a school had 690 students sign up for the trivia teams if they wanted to have nine teams with the same number of students on eac
1 answer:
Answer:
3 more students need to sign up
Step-by-step explanation:
Let the equal number of students in 9 teams be x.
Total number of signed up students = 690.
Let t be the required number of students to be signed.
Therefore, 9x = 690+t.
This means, 690+t is a multiple of 9.
The least value of t to make 690+t, a multiple of 9 is 3 and hence,
= 77
Hence, 3 more students need to sign up and each of the 9 teams consists of 77 students.
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Answer:
y = 2x³ +x² -3x +6
Step-by-step explanation:
The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)
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If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.
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<em>Writing the equations</em>
... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing
For x = -1:
... -a +b -c +6 = 8
For x = 1
... a + b + c + 6 = 6
For x = 2
... 8a +4b +2c +6 = 20
In augmented matrix terms, this set of linear equations looks like ...
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<em>Solving the equations</em>
There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.
If you add the first two equations, you get ...
... 2b = 2 ⇒ b = 1
Substituting that into the first equation allows you to simplify it to ...
... -a -c = 1
Dividing the third equation by 2 (and substituting for b) makes it ...
... 4a +c = 5
Adding these equations gives ...
... 3a = 6 ⇒ a = 2
Then ...
... c = -a -1 = -2 -1 = -3
And our polynomial function is ...
... y = 2x³ +x² -3x +6
To solve this problem you must apply the proccedure shown below:
1. You have the following equation of a parabola, given in the problem above:
x<span>=1/16y^2
2. Then, based on the graph attached, you have:
p=y^2/4x
p=8^2/(4)(4)
p=64/16
p=4
3. The directrix is:
directrix=h-p
directrix=0-4
directrix=-4
The answer is:-4</span>
1. You have the following equation of a parabola, given in the problem above:
x<span>=1/16y^2
2. Then, based on the graph attached, you have:
p=y^2/4x
p=8^2/(4)(4)
p=64/16
p=4
3. The directrix is:
directrix=h-p
directrix=0-4
directrix=-4
The answer is:-4</span>