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3 years ago

Write the equation of a line passing through (6,-2) and perpendicular to -2x + 3y= -6

1 answer:

4 0

Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.

-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3

The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b

The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.

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the base of the founten is rectangular . its dimention 1 2/3 feet by 2 2/3 feet . what is the area of the base of the founten

Montano1993 [528]

The area of a rectangle is calculated by multiplying the length of the rectangle and the width of the rectangle. In this case, the length (the longer side) is 2 2/3 feet while the width (shorter side) is 1 2/3 feet. To multiply fraction, first convert mixed numbers into improper fractions:

2 2/3 = 8/3
1 2/3 = 5/3
Multiplying the two fractions yield:
8/3 x 5/3 = 40/9 ft2

The final answer is 40/9 ft2 or 4 4/9 ft2.

3 0

3 years ago

A local water park has two types of season passes. Plan A costs a one-time fee of $125 for admission plus $8 for parking every t

Margarita [4]

Answer:

40+8X=50+23X

8X-23X=50-140

-15X=-90

X=-90/-15

X=7 TRIPS IS THE ANSWER.

PROOF:

140+8*6=50+23*6

140+48=50+138

188=188

4 0

3 years ago

It is your first semester at college and you take out a $5000 loan and in order to pay off that loan by the end of the semester

kakasveta [241]

Answer:

5000-1250x

Step-by-step explanation:

All you need to do is find the amount of money you get paid a month and use variable x to represent the months and then subtract that from the money you need to pay off.

8 0

3 years ago

A circular pool is 3.5 meters deep and has a radius of 9 meters. What is the volume

mote1985 [20]

Answer:

$890.75m^3$

Step-by-step explanation:

Step one:

given data

heigth/depth = 3.5m

radius= 9m

Step two:

The shape is that of a cylinder

Hence the volume of the pool is

$V= \pi r^2h$

substitute

$V= 3.142*9^2*3.5\\\\V=890.75 m^3$

7 0

3 years ago

The sales of a particular brand of children’s athletic shoes rose from $6,900,000 to $7,400,000. Find the percent of increase in

Sidana [21]

Answer: 7.2%

Step-by-step explanation:

First find the difference between the amounts.

7,400, 000 - 6, 900,000 = 500, 000

Now divide the obtain number by the original number which is 6,900,000

500, 000/ 6,900,000 = 0.07246

Multiply 0.07246 by 100 to convert it to a percent.

0.07246 = 7.2463..%

Round it to the nearest tenth of a percent.

7.2463.. rounded to the nearest tenth is 7.2%

8 0

2 years ago