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3 years ago

Write the equation of the line that passes through the points (-6, -9) and

Mathematics

1 answer:

e-lub [12.9K]3 years ago

3 0

Answer:

y - 7 = 16/13(x - 7)

General Formulas and Concepts:

Alg I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate

y₁ - y coordinate

m - slope

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (-6, -9)

Point (7, 7)

Step 2: Find slope m

Substitute: $m=\frac{7+9}{7+6}$
Add: $m=\frac{16}{13}$

Step 3: Write equation

y - 7 = 16/13(x - 7)

You might be interested in

The sum of two numbers is 30 and their difference is 6

Studentka2010 [4]

I'm going to assume that you are trying to find the two numbers. Based on the information in the problem, we can create the following equations (where $a$ and $b$ are the two numbers):

$a + b = 30$

$a - b = 6$

We have a systems of equations. In this case, it would be easier to use elimination by adding vertically. This produces the result:

$2a = 36$

$a = 18$

To find $b$ , substitute the value for $a$ into one of the earlier equations:

$18 + b = 30$

$b = 12$

The two numbers are 12 and 18.

4 0

3 years ago

Calculate the area of the shaded sector. 11.73 11.2 11.4 11.83

laiz [17]

The formula for the area of a circle is

A=πr²
plug in the data we know
A=π4²
A=16π

Since we only we need to find the area of the shaded section, we need to twerk this equation a bit. (remember that the shaded section is 84/360 of the original circle.)

A=84/360*16π
A=11.728
A=11.73 units²

answer: A=11.73 units²

4 0

3 years ago

Simplify, state all restrictions.

Kipish [7]

The simplified expression is $\frac{1 - x - y}{x + y}$ and the restriction is $y \ne -x$

<h3>How to simplify the expression?</h3>

The expression is given as:

$\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1$

Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions

$\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1$

Rewrite the expression as products

$\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1$

Cancel out the common factors

$\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1$

Express 4x^2 - y^2 as (2x - y)(2x + y)

$\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1$

Cancel out the common factors

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

Take the LCM

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

Hence, the simplified expression is $\frac{1 - x - y}{x + y}$ and the restriction is $y \ne -x$

Read more about expressions at:

brainly.com/question/723406

#SPJ1

7 0

2 years ago

PLEASE ANSWERRRRRRRRRRRRRRRRR

zhannawk [14.2K]

The graph suggests that the two lines meet at $(3,6)$

If this is true, that point must belong to both lines.

To check this, plug $x=3$ in both equations, and you must get $y=6$ once you simplifiy all the numbers.

In the first equation we have

$5\cdot 3-3y= -3 \iff 3y=15+3\iff 3y=18 \iff y=6$

In the second,

$3+3y=21 \iff 3y=18\iff y=6$

6 0

3 years ago

10. Three kinds of teas are worth $4.60 per pound, $5.75 per pound, and $6.50 per pound. They are to be

zepelin [54]

Answer:

The mass of the $4.60/lb tea that should be used in the mixture is 10 lb

The mass of the $5.75/lb tea that should be used in the mixture is 8 lb

The mass of the $6.50/lb tea that should be used in the mixture is 2 lb

Step-by-step explanation:

The parameters of the question are;

The worth of the three teas are

Tea A = $4.60/lb

Tea B = $5.75/lb

Tea C = $6.50/lb

The mass of the mixture of the three teas = 20 lb

The worth of the mixture of the three teas = $5.25 per pound = $5.25/lb

The amount of the $4.60 in the mixture = The sum of the amount of the other two teas

Therefore, given that the mass of the mixture = 20 lb, we have in the mixture;

The mass of tea A + The mass of Tea B + The mass of Tea C = 20 lb

The mass of tea A = The mass of Tea B + The mass of Tea C

Therefore;

The mass of tea A + The mass of tea A = 20 lb

2 × The mass of tea A in the mixture = 20 lb

The mass of tea A in the mixture = 20 lb/2 = 10 lb

The mass of tea A in the mixture = 10 lb

The mass of Tea B + The mass of Tea C = The mass of tea A = 10 lb

The mass of Tea B + The mass of Tea C = 10 lb

The mass of Tea B = 10 lb - The mass of Tea C

Where the mass of Tea C in the mixture = x, we have;

The mass of Tea B in the mixture = 10 lb - x

The cost of the 10 lb of tea A = 10 × $4.60 = $46.0

The worth of the tea mixture = 20 × $5.25 = $105

The worth of the remaining 10 lb of the mixture comprising of tea A and tea B is given as follows;

The worth of Tea B + The worth of Tea C in the mixture = $105.00 - $46.00 = $59.00

Therefore, we have;

x lb × $6.50/lb + (10 - x) lb × $5.75/lb = $59.00

x × $6.50 - x × $5.75 + $57.50 = $59.00

x × $0.75 = $59.00 - $57.50 = $1.50

x = $1.50/$0.75 = 2 lb

∴ The mass of Tea C in the mixture = 2 lb

The mass of Tea B in the mixture = 10 lb - x = 10 lb - 2 lb = 8 lb

The mass of Tea B in the mixture = 8 lb

Therefore, since we have;

Tea A = $4.60/lb

Tea B = $5.75/lb

Tea C = $6.50/lb

The mass of tea A in the mixture = 10 lb

The mass of tea B in the mixture = 8 lb

The mass of tea C in the mixture = 2 lb, we find;

The mass of the $4.60/lb tea that should be used in the mixture = 10 lb

The mass of the $5.75/lb tea that should be used in the mixture = 8 lb

The mass of the $6.50/lb tea that should be used in the mixture = 2 lb.

6 0

3 years ago