Answer:
Inverse of a relation
Reasoning:
the inverse of a function is a full function, this is just a set of pairs. A set of pairs, or relation, where x and y values interchange are inverse of the relation. A one to one function is when a function's inverse is also a function (doesn't have more than one y for each x) which can be tested for on the normal function's graph with a HORIZONTAL line test. A normal parabola isn't one to one. An onto function has to do with every value being used (I don't remember much about them, but once again this isn't a function, but rather a specific set of pairs/data)
Example of inverse of a relation:
Relation: {(0,5), (3,2)}
Inverse: {(5,0), (2,3)}
Example of inverse of a function:
f(x)=5x
f-1(x)=x/5
Example of a one to one function:
f(x)=x+1
Answer:
C
The integer with the greatest value is the one that is farthest to the right hand side of the number line
Step-by-step explanation:
The number line is constructed in a way such that we have a center point of zero with positive values to the right of the number line and negative values to the left of the number line.
Moving deeper right, we have an increase in positivity, with the more positive values rightwards, indicating an increase in the numbers to the right
Moving to the left, we have an increase in negativity, but a decrease in value. The negative numbers closer to zero are more positive and command higher values than the values which are farther from zero.
What these indicates is that the more rightward a number, the greater its value
v + m = 32 and v = 5 + 2m are the equations that are used to determine m, the number of stuffed animals Mariposa has
Number of stuffed animals Mariposa has is 9 and number of stuffed animals with Veronica is 23
<h3>
<u>Solution:</u></h3>
Let "v" be the number of stuffed animals with Veronica
Let "m" be the number of stuffed animals with Mariposa
Given that,
Together, they have 32 stuffed animals
Therefore,
v + m = 32 --------- eqn 1
Veronica has 5 more than double the number of stutted animals as her friend Mariposa
Therefore,
Number of stuffed animals with Veronica = 5 + 2(number of stuffed animals with Mariposa)
v = 5 + 2m ---------- eqn 2
Thus eqn 1 and eqn 2 can be used to determine m, the number of stuffed animals Mariposa has
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
5 + 2m + m = 32
5 + 3m = 32
3m = 32 - 5
3m = 27
<h3>m = 9</h3>
Substitute m = 9 in eqn 2
v = 5 + 2(9)
v = 5 + 18
<h3>v = 23</h3>
Thus number of stuffed animals Mariposa has is 9 and number of stuffed animals with Veronica is 23
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
The coordinate (h, k) represents a parabola's vertex.
In order to convert a quadratic function in standard form to the vertex form, we can complete the square.
y = 2x² - 5x + 13
Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.
y - 13 = 2x² - 5x
Factor out 2 on the right side of the equation.
y - 13 = 2(x² - 2.5x)
Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.
y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)
y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)
Add the constants on the left and factor the expression on the right to a perfect square.
y - 9.875 = 2(x - 1.25)²
Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.
y = 2(x - 1.25)² + 9.875
Vertex: (1.25, 9.875)
Solution: y = 2(x - 1.25)² + 9.875
Or if you prefer fractions
y = 2(x - 5/4)² + 79/8
