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3 years ago

The line with equation y=my+b is perpendicular to the line with equation y=16 - x/3. The value of m is ____?

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

8 0

Answer:

m=3

Step-by-step explanation:

Perpendicular lines intersect at 90 degrees or perpendicular angles. As such, their slopes are related. The slope of each line is the negative reciprocal of the other. For the equation, $y=16-\frac{x}{3}$ . The slope or $m=-\frac{1}{3}$ . This means the slope of the other line will be the negative reciprocal which is -(-3)=3

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The length of a 200 square foot rectangular vegetable garden is 4feet less than twice the width. Find the length and width of th

inna [77]

Answer:

Length = 18.099 ft

Width = 11.049 ft

Step-by-step explanation:

let the length of the field be x ft

and the width be y ft

as per the condition given in problem

x=2y-4 -----------(A)

Also the area is given as 200 sqft

Hence

xy=200

Hence from A we get

y(2y-4)=200

taking 2 as GCF out

2y(y-2)=200

Dividing both sides by 2 we get

$y(y-2)=100$

$y^2-2y=100$

subtracting 100 from both sides

$y^2-2y-100=0$

Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form

$ax^2+bx+c=0$

Here in our case

a=1

b=-1

c=-100

Putting those values in the formula and solving them for y

$y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

Solving first

$y=\frac{2+\sqrt{4+400}{2}$

$y=\frac{2+\sqrt{404}{2}$

$y=\frac{2+20.099}{2}$

$y=\frac{22.099}{2}$

$y=11.049$

Solving second one

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{2-\sqrt{4+400}{2}$

$y=\frac{2-\sqrt{404}{2}$

$y=\frac{2-20.099}{2}$

$y=\frac{-18.99}{2}$

$y=-9.045$

Which is wrong as the width can not be in negative

Our width of the field is

y=11.099

Hence the length will be

x=2y-4

x=2(11.049)-4

x=22.099-4

x=18.099

Hence our length x and width y :

Length = 18.099 ft

Width = 11.049 ft

4 0

3 years ago

A researcher conducts an experiment comparing two treatment conditions with 20 scores in each treatment condition.

Savatey [412]

To determine the number of subjects that are needed for the experiments, we multiply the number of independent variables with the number of scores. For example, there are n independent variables then, there are approximately,

number of subjects = 20 x n = 20n

6 0

3 years ago

I need help pleessse

wariber [46]

Answer:

1. 8/3

2. 1/7

3. 1/12

4. 1/27

Step-by-step explanation:

1. 3/8 * m = 1

Multiply by 8/3

8/3 * 3/8 m = 1* 8/3

m = 8/3

2. 7 * m = 1

Divide by 7

7*m /7 = 1/7

m = 1/7

3. 3 ÷m = 36

Multiply by m

3 ÷m * m = 36*m

3 = 36*m

Divide by 36

3/36 = 36*m/26

1/12 = m

4. 4/9 ÷m = 12

Multiply by m

4/9 ÷m * m = 12*m

4/9 = 12*m

Multiply by 1/12

4/9 *1/12 = 12*m * 1/12

4/12 *1/9 = m

1/3*1/9 =m

1/27

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3 years ago

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adoni [48]

Answer:

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Step-by-step explanation:

Let's set up a system of equations. Let x be a cookie and y be a brownie then...

x+2y=2x+y

x+y=1

We can solve this using substitution

x=1-y

1-y+2y=2(1-y)+y

1+y=2-2y+y

1+y=2-y

-1=-2y

y=1/2

One brownie costs 50 cents and one cookie costs...

x+1/2=1

x=1/2

One cookie costs 50 cents

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3 years ago

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