A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-squa
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System 1: The solution is (x, y) = (-4, 5)
System 2: The solution is
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
2x + 3y = 7 ------ eqn 1
-3x - 5y = -13 --------- eqn 2
We can solve by elimination method
Multiply eqn 1 by 3
6x + 9y = 21 ------ eqn 3
Multiply eqn 2 by 2
-6x - 10y = -26 ------- eqn 4
Add eqn 3 and eqn 4
6x + 9y -6x - 10y = 21 - 26
-y = -5
y = 5
Substitute y = 5 in eqn 1
2x + 3(5) = 7
2x + 15 = 7
2x = -8
x = -4
Thus the solution is (x, y) = (-4, 5)
<h3><em><u>Second system of equation is:</u></em></h3>8 - y = 3x ------ eqn 1
2y + 3x = 5 ----- eqn 2
We can solve by susbtitution method
From given,
y = 8 - 3x ----- eqn 3
Substitute eqn 3 in eqn 2
2(8 - 3x) + 3x = 5
16 - 6x + 3x = 5
3x = 16 - 5
3x = 11
Substitute the above value of x in eqn 3
y = 8 - 3x
Thus the solution is
Since x is the number of seconds it took the rock to hit the water, x is the value that we are looking for. When the rock hits the water, it's height is 0, therefore, f(x) = 0. So, we can set the expression on the right equal to 0, and solve for 0. Let's do just that:
We can divide by -16, nothing will happen because 0 divided by anything is 0:
To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":
So, for this specific question, let's find two numbers that add to -8 and multiply to 9. These are clearly 9 and -1. We can write it in this way now:
Both answers would be valid, but there can't be negative time, so your answer is "It takes 9 seconds for the rock to reach the water."
We can divide by -16, nothing will happen because 0 divided by anything is 0:
To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":
So, for this specific question, let's find two numbers that add to -8 and multiply to 9. These are clearly 9 and -1. We can write it in this way now:
Both answers would be valid, but there can't be negative time, so your answer is "It takes 9 seconds for the rock to reach the water."