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3 years ago

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A box of blueberries is 2/5 full. Janet and her friends had each eaten 1/10 of a box of blueberries. How many people are blueber

ries?

2 answers:

anyanavicka [17]3 years ago

7 0

In this problem, we have to find the factor which will make (1 / 10) equal to (2 / 5). Therefore we can write it as:

x (1 / 10) = 2 / 5

where x is the number of people who ate the blueberries

x = (2 / 5) / (1 / 10)

x = 4

<span>Therefore 4 people ate the blueberries.</span>

Citrus2011 [14]3 years ago

6 0

The question is about the number of people who ate blueberries. The sum of their consumption must equal to 2/5. Since each consumption is 1/10, the equation is written as

2/5 = (1/10)x
where x is the number of people who ate the blueberries
Cross-multiplying,
20 = 5x
x = 20/5 = 4

<em>Thus, there were 4 people who ate the blueberries.</em>

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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

3 years ago

Which of the following is not a solution to the system of linear equations below? 5y=3x+15 6x=10y-30 A. (5, 6) B. (–15, 12) C. (

Alecsey [184]

Option B is not a solution.

5y=3x+15
5(12)=3(-15)+15
60=-45+15
60≠-30

Hope I didn't mess up for your sake!

7 0

3 years ago

How much greater is 28.95 than 14.25?

patriot [66]

28.95 is 14.7 greater than 14.25

7 0

3 years ago

write an equation of the line that is parallel to the given line and that passes through the given point. y=5/2x - 10; (-6,-29)

dlinn [17]

Write the standard form of a line, the slope is 5/2 since they are parallel and then replace the coordinates.
y-(-29) = 5/2 (x-(-6)) -> y=5/2x-14

6 0

3 years ago

What is -3/2 - 7/4 + 1/8

Eddi Din [679]

Answer:

3/8

Step-by-step explanation:

-3/2 can change to -12/8

7/4 can change to 14/8

1/8 stays the same

-12/8 + 14/8 = 2/8 + 1/8 = 3/8

3 0

3 years ago