X² <span>+ 11x + 7
because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:
(-b </span>± √((b)² - 4ac))/(2a)
in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))
not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
(-11 ± √(121 - 28))/2
(-11 ± √93)/2
and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:
(x - (-11 - √93)/2) and (x + (-11 - √93)/2)
they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:
(x + (11 + √93)/2) (x - (11 - √93)/2)
and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
Answer:
Please check the explanation.
Step-by-step explanation:
- As we know that the values in the table represent a function only if there there is only 1 input for every output.
Given the table 1
x y
-12 2
-10 10
0 -2
5 -6
8 -11
15 -15
From the table, it is clear that for each input there exists a unique output.
i.e.
According to the given table,
y = 2 at x=-12
y = 10 at x=-1
0
y = -1 at x=0
y = -11 at x=8
y = -15 at x=15
From the table, it is clear that for each input x, it has a unique output y.
Hence, table 1 is a function.
Given the table 2
x y
9 -18
-20 0
-6 1
-17 16
9 17
11 19
This table does not produce a function, because the input x=9 produces two outputs.
i.e.
at x = 9, the y = -18
at x = 9, the y = 17
Therefore, the table 2 does not represent a function.
Answer:
-$13.5
Step-by-step explanation:
Let x be a random variable of a count of player gain.
- We are told that if the die shows 3, the player wins $45.
- there is a charge of $9 to play the game
If he wins, he gains; 45 - 9 = $36
If he looses, he has a net gain which is a loss = -$9
Thus, the x-values are; (36, -9)
Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6
Thus;
E(X) = Σ(x•P(X)) = (1/6)(36) + (5/6)(-9)
E(X) = (1/6)(36 - (5 × 9))
E(X) = (1/6)(36 - 45)
E(X) = -9/6 = -3/2
E(X) = -3/2
This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5
Answer:
2
Step-by-step explanation:
The height formula given is:
h = -16t^2 + 70
That means the object will be initially (t=0) at the height 70 feet, from where it will be dropped.
If we want to know the time when the object will be at height 6 feet, we just need to use h=6 in the equation, and then calculate the value of t:
6 = -16t^2 + 70
16t^2 = 64
t^2 =4
t = 2 s
So, it will take 2 seconds for the object to be 6 feet above the valley floor.
Answer:
a = 1/2
Step-by-step explanation:
a - 3/10 = 1/5
Add 3/10 to each side
a - 3/10 +3/10 = 1/5+3/10
a = 1/5+3/10
Get a common denominator
a= 1/5*2/2 +3/10
a = 2/10 +3/10
a = 5/10
Divide the top and bottom by 5
a = 1/2