The parallelogram is 45 square meters. Multiply the base by the height. The triangle is 36 square meters. Multiply the base by the height and divide by two. Thus, the answer is 81.
Answer:
(5.4582 ; 6.8618)
Step-by-step explanation:
Given the data:
6 10 2 6 3 3 3 6 6 6 6 5 8 9 10 10 7 9 3 6 5 10 9 9 10 3 8 6 6 3 3 6 6 5 4 10 9 3 5 7 10 6 3 8 6 8 3 3 5 5
Sample mean, xbar = Σx / n
n = sample size = 50
ΣX = 308
xbar = 308 / 50 = 6.16
Using a Calculator :
The sample standard deviation, s = 2.469
Confidence interval = xbar ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Tcritical at 95% ; df = 50 - 1 = 49
Tcritical = 2.010
Hence,
Margin of Error= 2.010 * (2.469/sqrt(50)) = 0.7018
Lower boundary : (6.16 - 0.7018) = 5.4582
Upper boundary : (6.16 + 0.7018) = 6.8618
(5.4582 ; 6.8618)
ANSWER
The solution is
(x,y)=(1,-5)
EXPLANATION
The equations are:
1st equation: 6x +5y=-19
2nd equation: 12x-8y=52
Multiply the first equation by 2:
3rd equation: 12x +10y=-38
Subtracy the 2nd equation from the 3rd equations.
12x-12x+10y--8y=-38-52
18y=-90
Divide both sides by 18.
y=-5
Put y=-5 into any of the equations and solve for x.
Preferably, the first equation will do.
6x +5(-5)=-19
6x -25=-19
6x=25-19
6x=6
x=1
The solution is
(x,y)=(1,-5)
Answer:
4 mi/h
Step-by-step explanation:
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
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<em>Additional comment</em>
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
