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9966 [12]
2 years ago
12

Find the equation of the line

Mathematics
1 answer:
amm18122 years ago
7 0

Answer:

y = 2x - 7

Step-by-step explanation:

The question is asking for slope-intercept form, y = mx + a.

Given:

(1, -5) and (9, 11)

Find the slope (m) between the two points:

m = (y2 - y1) / (x2 - x1)

x1 = 1

x2 = 9

y1 = -5

y2 = 11

m = ( 11 - (-5) )/(9 - 1)

= 16/8

m = 2

y = 2x + a

Use one of the two points to find a (I will use (1, -5)):

-5 = 2(1) + a

-5 = 2 + a

-7 = a

a = -7

y = 2x + (-7)

y = 2x - 7

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Answer:

A.

SA= \frac{2}{3} \pi rl+16 \pi r^2

Step-by-step explanation:

Surface area of the original cone

SA= \pi r l + \pi r^2... (1)

When, radius is quadrupled and slant height is reduced to one sixth

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Plug the above values of r and l in equation (1), new surface area becomes:

SA= \pi (4r)\times \frac{1}{6} l+ \pi (4r)^2

SA= \frac{4}{6} \pi rl+16 \pi r^2

\huge \purple {\boxed {SA= \frac{2}{3} \pi rl+16 \pi r^2}}

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There are 8 circles and 20 triangles. What’s the simplest ratio of circles to total shapes?
sleet_krkn [62]

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2:5

Step-by-step explanation:

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The cost to a rent paddleboat at the city park includes an initial fee of $7.00, plus $3.50 per hour. Which equation models the
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Use cramers Rule to solve the following system:
Jet001 [13]

Answer:

The solution to the system is x=1,y=-2 and z=-5

Step-by-step explanation:

Cramer's rule defines the solution of a system of equations in the following way:

x= \frac{D_x}{D}, y= \frac{D_y}{D} and z= \frac{D_z}{D} where D_x, D_y and D_z are the determinants formed by replacing the x,y and z-column values with the answer-column values respectively. D is the determinant of the system. Let's see how this rule applies to this system.

The system can be written in matrix form like:

\left[\begin{array}{ccc}5&-3&1\\0&2&-3\\7&10&0\end{array}\right]\times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}6&11&-13\end{array}\right]

Then each of the previous determinants are given by:

D_x = \left|\begin{array}{ccc}6&-3&1\\11&2&-3\\-13&10&0\end{array}\right|=199 Notice how the x-column has been substituted with the answer-column one.

D_y = \left|\begin{array}{ccc}5&6&1\\0&11&-3\\7&-13&0\end{array}\right|=-398 Notice how the y-column has been substituted with the answer-column one.

D_z = \left|\begin{array}{ccc}5&-3&6\\0&2&11\\7&10&-13\end{array}\right|=-995

Then, substituting the values:

x= \frac{D_x}{D}=\frac{199}{199}\\ x=1

x= \frac{D_y}{D}=\frac{-398}{199}\\ y=-2

x= \frac{D_z}{D}=\frac{-995}{199}\\ x=-5

3 0
3 years ago
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