Answer:
Step-by-step explanation:
y - 3 = -(x + 2)
y - 3 = -x - 2
y = -x + 1
There can only be two definite x-intercepts, so your goal it to find 2 numbers of x that, when plugged into the equation, give you the answer of 0. 1 is the first x-intercept(4-24+20 equals 0). The second one is 5 (100-120+20 equals 0). So the average is 3, so the axis of symmetry is 3 since 5+1=6, and 6/2=3
Honestly, there is an easier way to find the axis of symmetry. the equation would be -b/2a, where as b is the coefficient in the second part of the equation, while a is the first coefficient in the equation. -(-24) is 24, and 4*2=8, so 24/8=3
I hope I actually answered this the way you wanted. You asked for an equation, but I just answered the axis of symmetry with very simple equation initially and another equation
Answer:
Table 1 and 2 represent a function
Step-by-step explanation:
Given
<em>Table 1</em>
x 5 10 11
y 3 9 15
<em></em>
<em>Table 2</em>
x 5 10 11
y 3 9 9
<em>Table 3</em>
x 5 10 10
y 3 9 15
Required
Determine which of the tables represent that y is a function of x
For a relation to be a function; the x values must be unique.
In other words, each x value must not be repeated;
Having said that;
Analyzing Table 1
<em>Table 1</em>
x 5 10 11
y 3 9 15
<em></em>
Note that the x rows are unique as no value were repeated;
Hence, Table 1 is a function
<em>Table 2</em>
x 5 10 11
y 3 9 9
Note that the x rows are unique as no value were repeated;
Hence, Table 2 is a function
<em>Table 3</em>
x 5 10 10
y 3 9 15
Note that the x rows are not unique because 10 was repeated twice;
Hence, Table 3 is not a function
Hello there.
<span>
(X+Y)+Y=1.10
</span>
<span><span><span>x+y</span>+y</span>=1.1</span>
<span><span><span>x+<span>2y</span></span>+<span>−<span>2y</span></span></span>=<span>1.1+<span>−<span>2y</span></span></span></span><span>x=<span><span>−<span>2y</span></span>+1.1</span></span>
Answer:x=<span><span>−<span>2y</span></span>+<span>1.1</span></span>
![{3x}^{2} - 5x = - 8 \\ {3x}^{2} - 5x + 8 = 0](https://tex.z-dn.net/?f=%20%7B3x%7D%5E%7B2%7D%20%20-%205x%20%3D%20%20-%208%20%5C%5C%20%20%7B3x%7D%5E%7B2%7D%20%20-%205x%20%2B%208%20%3D%200)
This equation has the next form:
![{ax}^{2} + bx + c = 0](https://tex.z-dn.net/?f=%20%7Bax%7D%5E%7B2%7D%20%20%2B%20bx%20%2B%20c%20%3D%200)
To find if the equation has two complex solutions we have to check if the discriminant is negative, as follows:
![{b}^{2} - 4ac \\ ( { - 5})^{2} - 4 \: . \: 3 \: . \: 8 = 25 - 96 = - 71 < 0](https://tex.z-dn.net/?f=%20%7Bb%7D%5E%7B2%7D%20%20-%204ac%20%5C%5C%20%28%20%7B%20-%205%7D%29%5E%7B2%7D%20%20-%204%20%5C%3A%20.%20%5C%3A%203%20%5C%3A%20.%20%5C%3A%208%20%3D%2025%20-%2096%20%3D%20%20-%2071%20%3C%200)
Then, the first case has two complex solutions.
In the second case,
![{2x}^{2} = 6x - 5 \\ {2x}^{2} - 6x + 5 = 0](https://tex.z-dn.net/?f=%20%7B2x%7D%5E%7B2%7D%20%20%3D%206x%20-%205%20%5C%5C%20%20%7B2x%7D%5E%7B2%7D%20%20-%206x%20%2B%205%20%3D%200)
The discriminant in this case is:
![( { - 6})^{2} - 4 \: . \: 2 \: . \: 5 = 36 - 40 = - 4 < 0](https://tex.z-dn.net/?f=%28%20%7B%20-%206%7D%29%5E%7B2%7D%20%20-%204%20%5C%3A%20.%20%5C%3A%202%20%5C%3A%20.%20%5C%3A%205%20%3D%2036%20-%2040%20%3D%20%20-%204%20%3C%200)
Then, the second case has two complex solutions.
In the third case,
![12x = {9x}^{2} + 4 \\ { - 9x}^{2} + 12x - 4 = 0](https://tex.z-dn.net/?f=12x%20%3D%20%20%7B9x%7D%5E%7B2%7D%20%20%2B%204%20%5C%5C%20%20%7B%20-%209x%7D%5E%7B2%7D%20%20%2B%2012x%20-%204%20%3D%200)
The discriminant in this case is:
![{12}^{2} - 4 \: . \: ( - 9) \: . \: ( - 4) = 144 - 144 = 0](https://tex.z-dn.net/?f=%20%7B12%7D%5E%7B2%7D%20%20-%204%20%5C%3A%20.%20%5C%3A%20%28%20-%209%29%20%5C%3A%20.%20%5C%3A%20%28%20-%204%29%20%3D%20144%20-%20144%20%3D%200)
Then, the third case has two real solutions.
In the fourth case,
![{ - x}^{2} - 10x = 34 \\ { - x}^{2} - 10x - 34 = 0](https://tex.z-dn.net/?f=%20%7B%20-%20x%7D%5E%7B2%7D%20%20-%2010x%20%3D%2034%20%5C%5C%20%20%7B%20-%20x%7D%5E%7B2%7D%20-%2010x%20-%2034%20%3D%200)
The discriminant in this case is:
![( { - 10})^{2} - 4 \: . \: ( - 1) \: . \: ( - 34) = 100 - 136 = - 36 < 0](https://tex.z-dn.net/?f=%28%20%7B%20-%2010%7D%29%5E%7B2%7D%20%20-%204%20%5C%3A%20.%20%5C%3A%20%28%20-%201%29%20%5C%3A%20.%20%5C%3A%20%28%20-%2034%29%20%3D%20100%20-%20136%20%3D%20%20-%2036%20%3C%200)
Then, the fourth case has two complex solutions.