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3 years ago

An eye doctor charges an exam fee, plus a charge for the number of boxes of contact lenses purchased.

Mathematics

1 answer:

LiRa [457]3 years ago

5 0

Answer:

to get the exam fee

$112•97 ÷ 2

45•49

$272•93 ÷ 3

56•49

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Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)

jeyben [28]

Answer:

The vertex: $(\frac{3}{4},-\frac{41}{4} )$

The vertical intercept is: $y=-8$

The coordinates of the two intercepts of the parabola are $(\frac{3+\sqrt{41} }{4} , 0)$ and $(\frac{3-\sqrt{41} }{4} , 0)$

Step-by-step explanation:

To find the vertex of the parabola $4x^2-6x-8$ you need to:

1. Find the coefficients a, b, and c of the parabola equation

$a=4, b=-6, \:and \:c=-8$

2. You can apply this formula to find x-coordinate of the vertex

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

$x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}$

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ( $f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c$ )

$f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}$

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

$f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8$

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$x^2-6x-8+8=0+8$

$\mathrm{Simplify}$

$4x^2-6x=8$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2$

$\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{41}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}$

4 0

3 years ago

WHO EVERY GETS THIS RIGHT GETS 20 PTS

MariettaO [177]

The function is f(x) = 9,000(0.95)x

7 0

3 years ago

What is the second step to solving this equation? 9x - 23 = 49

Anna11 [10]

Answer:

Divide 9 from both sides.

Step-by-step explanation:

The first step to solving this equation is to add 23 to both sides.

9x - 23 (+23) = 49 (+23)

9x = 49 + 23

9x = 72

The second step is to isolate the x and divide 9 from both sides:

(9x)/9 = (72)/9

x = 72/9

x = 8

6 0

4 years ago

What is the slope of the line that goes through (-9,-6) and 3,-9)?

Lisa [10]

Answer:

-3/12

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

Which point is a reflection of T(-6.5, 1) across the x-axis and the y-axis?

drek231 [11]

First, start off with the x-axis. -6.5, 1 becomes 6.5, 1. This is because point T is 6.5 to the left of the x-axis line, so our new point would be 6.5 to the right of the x-axis line. Same thing for the y-axis, (6.5, 1) would become (6.5, -1).

8 0

3 years ago