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3 years ago

Simplify the following expression. 2x^5+ 3x^3 - 5x^2 + x^2 +7x+1+7x^5 - 3x^3 - 4

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

9x^5-4x^2+7x-3 is the simplified version of your answer.

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Solve for "r": 4/3πr^3 = V

boyakko [2]

$\frac{4}{3} \pi r^3=V
\\
\\4\pi r^3=3V
\\
\\ r^3= \frac{3V}{4\pi}
\\
\\r= \sqrt[3]{\frac{3V}{4\pi}}$

8 0

3 years ago

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

(3 sqrt-1)-(9 sqrt-16)

Cerrena [4.2K]

I hope this helps you

7 0

3 years ago

Is 5:2 the same as 2:5

Neporo4naja [7]

Answer:

It is not the same

Step-by-step explanation:

Is 5/2 greater than 2/5? Is 5/2 bigger than 2/5? Is 5/2 larger than 2/5? These are all the same questions with one answer.

When comparing fractions such as 5/2 and 2/5, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below: 5/2 = 2.5

2/5 = 0.4 Therefore, 5/2 is greater than 2/5 and the answer to the question "Is 5/2 greater than 2/5?" is yes.

6 0

3 years ago

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Which algebraic rule describes the transformation?

Eddi Din [679]

Did you ever get it right? I need help

3 0

3 years ago