The solution to the equation are (2, 9) and (-1, 0)
Given the functions as shown below:
- y = –x2 + 4x + 5
- y = x2 + 2x + 1
Equating both equations will give;
–x^2 + 4x + 5 = x^2 + 2x + 1
Collect the like terms to have:
–x^2 + 4x + 5 –x^2 - 2x - 1 = 0
-2x^2 + 2x + 4= 0\
2x^2 - 2x - 4 = 0
x^2 - x - 2 =0
Factorize to have:
x^2 - x - 2 =0
x^2 - 2x + x - 2 = 0
x(x-2)+1(x-2) = 0
x = 2 and -1
If x = 2
y = 2^2 + 2(2) + 1
y = 9
If x = -1
y = (-1)^2 + 2(-1) + 1
y = 1 - 2 + 1
y = 0
Hence the solution to the equation are (2, 9) and (-1, 0)
Learn more on equations here: brainly.com/question/16863577
Answer:
a) 297°
b) 4.52 minutes
Step-by-step explanation:
a) Consider the attached figure. The boat's actual path will be the sum of its heading vector BA and that of the current, vector AC. The angle of BA north of west has a sine equal to 5/11. That is, the heading direction measured clockwise from north is ...
270° + arcsin(5/11) = 297°
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b) The "speed made good" is the boat's speed multiplied by the cosine of the angle between the boat's heading and the boat's actual path. That same value can be computed as the remaining leg of the right triangle with hypotenuse 11 and leg 5.
boat speed = √(11² -5²) = √96 ≈ 9.7980 . . . . miles per hour
Then the travel time will be ...
time = distance/speed
(3900 ft)×(1 mi)/(5280 ft)×(60 min)/(1 h)/(9.7980 mi/h) ≈ 4.523 min
Answer: a= 40.5 b= 82.85
Step-by-step explanation:
Answer:
506
Step-by-step explanation:
The side length of the largest square Jacob could seed if he purchases 5 bags is 70.71feet.
The formula for the area of square is given by,
Area = (side)2 = s2
Where, s = length of the side of a square
Now according to the question we have been given that 1 bag will cover 1000 square feet of lawn.
And Jacob bought 5 of those bags. First we will find how many square feet of lawn can be covered by these 5 bags.
Therefore, 1bag = 1000 sq.ft
5 bag = 5*1000sq.ft
= 5000sq.ft
Thus 5 bags will cover 5000sq.ft of lawn which will be equal to the area of the lawn
That is, Area of the lawn = Area covered by the 5 bags.
Area = 5000sq.ft
Putting the value of area in equation (1) we get,
5000 = s2
Or, s2 = 5000
s = √5000
s = 70.71ft
Hence the side length of the square lawn will be 70.71ft.
Learn more about area of square here : https://brainly.in/question/48541960
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