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.
Answer: the height of the building is 40ft
Step-by-step explanation:
Looking at the right angle triangle formed,
With angle P as the reference angle, the length shadow of the building on ground represents the adjacent side of the right angle triangle.
The height of the building represents the opposite side of the right angle triangle.
a) to determine the height of the building, x, we would apply the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side. Therefore, the equation becomes
Tan P = x/50
b) 0.8 = x/50
x = 50 × 0.8
x = 40 ft
306 / 18 = 17
So he's on $17 / hour
$204 / $17 = 12.
Therefore he'd make $204 in 12 hours.
Answer:
And we can find this probability with this difference and using the normal standard table:
Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference and using the normal standard table:
Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women
Answer:
s=64
Step-by-step explanation:
