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3 years ago

0.08 Divided by 3.84

Mathematics

2 answers:

Cloud [144]3 years ago

8 0

Around 0.02 or more precise, 0.02083

notsponge [240]3 years ago

6 0

0.08 / 3.84 = 1 / 48

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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

Felicity's dog eats two cups of dog food per day. Felicity's dog eats at least one-quarter cup more than one-half of the amount

cupoosta [38]

Answer:

2 > $\frac{1}{2} m + \frac{1}{4}$

Step-by-step explanation:

Given:

Felicity's dog eats two cups of dog food per day :2

If the amount of food that Martin's dog eats is represented by using m

Felicity's dog eats at least one-quarter cup more than one-half of the amount Martin's dog eats: $\frac{1}{2} m + \frac{1}{4}$

So we have the inequality represents the situation is:

2 > $\frac{1}{2} m + \frac{1}{4}$

4 0

2 years ago

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Ne4ueva [31]

Answer: bd=8 dc=2 and ae=4 so value of ab=16

Step-by-step explanation:

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2 years ago

Many experts have argued for the elimination of rote memorization as a method for learning mathematical facts such as basic oper

N76 [4]

I think they should keep it around, even if it might not be the most efficient strategy. After all, what if you need to solve a problem using multiple strategies?

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3 years ago

A mathematical formula designed to predict population fluctuations in a community could be called a(an)

kvasek [131]

It would be called an ecological model.

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