ANSWER: FG = 69
FG = FK + KG
KG = 1/2(FK)
FK = 46
RULE: When it comes to centroids, the longer section of the line is always 2/3 of the entire line (+ the shorter section of the line is always 1/3). This means that the shorter section of the line is HALF of the longer section of the line.
FG = FK + KG
FG = 46 + 46/2
FG = 46 + 23
FG = 69
CHECK:
FK = 2/3(FG)
46 = 2*69/3
46 = 138/3
46 = 46 ✔️
or
KG = 1/3(FG)
1/2(FK) = 1/3(FG)
46/2 = 69/3
23 = 23 ✔️
<u>End behavior: </u>
The parent function is: f(x) = x³, which starts (from the left side) at -∞ and ends (on the right side) at +∞.
<u>Zeroes:</u>
f(x) = x³ + 2x² - 8x
0 = x³ + 2x² - 8x
0 = x(x² + 2x - 8)
0 = x(x + 4)(x - 2)
0 = x 0 = x + 4 0 = x - 2
x = 0 x = -4 x = 2
<u>Intervals:</u>
Put the zeroes in order: -4, 0, 2
since f(x) is increasing from the left then the interval from -4 to 0 is positive and the interval from 0 to 2 is negative.
<u>Graph:</u>
see attachment
Answer:
56x+12y-10.6
Step-by-step explanation:
The multiple choice answer is B.
Answer:
letter C: 100
Step-by-step explanation:
This problem can be configured as an arithmetic progression:
The first value is 10, the ratio is also 10 (the multiples of ten are 20, 30, 40, ...) and the number of terms is 19 (10, 20, 30, ... , 180, 190 -> total of 19 numbers).
So, we can use the following formula to calculate the sum of all these numbers:
Sn = n(a1 + an)
/2
where Sn is the sum, n is the number of terms, a1 is the first term and an is the last one.
The result we want is the average of the sum, so we need to divide Sn by n:
Average = Sn/n = n(a1 + an)
/2n = (a1 + an)
/2 = (10+190)/2 = 200/2 = 100
The correct option is letter C.
Lets first numbers is x, second is (x+2), third is x+4
sum is x+(x+2)+(x+4)=87
3x+6=87
3x=81
x=27
Answer: smallest number is 27
