Item A and B are in decimal format, convert Item C to decimal by changing the fraction to a decimal by dividing 11 by 16:
11 / 16 = 0.6875
This makes Item C 3.6875
Now you have the 3 items as decimal format now put them in order from smallest to largest:
3.65, 3.6875, 4.1
Item A, Item C, Item B
Might have to experiment a bit to choose the right answer.
In A, the first term is 456 and the common difference is 10. Each time we have a new term, the next one is the same except that 10 is added.
Suppose n were 1000. Then we'd have 456 + (1000)(10) = 10456
In B, the first term is 5 and the common ratio is 3. From 5 we get 15 by mult. 5 by 3. Similarly, from 135 we get 405 by mult. 135 by 3. This is a geom. series with first term 5 and common ratio 3. a_n = a_0*(3)^(n-1).
So if n were to reach 1000, the 1000th term would be 5*3^999, which is a very large number, certainly more than the 10456 you'd reach in A, above.
Can you now examine C and D in the same manner, and then choose the greatest final value? Safe to continue using n = 1000.
Answer:
Step-by-step explanation: Let x be the smaller and y be the largest number.
Since x+y=13, we deduce y=13-x
Now, for the translation: "two more than the larger number" is y+2 , while "twice the smaller" is 2x
Their sum is y+2+2x
And since we know that y=13-x, we have y+2+2x=13-x+2+2=15+x
I would start by multiplying both sides of the inequality by 4 to eliminate the fraction
y + 8 >/= 12
Then subtract 8 from both sides
y >/= 4
Because it is greater than OR equal to, when you graph, you use a solid circle. Greater than means the arrow goes to the right on the line.
So, solid circle on the line on 4, arrow pointing to the right. (Third option from the right)
Find two numbers that multiply to -30 (last term) and add to 7 (middle coefficient)
The two numbers are 10 and -3
10 times -3 = -30
10 plus -3 = 7
Using those two values gets us the two factors (y+10) and (y-3)
Therefore, y^2+7y-30 factors to (y+10)(y-3)
The equation y^2+7y-30 = (y+10)(y-3) is true for all values of y.
