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2 years ago

A line includes the points (10, -10) and (1,8). What is its equation in slope-intercept form?

Mathematics

1 answer:

Anettt [7]2 years ago

4 0

Answer:

y=-2x+10

Step-by-step explanation:

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

m=(8-(-10))/(1-10)

m=(8+10)/-9

m=18/-9

m=-2

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y-y1=m(x-x1)

y-(-10)=-2(x-10)

y+10=-2x+20

y=-2x+20-10

y=-2x+10

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For the following linear system, put the augmented coefficient matrix into reduced row-echelon form.

Anni [7]

Answer:

The reduced row-echelon form of the linear system is $\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right]$

Step-by-step explanation:

We will solve the original system of linear equations by performing a sequence of the following elementary row operations on the augmented matrix:

Interchange two rows
Multiply one row by a nonzero number
Add a multiple of one row to a different row

To find the reduced row-echelon form of this augmented matrix

$\left[\begin{array}{cccc}2&3&-1&14\\1&2&1&4\\5&9&2&7\end{array}\right]$

You need to follow these steps:

Divide row 1 by 2 $\left(R_1=\frac{R_1}{2}\right)$

$\left[\begin{array}{cccc}1&3/2&-1/2&7\\1&2&1&4\\5&9&2&7\end{array}\right]$

Subtract row 1 from row 2 $\left(R_2=R_2-R_1\right)$

$\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\5&9&2&7\end{array}\right]$

Subtract row 1 multiplied by 5 from row 3 $\left(R_3=R_3-\left(5\right)R_1\right)$

$\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right]$

Subtract row 2 multiplied by 3 from row 1 $\left(R_1=R_1-\left(3\right)R_2\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right]$

Subtract row 2 multiplied by 3 from row 3 $\left(R_3=R_3-\left(3\right)R_2\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&0&0&-19\end{array}\right]$

Multiply row 2 by 2 $\left(R_2=\left(2\right)R_2\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&-19\end{array}\right]$

Divide row 3 by −19 $\left(R_3=\frac{R_3}{-19}\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&1\end{array}\right]$

Subtract row 3 multiplied by 16 from row 1 $\left(R_1=R_1-\left(16\right)R_3\right)$

$\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&-6\\0&0&0&1\end{array}\right]$

Add row 3 multiplied by 6 to row 2 $\left(R_2=R_2+\left(6\right)R_3\right)$

$\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right]$

8 0

3 years ago

A tile is chosen at random from a bag containing the following tiles: 7 blue, 3 green, 6 yellow, and 5 purple. Let P be the prob

weeeeeb [17]

Answer:

P(blue) = 0.33

P(green) = 0.14

P(purple) = 0.24

P(yellow) = 0.29

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, we have that:

7+3+6+5 = 21 tils.

7 of them are blue. So

P(blue) = 7/21 = 0.33

3 of them are green. So

P(green) = 3/21 = 0.14

6 of them are yellow. So

P(yellow) = 6/21 = 0.29

5 of them are purple. So

P(purple) = 5/21 = 0.24

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3 years ago

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Cassidy places 49 stamps on each of 8 albums pages how many stamps does she place?

stiks02 [169]

Cassidy places 392 stamps

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3 years ago

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Find the missing side length. Leave your answer in simplest radical form.

exis [7]

Answer:

4√3

Step-by-step explanation:

For isosoles triangles the legs are congruent

v = u

--------------------

using the pythagorean theorem

(4√6)² = v² + v²

(16 * 6) = 2v²

Divide both sides by 2

16 * 3 = v²

Take the square root of both sides

4√3 = v

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3 years ago

The left and right page numbers of an open book are two consecutive integers whose sum is 577. Find these page numbers.

JulsSmile [24]

Answer:

288 and 289 are the two pages.

Step-by-step explanation:

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2 years ago