√x)/2a= (6 +6√-1)/18

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a =( 6-√-36)/18

(-b-√x)/2a= (6 -6√-1)/18

(-b-√x)/2a= (1-√-1)/3

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Does anyone know these?​
Lyrx [107]

Answer:

1a. triangle

1b. triangle

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The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan
torisob [31]

The point slope form of the line which passes through the points (-5,-1) and (10,-7) is \fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}} i.e., \fbox{\begin\\\ \bf option C\\\end{minispace}}.

Further explanation:

It is given that line passes through the points (-5,-1) and (10,-7).

The objective is to determine the point slope form of the line which passes through the points (-5,-1) and (10,-7).

The options given are as follows:

Option A: 2x-5y=-15

Option B: 2x-5y=-17

Option C: 2x+5y=-15

Option D: 2x+5y=-17

Consider the point (-5,-1) as (x_{1},y_{1}) and (10,-7) as (x_{2},y_{2}).

Slope of a curve is defined as the change in the value of y with respect to change in value of x.

The slope of the line is calculated as follows:

\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}

To obtain the value of slope substitute the value of x_{1},y_{1},x_{2},y_{2} in the above equation.

\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}

Therefore, the slope of the line is \fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}

The general way to express the equation of a line in its point slope form is as follows:

\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}

To obtain the point slope form of the equation of the line substitute the value of m, x_{1} and y_{1} in the above equation.

\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}

From the above calculation it is concluded that the point slope form the equation of a line is \fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}

Figure 1 (attached in the end) represents the graph of the function 5y+2x=-15.

This implies that the correct option for the point slope form of the line is option C.

Therefore, the point slope form of the line which passes through the points (-5,-1) and (10,-7) is 2x+5y=-15 i.e., option C.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613  

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445.

Answer details

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.  

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