An item is regularly priced at $64. Amy bought it at a discount of 10% off the regular price.

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

Anastasy [175]

Answer:

$y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}$

Step-by-step explanation:

An equation in the vertex form is written as

$y = a (x-h) + k$

Where the point (h, k) is the vertex of the equation.

For an equation in the form $ax ^ 2 + bx + c$ the x coordinate of the vertex is defined as

$x = -\frac{b}{2a}$

In this case we have the equation $y = 9x^2 + 9x - 1$ .

Where

$a = 9\\\\b = 9\\\\c = -1$

Then the x coordinate of the vertex is:

$x = -\frac{9}{2(9)}\\\\x = -\frac{9}{18}\\\\x = -\frac{1}{2}$

The y coordinate of the vertex is replacing the value of $x = -\frac{1}{2}$ in the function

$y = 9 (-0.5) ^ 2 + 9 (-0.5) -1\\\\y = -\frac{13}{4}$

Then the vertex is:

$(-\frac{1}{2}, -\frac{13}{4})$

Therefore The encuacion excrita in the form of vertice is:

$y = a(x +\frac{1}{2}) ^ 2 -\frac{13}{4}$

To find the coefficient a we substitute a point that belongs to the function $y = 9x^2 + 9x - 1$

The point (0, -1) belongs to the function. Thus.

$-1 = a(0 + \frac{1}{2}) ^ 2 -\frac{13}{4}$

$-1 = a(\frac{1}{4}) -\frac{13}{4}\\\\a = \frac{-1 +\frac{13}{4}}{\frac{1}{4}}\\\\a = 9$

<em>Then the written function in the form of vertice is</em>

$y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}$

7 0

3 years ago

A plane intersects a sphere with a volume of about 44.6 cubic meters through the center of the sphere. What is the area of the c

san4es73 [151]

From the above definition, we can say that the cross-section, as a result of the plane intersecting the sphere through its centre, will be a circle with the radius "r" same as that of the given sphere. Thus, the area of the cross section is 15.2 m²

5 0

2 years ago

Hi this is work out the missing angle will give brainliest

Brums [2.3K]

Answer is
65
Hehehhehehe

3 0

2 years ago

4(X+Y)+Y+2(Y+5)+6x <br> Need help full steps

34kurt

4(X+Y)+Y+2(Y+5)+6X
4X + 4Y + Y + 2Y + 10 + 6X
4X + 6X + 4Y + Y + 2Y + 10
10X + 7Y + 10

6 0

3 years ago

Suppose that in a bowling league, the scores among all bowlers are normally distributed with mean µ = 182 points and standard de

exis [7]

Answer:

209 points

Step-by-step explanation:

Mean points scored (μ) = 182 points

Standard deviation (σ) = 14 points

The z-score for any given game score 'X' is defined as:

$z=\frac{X-\mu}{\sigma}$

At, the 97th percentile of a normal distribution, the z-score, according to a z-score table, is 1.881.

Therefore, the minimum score, X, needed for a bowler to receive a trophy is:

$1.881=\frac{X-182}{14}\\X=208.334$

Since only whole point scores are possible, X=209 points.

3 0

3 years ago