You want 9x^2 + bx + 9a to be a perfect square trinomial. Note that 9 x 2 is incorrect and should be written as 9x^2, where "^" represents "exponentiation."
What about a? Are we supposed to find a also?
One way in which to do this problem is to factor 9 out of the trinomial:
9 (x^2 + (b/9)x + a )
Concentrate now on making x^2 + (b/9)x + a into a perfect square trinomial.
x^2 + (b/9)x + a
Take half of the coefficient (b/9) and square the result: [(b/9)/2]^2 = b^2/81.
Then, x^2 + (b/9)x + b^2/81 - b^2/81 + a.
The above quadratic expression can be re-written as
(x + b/9)^2 - b^2/81 + a. This is a perfect square trinomial if
-b^2/81 + a = 0. Solve for b: b^2/81 = a,
b/9 = sqrt(a)
b = 9 sqrt a
(6 x (7+5)) + 3 = 75
6 x 12 + 3 = 75
72 +3 = 75
I hope this helped you <3
Answer:
(3, 50) and (14,303)
Step-by-step explanation:
Given the system of equations;
y=23x–19 ....1
x²–y= – 6x–23 ...2
Substitute 1 into 2;
x²–(23x-19)= – 6x–23
x²–23x+19= – 6x–23 .
x²-23x + 6x + 19 + 23 = 0
x² - 17x + 42 = 0
Factorize;
x² - 14x - 3x + 42 = 0
x(x-14)-3(x-14) = 0
(x-3)(x-14) = 0
x = 3 and 14
If x = 3
y = 23(3) - 19
y = 69-19
y = 50
If x = 14
y = 23(14) - 19
y = 322-19
y = 303
Hence the coordinate solutions are (3, 50) and (14,303)
Answer:
52500
Step-by-step explanation:
5% of 50000 is 2500
(50000 * 0.05 = 2500)
50000 + 2500 = 52500
another way to do it is just multiply 50000 by 1.05 (105%)
Answer:
53.33% probability that one woman and one man will be chosen to be on the committee
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the members are chosen is not important, so we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
What is the probability that one woman and one man will be chosen to be on the committee?
Desired outcomes:
One woman, from a set of 2, and one man, from a set of 4. So
![D = C_{2,1}*C_{4,1} = \frac{2!}{1!1!}*\frac{4!}{1!3!} = 8](https://tex.z-dn.net/?f=D%20%3D%20C_%7B2%2C1%7D%2AC_%7B4%2C1%7D%20%3D%20%5Cfrac%7B2%21%7D%7B1%211%21%7D%2A%5Cfrac%7B4%21%7D%7B1%213%21%7D%20%3D%208)
Total outcomes:
Two members from a set of 2 + 4 = 6. So
![T = C_{6,2} = \frac{6!}{2!4!} = 15](https://tex.z-dn.net/?f=T%20%3D%20C_%7B6%2C2%7D%20%3D%20%5Cfrac%7B6%21%7D%7B2%214%21%7D%20%3D%2015)
Probability:
![p = \frac{D}{T} = \frac{8}{15} = 0.5333](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7BD%7D%7BT%7D%20%3D%20%5Cfrac%7B8%7D%7B15%7D%20%3D%200.5333)
53.33% probability that one woman and one man will be chosen to be on the committee