0.0098 to 3 decimal places

What is an equation of the line that passes through the point ( 6 , − 2 ) (6,−2) and is perpendicular to the line 6 x + y = 2 6x

Diano4ka-milaya [45]

Answer:

An equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:

$y=\frac{1}{6}x-3$

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept.

Given the line

6x+y=2

Simplifying the equation to write into the slope-intercept form

y = -6x+2

So, the slope = -6

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.

Thus, the slope of the perpendicular line will be: -1/-6 = 1/6

Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 1/6 and the point (6, -2)

$y-\left(-2\right)=\frac{1}{6}\left(x-6\right)$

$y+2=\frac{1}{6}\left(x-6\right)$

subtract 2 from both sides

$y+2-2=\frac{1}{6}\left(x-6\right)-2$

$y=\frac{1}{6}x-3$

Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:

$y=\frac{1}{6}x-3$

5 0

2 years ago

Solve the following system. y = x 2 - 9x + 10 and x + y + 5 = 0. The solutions are

shepuryov [24]

X+y+5=0

y=-x-5

If a solution exists y=y so we can say

x^2-9x+10=-x-5 add x+5 to both sides

x^2-8x+15=0 now factor

x^2-3x-5x+15=0

x(x-3)-5(x-3)

(x-5)(x-3) so x=3 and 5, using y=-x-5

y(3)=-8 and y(5)=-10

So the two solutions are:

(3,-8) and (5,-10)

6 0

2 years ago

Read 2 more answers

Ava bought some pens for $ 2 each and some pencils for $ 1 each. She bought 3 more pens than pencils and spent a total of $ 12.

Rudiy27

Answer:

Step-by-step explanation:

price of 1 pen= $ 2

price of 1 pencil= $1

total money spent= $12

Let the number of pen be a and number of pencil be b.

2 a + b = 12 ----------------Equation 1

We have, she bought 3 more pens than pencils

a - b = 3 ------------------ Equation 2

Equation 1 +Equation 2,

2 a + b + a - b = 12 + 3

3a = 15

a = 5

Substituting in equation

5 - b = 3

b = 2

Number pencils Ava bought = 2

5 0

3 years ago

Find the volume of soup can if the diameter is 6.5 in and the height is 9 in

Nitella [24]

Answer:

V =298.49625 in^3

Step-by-step explanation:

Volume of a cylinder is given by

V = pi * r^2 *h

We know the diameter so we can find the radius

r = d/2 =6.5/2 = 3.25

and we know the height =9

V = pi * (3.25)^2 *9

V = pi*95.0625

If we approximate by 3.14

V = 3.14*95.0625

V =298.49625 in^3

5 0

2 years ago

Read 2 more answers

Select all expressions that are equivalent to 2x+3x+8-3x-2.

dedylja [7]

Answer:

2x+6 since the +3 and -3x cancel each other out your only left with 2x

4 0

2 years ago