2y+4x=12
Move 4x to the other side as a negative number
2y=-4x+12
Divide all terms by 2
y=-2x+6
Now, in order for two lines to be perpendicular, their gradients have to multiply obeyed to get -1 (let a be the gradient of the given line and let b be the gradient of the line we're trying to find)
So, we do -2*b=-1
so, b is equal to 1/2
Now, we are given a coordinate so we substitute it in y-y1=m(x-x1)
y-1=1/2(x-8)
Expand brackets
y-1= 1/2x-4
Take -1 to the other side as a positive number
y=1/2x-3
So, the equation of the line is y=1/2x-3
Answer:
First space: 15
Second space: 20
Third space: 0
Fourth space: 20
Step-by-step explanation:
If the florist decrease x times the value of the bouquet by 1, the number of bouquets sold is 30 plus 3 times x, so we have that:
P(x) = (20 - x)*(30+3x)
P(x) = 600 +30x - 3x2
The vertical axis of the graph represents the profit P(x) of the florist.
So observing the graph, we can see that the maximum profit is 675, and occurs when the value of x is 5, that is, the price of the bouquet is 20 - 5*1 = $15
Looking again to the graph, we see that when x = 20 her profit is zero (the price of each bouquet will be 20 - 20*1 = 0)
The interval of x for which the florist have a positive profit (P(x) > 0) is between x = -10 and x = 20, but the florist cannot make a negative number of one-dollar decrease, so the lower number in the interval should be 0
Step-by-step explanation:
since PQRT is a rhombus,
URQ=TPU
y=180-90-24=66
x=180-32-90-24=34
Here's the answer. I hope it will help you :)
