Answer:y=-5(x+11)^2 -28
Step-by-step explanation: Okay think about what you know about translations and transformations of parent functions. In this case, the parent function is x2. So what now?
First, the problem states that the parabola opens DOWN. This means that you should look for a negative leading coefficient. This narrows your options down to C or D. (-5 is the leading coefficient)
Now starting with the x2, the vertex would be at (0,0), but in this problem it is at (-11,-28). That means it was TRANSLATED 11 spots in the negative x-direction and 28 spots in the negative y-direction.
Look at your options, when a number is being added directly unto the x variable, such as in answer C, it moves in the negative x-direction. This tells you that C has to be your answer.
I hope that helps!
In the ordered pair (2, 12), x = 2 and y = 12.
Substitute these values into each inequality to see if the resulting inequality is true.
y > 2x + 4
12 > 2(2) + 4 Twelve is greater than 2 times 2 plus 4 ...hmmm
12 > 4 + 4
12 > 8 Twelve is greater than 8 ....this is TRUE...go to the next inequality
y < 3x + 7
12 < 3(2) + 7 Twelve is less than 3 times 2 plus 7 ...interesting
12 < 6 + 7
12 < 13 Twelve is less than 13 ... this is TRUE also
Therefore; the answer is b. Yes
It must create a true inequality for BOTH inequalities in order for the ordered pair to be a solution
Answer:
The approximate diameter of the larger tank is 8.10 meters
Step-by-step explanation:
Here, we want to calculate the diameter of the larger tank
The volume of a sphere
V = 4/3 * π * r^3
Let us calculate the volume of the standard model
That will be;
Since diameter is 6 and r = d/2
r = 6/2 = 3 meters
V = 4/3 * π * 3^3 = 36 π m^3
Now, the volume of the larger tank is 2.5 times of this;
The volume of the larger tank is 2.5 * 36 π = 90 π m^3
So we can calculate the radius of this before we calculate its diameter
4/3 * π * r^3 = 90 π
4r^3/3 = 90
r^3 = 270/4
r^3 = 67.5
r = 3x√(67.5)
r = 4.07 m
Diameter here is 2 times this
= 4.07 * 2 = 8.14
Answer:
Option D. 
Step-by-step explanation:
Remember that
In a inscribed quadrilateral opposite angles are supplementary
so
In this problem
we have
substitute the values and solve for x
