Answer:
AB ≈ 2.8 units
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = A(1, 1) and (x₂, y₂ ) = B(3, 3)
AB = 
= 
= 
= 
≈ 2.8 units ( to the nearest tenth )
Answer:
Step-by-step explanation:
we have the expression
Apply the distributive property
therefore
eight square root of five end root plus three square root of thirty
Answer:
10 inches
Step-by-step explanation:
The formula for the triangle area is the following:
A = b * h / 2
Where b is the length of the base side and h is the height.
So, as the height is 4 less than the base, we have that:
h = b - 4
Using this value in the area equation, we have that:
A = b * (b - 4) / 2
30 = (b^2 - 4b) / 2
b^2 - 4b = 60
b^2 - 4b - 60 = 0
Using Bhaskara's formula to solve the quadratic equation, we have:
Delta = 4^2 + 4*60 = 256
sqrt(Delta) = 16
b1 = (4 + 16)/2 = 10
b2 = (4 - 16)/2 = -6 (negative value does not fit for this problem)
So the length of the base is 10 inches.
Answer:
rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour
Step-by-step explanation:
We will make a table of the trip there and back using the formula distance = rate x time
d = r x t
there
back
The distance there and back is 264 miles, so we can split that in half and put each half under d:
d = r x t
there 132
back 132
It tells us that the trip there is with the wind and the trip back is against the wind:
d = r x t
there 132 = (r + w)
back 132 = (r - w)
Finally, the trip there took 3 hours and the trip back took 6:
d = r * t
there 132 = (r + w) * 3
back 132 = (r - w) * 6
There's the table. Using the distance formula we have 2 equations that result from that info:
132 = 3(r + w) and 132 = 6(r - w)
We are looking to solve for both r and w. We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:
132 = 3r + 3w and
132 - 3w = 3r so
44 - w = r. Subbing that into the second equation:
132 = 6(44 - w) - 6w and
132 = 264 - 6w - 6w and
-132 = -12w so
w = 11
Subbing w in to solve for r:
132 = 3r + 3(11) and
132 = 3r + 33 so
99 = 3r and
r = 33
Answer:
2n+8=25
Equation
Step-by-step explanation:
n=8.5
This is the answer
