Write an algebraic expression for the perimeter

What is the standard form of the points (-3,4) (2,-6)

Bas_tet [7]

The standard form equation of the line connecting the two points is $2x + y = -2$

Linear equation in a standard form is given as $Ax + By = C$

where,

A, B, and C are constants or numbers

x and y are the variables.

To solve this problem, the following steps would be taken:

Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1}$

where,

$(x_1, y_1) = (-3,4)\\(x_2, y_2) = (2,-6)$

Substitute

$slope (m) = \frac{-6 - 4}{2 -(-3)} \\m = \frac{-10}{5}\\m = -2$

Step 2: Find the y-intercept (b) of the line by substituting $(x, y) = (-3,4)$ and $m = -2$ into $y = mx + b$ (slope-intercept form)

$4 = -2(-3) + b\\4 = 6 + b\\4 - 6 = 6 + b - 6\\-2 = b\\b = -2$

Step 3: Write the equation of the line in slope-intercept form by substituting $m = -2$ and $b = -2$ into $y = mx + b$

$y = -2x + (-2)\\y = -2x - 2$

Step 4: Rewrite the equation in standard form $(Ax + By = C)$

$y = -2x - 2\\$

Add $2x$ to both sides

$2x + y = -2x - 2 + 2x\\2x + y = -2$

The standard form equation of the points (-3,4) and (2,-6) is $2x + y = -2$

Learn more about standard form of two points of a linear equation here:

brainly.com/question/18446164

6 0

3 years ago

2. Given the equation of a circle in standard form, identify the center, radius, and graph the circle.

Varvara68 [4.7K]

Answer:

Center: ( -1 , 2 )

Radius: 6

Step-by-step explanation:

The equation for a circle is given as follow:

$(x-h)^{2} +(y-k)^{2} =r^{2}$

Where,

the Center is: ( h , k ) (note that the signs of the number are different)

and the radius is: r

So if we compare the original circle equation to the equation in the question we can see that:

$(x+1)^{2} +(y-2)^{2} =36$

the Center is: (-1,2)

and the radius is: $\sqrt{36}$ = 6

2. To draw the graph find points that lay on the circle, it's better to take the values of x and y from the Center:

first sub y=2 in the equation to find the values for x:

$(x+1)^{2} +(y-2)^{2} =36$

$(x+1)^{2} +(2-2)^{2} =36$

$(x+1)^{2} +(0)^{2} =36$

$(x+1)^{2} =36$

$x+1 =±\sqrt{36}$

$x=6-1$ AND $x=-6-1$

$x=5$ AND $x=-7$

The points are A(5,2) and B(-7,2)

second sub x= -1 in the equation to find the values for y:

$(x+1)^{2} +(y-2)^{2} =36$

$(-1+1)^{2} +(y-2)^{2} =36$

$(0)^{2} +(y-2)^{2} =36$

$(y-2)^{2} =36$

$y-2=±\sqrt{36}$

$y=6+2$ AND $y=-6+2$

$y=8$ AND $y=-4$

The points are D(-1,8) and E(-1,-4)

After finding the points write them in the graph and match them together to get the like the circle in the picture below:

8 0

3 years ago

Please help and thank you

worty [1.4K]

I believe 2 dollars and 50 cents

6 0

3 years ago

Read 2 more answers

Determine whether the study depicts an observational study or an experiment.

USPshnik [31]

Answer:

Option c

Step-by-step explanation:

The study is an observational study. An observational study is made when the researchers collect data based on what they see, hear or observe without any form of manipulation or treatment plan from the researchers. Thus, in this case, the study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable/influence their responses.

6 0

3 years ago

The ratio of 600m to 3km in simplest form

never [62]

3 km = 3000m
600m:3000m divide by 10
60:300 divide by 10
6:30 divide by 3
2:10 divide 2
*1:5* (simplest form)

6 0

3 years ago