a = 3, b= - 4 and c = - 4
expand the left side using FOIL
(2x + 1)(ax + b) = 2ax² + 2bx + ax + b = 2ax² + x(2b + a) + b
compare the coefficients of expressions on left and right sides.
compare 2ax² + x(2b +a) + b with 6x² - 5x + c
coefficients of x² terms → 2a = 6 ⇒ a = 3
coefficients of x terms → 2b + a = - 5 → 2b + 3 = - 5 → 2b = - 8 ⇒ b = - 4
constant terms c = b = - 4
Answer:
C
Step-by-step explanation:
In general for arithmetic sequences, recursive formulas are of the form
aₙ = aₙ₋₁ + d,
and the explicit formula (like tₙ in your problem), are of the form
aₙ = a₁ + (n - 1)d,
where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.
But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So
tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript
tₙ₊₁ = tₙ + d
Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.
Your answer should be 314
4 x 16=64
10 x 25 (25 is the height)=250
64 + 250=314
Answer:
C. 4 miles; it represents the original distance of the bee from its hive
Step-by-step explanation:
We are given,
The graph showing the distance between a bee hive for a certain amount of time.
Now, from the graph, we see that,
When the time is 0 mins, then the distance from the bee hive is 4 miles.
<em>Thus, the initial value of the graph is 4 miles and it represents the original distance of the bee hive from the hive.</em>
So, option C is correct.
Answer: b=9
Step-by-step explanation: To find the slope we use: y2-y1/x2-x1
Which would then be: 5-b/-2-7= 5-b/-9
Then we have to find a number for b that would give us -4 as the numerator. That number would be 9
This would give us 4/9 which is the slope we already had.
