Answer:
D. 
and 
Step-by-step explanation:
The vertex of a function is controlled by the translations of the x and y value. Moving a vertex up and down is connected to the vertical position or the y-value. The y-value is the value that is added to the variable and is not squared.
Vertex form of a function is 
. In this case, k controls the vertical position of the vertex. If k is negative then the vertex will be moved down. So, if you want to move a vertex down by 5 units, then the k value must be -5.
Plug this into the formula to get the equation for k(x). This means that k(x) must equal 
.
As you can see, 4 of the 24 students don't partecipate in any activity. This clearly implies a ratio of 4:24, or 1:6.
We could infer that this ratio holds for the whole school, or even for all the boys and girls of that age.
That's the point of surveys and inferring: you gather data about a relatively small group, and then assume that the proportions you have are valid for a much larger group.
That's why it is important that the group that you survey is balanced and unbiased.
Answer
Find out the value of x .
To proof
SAS congurence property
In this property two sides and one angle of the two triangles are equal.
in the Δ ADC and ΔBDC
(1) CD = CD (common side of both the triangle)
(2) ∠CDA = ∠ CDB = 90 °
( ∠CDA +∠ CDB = 180 ° (Linear pair)
as given in the diagram
∠CDA = 90°
∠ CDB = 180 ° - 90°
∠ CDB = 90°)
(3) AD = DB (as shown in the diagram)
Δ ADC ≅ ΔBDC
by using the SAS congurence property .
AC = BC
(Corresponding sides of the congurent triangle)
As given
the length of AC is 2x and the length of BC is 3x - 5 .
2x = 3x - 5
3x -2x =5
x = 5
The value of x is 5 .
Hence proved
The answer is -3
-12c = 43 - 7
-12c = 36
÷ -12 ÷-12
c = -3
