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Ilya [14]
3 years ago
10

A line has a slope of 3 and includes the points (8,9) and (7,c) what is the value of c

Mathematics
1 answer:
lozanna [386]3 years ago
5 0
C=6. Slope is the change in y value over the change in x value. Since the change in x is 1 between the two points, then the change in y will be 3.
You might be interested in
What is 1 1/4 + (3 2/3 +5 3/4)?
n200080 [17]

Answer:

Step-by-step explanation:

Because this whole problem focuses on the addition of mixed numbers, we can drop the parentheses right now without affecting the problem solution.

The two denominators shown are 4 and 3; the LCD is therefore 12.

Rewriting the problem, we get:

1 3/12 + 3 8/12 + 5 9/12, or

                  3 + 8 + 9

1 + 3 + 5 + ----------------

                         12

This simplifies to 9 20/12, or 10 8/12, or 10 2/3 (answer)

6 0
3 years ago
Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th
saul85 [17]

Answer:

The standard form of the ellipse is \frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1.

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y) (1)

If we know that V_{1} (x,y) = (4,0) and V_{2}(x,y) = (4, 14), then the coordinates of the center are, respectively:

(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)

(h,k) = (2,0) + (2, 7)

(h, k) = (4, 7)

The length of each semiaxis is, respectively:

a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}

a = 3

b = \sqrt{(4-4)^{2}+(0-7)^{2}}

b = 7

The standard equation of the ellipse is described by the following formula:

\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1

Where:

h, k - Coordinates of the center of the ellipse.

a, b - Length of the orthogonal semiaxes.

If we know that h = 4, k = 7, a = 3 and b = 7, then the standard form of the ellipse is:

\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1

4 0
3 years ago
How do I do this? please detail steps.
vladimir2022 [97]
Define
{x} =   \left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right]

Then
x₁ = cos(t) x₁(0) + sin(t) x₂(0)
x₂ = -sin(t) x₁(0) + cos(t) x₂(0)

Differentiate to obtain
x₁' = -sin(t) x₁(0) + cos(t) x₂(0)
x₂' = -cos(t) x₁(0) - sin(t) x₂(0)

That is,
\dot{x} =   \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right] x(0)

Note that
\left[\begin{array}{ccc}0&1\\-1&09\end{array}\right]   \left[\begin{array}{ccc}cos(t)&sin(t)\\-sin(t)&cos(t)\end{array}\right] =  \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right]

Therefore
x(t) =   \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] x(t)

7 0
3 years ago
How do You supposed to do this i need many method to do it.
defon
I like the substitution method. Which is when you make one equation equal only x or y and plug it into the other equation)

There is also the graphing method. If you graphed it, it might not be quite as accurate (at least on hand, on computer you would be pretty exact)

Then there is the elimination method. You multiply one of the equations by a coefficient so that you can eliminate x or y from the equation. 
4 0
3 years ago
What is the GCF of:<br> 15x^2y and 20xy
azamat

Answer:

5xy

Step-by-step explanation:

x and y can only go into both into once

3 0
3 years ago
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