There are standard formulas for this type of problem. However, it can also be solved by a combination of simple steps.
First, the shortest distance from the point (3,5) to the line y = x +4 (line1) will be along a straight line perpendicular to line1. Give the perpendicular line the name line2. Since the slope of line1 is 1, the slope of line2 will be -1.
Second, since line2 must go through (3,5) and also have a slope of -1, the point slope form can be used for line2:
y - 5 = (-1) (x -3)
So the equation of line2 is y = -x +8.
Third, the point of intersection of line1 and line2 can be found by solving the set of equations:
y = x +4
y = -x + 8
The solution of this set of two equations is x = 2, y = 6 i.e. the point (2,6) .
Fourth, the distance formula can be used to find the distance between (3,5) and (2,6)
d = sqrt( (3-2)2 + (5-6)2 ) = sqrt(2)
This is the desired distance.
For x and y
When you subtract 2 from x, you will subtract 7 from y
Answer:I might be wrong but im pretty sure the answer is 5.4
Step-by-step explanation:
Answer:
7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.
Step-by-step explanation:
- Let the number of tomatoes=t
- Let the number of cucumber planted=c
- Let the number of zucchini planted=z
- Total Number of Plants=43
She planted twice as many cucumbers as zucchini, this is written as:
She also planted eight more tomatoes than cucumbers, this is written as:
In total, she planted 43 plants
Therefore:
z+(2z)+(2z+8)=43
5z+8=43
5z=43-8
5z=35
Divide both sides by 5
z=7
Number of Cucumbers, c=2z=2 X 7 =14
Number of Tomatoes, t=c+8=14+8=22
Therefore, she planted 7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.
