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just olya [345]
3 years ago
11

Write 5,002,190 in expanded form

Mathematics
2 answers:
Svetradugi [14.3K]3 years ago
8 0
Five million twothousand onehundred and ninety 
mina [271]3 years ago
4 0
5,000,000 + 2000 + 100 + 90

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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}

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3 years ago
Answer asap 30 points!!!!!!!!!!!!!!!!!!!!!!!!!What is the lateral surface area of the cone?
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Answer:

it would be a

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3 years ago
How would I turn 0.46 into a fraction
Pepsi [2]
<span>Step 1: 0.46 = 46⁄100</span> 
<span>Step 2: Simplify 46⁄100 = 23⁄50</span><span>  hope this helped u</span>
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1) Jessica charges $8 an hour for babysitting
nordsb [41]
A. The independent variable is time, as time is manipulating the value of her salary.

b. The dependent variable is her cost because what she charges for babysitting depends on how long she works.

c. y = 8x
y = how much she charges for this job
8 = the amount she charges per hour
x = number of hours babysat
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3 years ago
1000ml:300ml to its simplest form
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<h2>HI MATE YOUR ANSWER SHOULD BE 10/3</h2>
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