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2 years ago

12

A pillow that usually costs $18 is marked down 25%. Use the table to find the pillow’s new price.

1 answer:

snow_tiger [21]2 years ago

4 0

It would be 13.50 because 50% off of 18$ is 9$ but it’s not 50% off itS 25% off so If you take the 50% Off price of 9$ and add 4.50 (One more 1/4th) you get $13.50

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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 <em>a</em>, <em>b</em>, and <em>c </em>of the parabola equation

<em> $a=4, b=-6, \:and \:c=-8$ </em>

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

2 years ago

An example of financial responsibility is

Maurinko [17]

Answer:

keeping financial records organized

4 0

3 years ago

What is the slope of a line that is parallel to the line represented by the equation 3x+4y=12?

mash [69]

Slope-intercept form is:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

(there is probably another way to do this, but I will be doing it this way)

Isolate the "y" in the equation

3x + 4y = 12 Subtract 3x on both sides

4y = 12 - 3x Divide 4 on both sides

$y=3-\frac{3}{4}x$ or $y=-\frac{3}{4} x+3$ The slope is -3/4

For lines to be parallel, they have to have the SAME slope. The given line's slope is -3/4, so the slope of the parallel line is also $-\frac{3}{4}$

8 0

3 years ago

Help me please!!!!!!

Verdich [7]

Answer:

c.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

a square measuring 9 inches by 9 inches is cut from the corners of a square measuring 15 inches by 15 inches what is the area of

Alexandra [31]

Answer:

Step-by-step explanation:

It would be the area of the big square minus the area of the small square.

6 0

3 years ago