Answer:
OR
Step-by-step explanation:
Vertex form of a parabola is given as:
Where (
) is the vertex and 
are the points on the parabola.
We are given that, the vertex is (3, -2) and another point on parabola is given as (2, 3).
First of all, putting the vertex in the vertex equation as given above:
Now, putting the values of 
as 2, 3 and let us find the unknown variable 
:
Therefore, the equation in vertex form can be written as:
OR
Answer:
c. 12
Step-by-step explanation:
To isolate the variable, you need to cancel out whatever's on the same side of the variable by using the inverse of the operation.
Hope this helps!! Have an awesome day φ(*^0^)
Answer:
Option B. 1/2
Step-by-step explanation:
The smaller triangle is a dilation of the larger triangle with the center of dilation at (2, -1).
we have to calculate the scale factor of the dilation.
One point of the large triangle is (-4, -1). After dilation it has become (-1, -1) of the smaller one.
If we consider the x coordinates of the point x = -4 has reduced down to -1 therefore scale factor = side of small triangle/side of the large triangle = (2 + 1)/(2 + 4) = 3/6 = 1/2
Therefore Option B. 1/2 is the answer.
Answer:
Step-by-step explanation:
First, note that the angles shown are vertical angles. In other words, the two equations are equivalent to each other.
Therefore, set the equations equal to each other and solve for x;
Add 17 to both sides:
Subtract 6x from both sides:
Divide both sides by 2:
Therefore, the value of x is 12.
And we're done!
If x = # of quarters, then, the # of dimes will be equal to 2x. The total value (z) would be equal to:
z = 0.25x + 0.10(2x)
Then, since you switch the quarters and the dimes, and you have a new total, the resulting equation will be:
1.2 + z = 0.25(2x) + 0.10(x)
Plug in the values you know:
1.2 + (0.25x + 0.10(2x)) = 0.25(2x) + 0.10(x)
Solve for x:
1.2 + (0.25x + 0.20x) = 0.50x + 0.10x
1.2 + 0.45x = 0.60x
1.2 = 0.15x
x = 1.2/0.15 = 8
This means that there are 8 Quarters in her bag right now. So, the amount of dimes is just 2x which is 16. So your answer will be:
She has 8 Quarters and 16 Dimes in her bag right now. Or, $3.60.
If this doesn't make sense, then tell me. I have some resources where I got the answer from to put it into simplest terms. I have the website if you want.
