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2 years ago

Write the equation of the line that passes through the points (2 , -1) and has a slope of - 3

Mathematics

2 answers:

Tanzania [10]2 years ago

7 0

Answer:

$\boxed {\boxed {\sf y= -3x+5}}$

Step-by-step explanation:

We are asked to find the equation of the line that passes through the point (2, -1) and has a slope of -3.

We are given a point and the slope, so we can use the point-slope formula.

$y-y_1=m(x-x_1)$

In this formula, m is the slope and (x₁, y₁) is the point the line passes through.

The line has a slope of -3 and passes through (2, -1).

m= -3
x₁= 2
y₁= -1

Substitute the values into the formula.

$y--1= -3 (x-2)$

$y+1= -3 (x-2)$

Distribute the -3 on the right side. Multiply each term inside the parentheses by -3.

$y+1 = (-3*x) + (-3*-2)$

$y+1=(-3x) + (6)$

$y+1=-3x+6$

Subtract 1 from both sides of the equation to isolate the variable y.

$y+1-1=-3x+6-1$

$y=-3x +5$

The equation of the line is y= -3x+5.

svetlana [45]2 years ago

5 0

Answer:

y=-3x+5

Step-by-step explanation:

y=mx+b

m=slope or gradient (=-3)

y=-3x+b

Add your points

(2, -1)

-1=(-3 x 2)+b

-1= -6+b

-1+6=b

b=5

y=-3x+5

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ArbitrLikvidat [17]

Answer:

y = -2

Step-by-step explanation:

First, we subtract 2y on both sides:

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Then, we divide 12 on both sides:

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6 0

3 years ago

A survey was conducted that asked 1003 1003 people how many books they had read in the past year. results indicated that x overb

kirill115 [55]

The confidence interval is

$10.5\pm1.35 = (9.15, 11.85)$ . This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.

To find the confidence interval, we first find the z-score associated with it:

Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.

We calculate the margin of error using

$ME=z*\frac{s}{\sqrt{n}}
\\
\\=2.575*\frac{16.6}{\sqrt{1003}}=1.35$

This means that the confidence interval is
$10.5\pm1.35$

The lower limit is given by 10.5-1.35 = 9.15.
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5 0

2 years ago

The ratio of workers to supervisors and factories 32 to 2. The ratio of male workers to female workers is 6 to 5. If there are 8

Margarita [4]

Answer:

The number of supervisor in the factory is 9 .

Step-by-step explanation:

Given as :

The ratio of workers to supervisors and factories 32 : 2

let the number of workers = 32 x

And The number of supervisors = 2 x

The ratio of male workers to female workers is 6:5