In this question, they gave you the system of equations. You just need to use the two of them.
We want to find the m or the number of the multiple-choice questions. So we need to turn our last equation in the form of 'm's by translating the 'f's into 'm's.
If we know the m form of f, we can convert the second equation and find the answer:
Plug in the m value of f:
Distribute the 5:
Subtract -75 from both sides:
Combine like terms:
Divide both sides by -2:
So, we learned that the number of the multiple-choice questions is 12.
The longest diagonal is about 8.9 inches. The longest length is going to be between the two longest lengths, the width and the height. The Pythagorean theorem is a^2 + b^2 = c^2. Plug the width and height into a and b of the Pythagorean equation. (4)^2 + (8)^2 = c^2. Now simplify the equation. 16 + 64 = c^2. 80 = c^2. Now find the square root of each side. (sqrt)80 = (sqrt)c^2. If you simplify this, you will find that c is equal to about 8.9 inches.
So three consecutive integers 2k,2(k+1),2(k+2)
there sum will be
2k+2(k+1)+2(k+2)
2k+2k+2+2k+4
6k+6
so setting the inequality
102<6k+6<116
subtracting 6 from all sides
96<6k<110
16<k<18.3333
since k is an integer
the only integers between 16 and 18.3
are 17 and 18
so
when k=17
2(17),2(17+1),2(17+2)
34,36,38
when k=18
2(18),2(18+1),2(18+2)
36,38,40
so to check are soultion we substitute
34+36+38=108 which is between 102 and 116
36+38+40=114 which is between 102 and 116
so our soultion is correct
the final answer will be
{{36,38,40},{38,40,42}}
Step-by-step explanation:
Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions.
The fact that the slopes of HF and GH are negative reciprocals proves that FGH is a right triangle.
The slope of HF is given by
m = (-4-4)/(-3-2) = -8/-5 = 8/5
The slope of GH is given by
m = (-4--9)/(-3-5) = (-4+9)/(-3-5) = 5/-8 = -5/8
These are reciprocals and opposite sides. This only occurs if the lines are perpendicular; thus they make a right angle.