What is the slope of the line that contains the points (3, 4) and (1, 2)?

What are the theorems I feel like I got at least 1 wrong already ╥﹏╥

OLEGan [10]

$\begin{gathered} m\angle2=m\angle6\text{ are corresponding angles} \\ \angle2\cong\angle6\text{ are the same because the both angles are corresponding} \end{gathered}$ $\begin{gathered} m\angle2+m\angle3=180\text{ are angles on a straight line.} \\ \text{angles on straight line =180 degree} \end{gathered}$ $\begin{gathered} m\angle3+m\angle6=180\text{ are supplementary angles} \\ \text{supplementary angles = 180 degree} \end{gathered}$ $\begin{gathered} m\angle2+m\angle3=m\angle3+m\angle6 \\ angles\text{ on a straight line(180 degree)=supplementary angles(180 degree)} \end{gathered}$

3 0

11 months ago

Which equation represents a circle that contains the point (-5, 3) and has a center at (-2, 1)? Distance formula: vaa -02 (x - 1

natali 33 [55]

Given:

The center of the circle = (-2,1).

Circle passes through the point (-5,3).

To find:

The equation of the circle.

Solution:

Radius is the distance between the center of the circle and any point on the circle. So, radius of the circle is the distance between the points (-2,1) and (-5,3).

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(-5-(-2))^2+(3-1)^2}$

$r=\sqrt{(-5+2)^2+(2)^2}$

$r=\sqrt{(-3)^2+(2)^2}$

On further simplification, we get

$r=\sqrt{9+4}$

$r=\sqrt{13}$

The standard form of a circle is:

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

Where, (h,k) is the center of the circle and r is the radius of the circle.

Substitute h=-2, k=1 and $r=\sqrt{13}$ .

$(x-(-2))^2+(y-1)^2=(\sqrt{13})^2$

$(x+2)^2+(y-1)^2=13$

Therefore, the equation of the circle is $(x+2)^2+(y-1)^2=13$ .

8 0

3 years ago

write the slope - intercept equation of the line that passes through the point (6, "-1)" and has a slope of "-1/3"

TEA [102]

Answer:

y = - $\frac{1}{3}$ x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{1}{3}$ , then

y = - $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute (6, - 1 ) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - $\frac{1}{3}$ x + 1 ← equation of line

8 0

2 years ago

We want to solve the following system of equations using the substitution method.

inna [77]

In the second equation you are given what Y equals, which is (-5x - 3). You would use this equation and plug it into the y value given in the first equation where it says 2y and solve

That would be

3x - 2(-5x - 3) = -6
3x + 10x + 6 = -6
3x + 10x = -6 - 6
13x = -12
X = -12/13

Then if you want to solve for Y you can use any equation and plug in the x-value found.

I’m going to use equation 2.

Y = -5x - 3
Y = -5(-12/13) - 3
Y = 4.615 - 3
Y = 1.615

(-12/13, 1.615)

Therefore the x-value is -12/13 and the y-value is 1.615.

5 0

2 years ago

7)

Llana [10]

Answer:

Step-by-step explanation:

If the first floor of the Willis Tower is 21 feet high. and each additional floor is 12 feet high, then the floor heights as we move from one floor to another we keep increasing by 12feets and forms an arithmetic progression as shown;

21, (21+12), (21+12+12), ...

21, 33, 45...

a) To write an equation for the nth floor of the tower, we will have to find the nth term of the sequence using the formula for finding the nth term of an arithmetic sequence.

The nth term of an arithmetic sequence is expressed as $T_n = a + (n-1)d$