Answer:
Compress the graph
Flip the graph
Shift the graph 4 units to the left
Step-by-step explanation:
When functions are transformed there are a few simple rules:
- Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
- Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
- Multiplying the function by a number less than 1 compresses it towards the x-axis.
- Multiplying the function by a number greater than 1 stretches it away from the x-axis.
This graph has been multiplied by -1/3 which is less than 1. It will be compressed.
It will also flip the graph since it is changing to a negative and be an upside down U.
This graph has x added to by 4. It will shift left 4 units.
Given:
In ABCD, AB=BC, AD=CD.
To find:
The additional information that can be included in the figure showing kite ABCD with diagonals AC and BD.
Solution:
We know that, a quadrilateral is a kite if,
1. Two pairs of congruent sides which are adjacent to each other.
2. One diagonal is perpendicular bisector of other.
From the given information, we have two pairs of consecutive congruent sides AB=BC and AD=CD.
ABCD is a kite if it holds the second property, i.e., one diagonal is perpendicular bisector of other.
So, the required additional information is "segment BD is perpendicular bisector of segment AC".
Therefore, the correct option is B.
Answer:
<em>m∠EBC = 34° </em>
Step-by-step explanation:
m∠DBC = m∠DBE + m∠ EBC
m∠DBC - m∠DBE = m∠EBC
(12x - 3)° - (5x + 12)° = (3x + 13)°
12x - 5x - 3 - 12 = 3x + 13
4x = 28
x = 7
<em>m∠EBC </em>= (3(7) + 13)° <em>= 34° </em>
I assumed that it would like this, the greater than or equal to sign in the expression k≥12. We begin with the left side of the interval notation.Since you entered an equal sign, this interprets to [ since we include the number 12 Based on the ≥ you entered, the right side of the interval notation will encompass to positive infinity, which is signified as +∞
So it would look like [12, +∞)
The set builder notation would look like:{K | X ≥ 12} where “|” denotes such that.
The display for the representation is:12,13,14,15,16,17,18,19,20,21,22,...,∞
X=-b/2a is the formula for finding the axis of symmetry
So x= -30/2(5)
X=-30/10
X=-3
Because the axis of symmetry is -3, we know where to place our line, and we also know that the parabola is open downwards, which means that the vertex will be maximum. To find the vertex, plug in your values with the axis of symmetry as a midway point. Plug that in for x and so you should have the following:
F(x)
Y(f(x) and y variables are interchangeable) =5(-3)^2-30(-3)+49
Solve for y(f(x))
5(-3)^2-30(-3)+49
(-3)^2=3^2
3^2*5+30*3+49
Multiply
3^2*5+90+49
Add numbers
3^2*5+139
9*5=45
45+139=184
Y=184
So, your vertex would be
(-3,184) and it would be maximum. From there you can plug in the rest of your table of values.