Searches related to which ordered pair (ab) is a solution to the given system (2a -5b=1, 3a+5b=14
2 answers:
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Answer:
(Answer in attachment, explanation below)
Step-by-step explanation:
The answer is B. 5P5 x 20P15.
This is because to make the second grade students to sit in the first row we have 5 seats and 5 students so we will permute the 5 students to those 5 seats. So 5P5.
Now we are left with 20 seats and 15 first grade students so we can simply permute those 15 students into those 20 seats. So 20P15.
Finally using the counting rule principle we will multiply both of these so 5P5 x 20P15.
No. of students from first grade = 15
No. of students from second grade = 5
There are 5 rows of seats
Each row contains 5 seats
Total seats = 25
No. of ways for second-grade students occupy the first row(i.e first 5 seats) =
Remaining seats = 20
No. of students from first grade = 15
So, No. of ways for first-grade students occupy remaining seats =
So, No. of ways for the students can be seated if all of the second-grade students occupy the first row =
So, Option B is true
Hence No. of ways for the students can be seated if all of the second-grade students occupy the first row is
9514 1404 393
Explanation:
1) 2x^2 -5x -3 = 0 . . . . standard form equation
To convert this to factored form, you can look for factors of the product (2)(-3) that have a sum of -5. It can help to start by listing the ways that -6 can be factored. Since we want the sum of factors to be negative, we want to have larger negative factors.
-6 = (1)(-6) = (2)(-3)
The sums of these factor pairs are -5 (what we want) and -1 (not relevant). We can call these factors p=1 and q=-6.
If a = 2 is the leading coefficient of our standard form quadratic, we want to use these factors in the form ...
(ax +p)(ax +q)/a . . . . . factored form of the quadratic
(2x +1)(2x +(-6))/2 . . . .fill in the values we know
(2x +1)(x -3) . . . . . . . factor 2 from the second binomial
So, the factored form of the quadratic equation is ...
(2x +1)(x -3) = 0 . . . . factored form equation
__
2) f(x) = x^2 +7x +10 . . . . standard form quadratic function
Using the thinking process described above, we are looking for factors of 10 that have a sum of 7. We know those are 2 and 5. So, the factored form of the function is ...
f(x) = (x +2)(x +5) . . . . . . factored form quadratic function
The leading coefficient is 1, so we have no further work to do.
<u>Roots, x-intercepts, zeros</u>
The graph attached below shows this function crosses the x-axis when x=-2 and x = -5. These values of x are variously called "roots", "x-intercepts", and "zeros" of the function. They are values for which the factors and the function are zero. (x+2=0 when x=-2, for example)
<u>Solutions</u>
Often, we are interested in solving the equation ...
f(x) = 0
For that equation, the <em>solutions</em> <u>are</u> the <em>zeros</em> or <em>x-intercepts</em> or <em>roots</em>. The graph attached also shows solutions for ...
f(x) = 4
Those solutions are x = -6 and x = -1. The function value is not zero for these values of x, so the <em>roots</em>, <em>x-intercepts</em>, or <em>zeros</em> <u>are not</u> <em>solutions</em> to this equation.
