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2 years ago

Whats the number of pi

Mathematics

2 answers:

Alchen [17]2 years ago

7 0

Pi is approximately 3.14 and is commonly used in academic equations.

The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

Nitella [24]2 years ago

7 0

3.14 is what’s most used

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Write an expression for the volume of a rectangularprism if the length is 25 cm shorter than some given amount, x, and the width

seraphim [82]

The volume of a prism is given by:

$V=lwh$

We know that the height is x. The length is 25 shorter than x, this can be express as:

$x-25$

The width is 14 longer than x, this can be express as:

$x+14$

Plugging the expressions for the length, the width and the height we have that:

$\begin{gathered} V=(x-25)(x+14)x \\ V=x(x-25)(x+14) \end{gathered}$

Therefore, the volume of the prism is:

$V=x(x-25)(x+14)$

8 0

1 year ago

What is the prime factorization of 155

xenn [34]

The factors of 155 are 1, 5, 31, and 155, thus the prime factorization should be 5 and 31.

5 0

3 years ago

Can you help me solve this equation?

dem82 [27]

Sure

Answer:

x = -2

If the steps aren't belong to the lesson that you want, just tell me the lesson title so I can get the answer for you !!!!

...

The steps

Multiply all terms by (x-3)(x+3) and cancel:

x(x+3)+2x(x−3)=18

3x2−3x=18(Simplify both sides of the equation)

3x2−3x−18=18−18(Subtract 18 from both sides)

3x2−3x−18=0

3(x+2)(x−3)=0(Factor left side of equation)

x+2=0 or x−3=0(Set factors equal to 0)

x=−2 or x=3

Check answers. (Plug them in to make sure they work.)

x=−2 (Works in original equation)

x=3 (Doesn't work in original equation)

7 0

2 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

Plz help ->

Paraphin [41]

Answer: ok so for 5 and 125 it is 65 and 25

for 1 and 9 it is 5 and 3 and for 4 and 9 it is 13/2 and 6

6 0

3 years ago