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SashulF [63]
1 year ago
9

29. The table below represents the relationship of the price of carrots to their weight in ounces in a market: Price Weight, in

oz. $0.377.4 $0.44 8.8 $0.52 10.4 B Another market sells carrots at a rate of $4.80 for every 3 pounds. Which equation represents the market that sells their carrots at a lower rate per pound? y = 0.8x y = 1.2x ) y = 0,4x y = 1.6x​
Mathematics
1 answer:
Alinara [238K]1 year ago
3 0

The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

From the table, the rate is:

k = $8.8/4.4 = 2.

From the market, the rate is:

k = $4.8/3 = $1.6.

Hence the equation is y = 1.6x.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

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(0.98)(12)
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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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