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.
Answer:
the median would be 3
Step-by-step explanation:
Answer:
Mitchell needs to sell 120 stoves for the options to be equal.
Step-by-step explanation:
Company A gives Mitchell $12000 salary plus $150 commission per stove selling and Company B is offering Mitchell $24000 salary plus $50 commission per stove selling.
So, if Mitchell sells x number of stoves such that both the plans become equal, then we can write
12000 + 150x = 24000 + 50x
⇒ 100x = 12000
⇒ x = 120
Therefore, Mitchell needs to sell 120 stoves for the options to be equal. (Answer)
Problem One
Remark
If she doesn't mind having I kg left over, the minimum number would be 3 five kg boxes. If on the other hand, she must have exactly 14 kg then the minimum number is 6.
She needs 2 five kg boxes and 4 one kg boxes. <<<< Answer
Problem Two
There is a method of solving this that is called dimensional analysis. It is what should be used here. I'll do it at the end of the problem. In the meantime, you have to do it a slightly longer way.
1 portion = 100 grams.
x portions = 1kg which is 1000 grams.
x portions = 1000 grams.
Set up a proportion to find the number of servings in 1 kg
1 portion/x = 100 grams/1000 grams Cross multiply
1 * 1000 = 100 * x Divide by 100
1000/100 = x
x = 10 servings in 1 kg.
So each kg produces 10 portions
1 kg / 10 portions = 20 kg / x portions Cross multiply
x * 1 = 10 * 20
x = 200 portions <<<<< Answer
Dimensional Analysis
[1batch]*[1 portion/100g][1000g/kg][20kg/batch] the units cancel
1000 * 20 / 100 only the portions are left over.
200 portions is the answer.
Problem Three
1 kg = 1000 grams
x kg = 5000 grams Cross multiply
1*5000 = 1000 x
x = 5 kg
1 parcel weighs 5 kg
x = 15 kg
15 kg = 5 x
x = 15/5
x = 3
So he can carry 3 parcels per trip.
Since there are 5 such parcels, he will have to make 2 trips. The second one will not be a full load.
First Trip = 3 parcels
Second Trip = 2 parcels. <<<<Answer
