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3 years ago

Six times a number is greater than 20 more than that number. What are the possible values of that number?

Mathematics

1 answer:

Alex73 [517]3 years ago

3 0

Answer:

6x > x + 20,

x > 4

X belongs to a set of real numbers [0, +infinity)

Step-by-step explanation:

6x > x + 20

5x > 20

x > 4

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Please help! acellus

ch4aika [34]

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
$\displaystyle a^2 + b^2 = c^2$

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

[Pythagorean Theorem] Square root both sides [Equality Property]:
$\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}$

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}$

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

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Learn more about Trigonometry: brainly.com/question/27707750

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Topic: Trigonometry

3 0

2 years ago

Lizards can eat 45 ants per minute. How long would it take to eat 1,080 ants?

dsp73

Answer: 24 minutes!

Step-by-step explanation: As mentioned, it can eat 45 ants per minute, How long would it take to eat 1,080 ants?

It's simple, just divide 1080 by 45 and when you divide it, the answer is 24!

4 0

3 years ago

-7(-5x - 9) + 4x Your answer

ASHA 777 [7]

35x - 63 + 4x
35x + 4x -63
39x - 63

8 0

3 years ago

Read 2 more answers

How do you solve his with working

AlexFokin [52]

Check the picture below.

a)

so the perimeter will include "part" of the circumference of the green circle, and it will include "part" of the red encircled section, plus the endpoints where the pathway ends.

the endpoints, are just 2 meters long, as you can see 2+15+2 is 19, or the radius of the "outer radius".

let's find the circumference of the green circle, and then subtract the arc of that sector that's not part of the perimeter.

and then let's get the circumference of the red encircled section, and also subtract the arc of that sector, and then we add the endpoints and that's the perimeter.

$\bf \begin{array}{cllll}
\textit{circumference of a circle}\\\\ 
2\pi r
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{arc's length}\\\\
s=\cfrac{\theta r\pi }{180}
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\stackrel{green~circle}{perimeter}}{2\pi(7.5) }~-~\stackrel{\stackrel{green~circle}{arc}}{\cfrac{(135)(7.5)\pi }{180}}~+
\stackrel{\stackrel{red~section}{perimeter}}{2\pi(9.5) }~-~\stackrel{\stackrel{red~section}{arc}}{\cfrac{(135)(9.5)\pi }{180}}+\stackrel{endpoints}{2+2}
\\\\\\
15\pi -\cfrac{45\pi }{8}+19\pi -\cfrac{57\pi }{8}+4\implies \cfrac{85\pi }{4}+4\quad \approx \quad 70.7588438888$

b)

we do about the same here as well, we get the full area of the red encircled area, and then subtract the sector with 135°, and then subtract the sector of the green circle that is 360° - 135°, or 225°, the part that wasn't included in the previous subtraction.

$\bf \begin{array}{cllll}
\textit{area of a circle}\\\\ 
\pi r^2
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{area of a sector of a circle}\\\\
s=\cfrac{\theta r^2\pi }{360}
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\stackrel{red~section}{area}}{\pi(9.5^2) }~-~\stackrel{\stackrel{red~section}{sector}}{\cfrac{(135)(9.5^2)\pi }{360}}-\stackrel{\stackrel{green~circle}{sector}}{\cfrac{(225)(7.5^2)\pi }{360}}
\\\\\\
90.25\pi -\cfrac{1083\pi }{32}-\cfrac{1125\pi }{32}\implies \cfrac{85\pi }{4}\quad \approx\quad 66.75884$

7 0

3 years ago

Definition of Variable and Constant with examples! Spam free answers required!

ra1l [238]

Answer:

$\large\boxed{\boxed{\boxed{\mathfrak{variable}}}}$

Variable is a symbol that represents a quantity in a mathematical expression, as used in many sciences. Variable (research), a logical set of attributes. Variable star, a type of astronomical star.

$\large\boxed{\boxed{\boxed{\mathfrak{constant}}}}$

A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. A function, equation, etc., is said to "be constant" (or be a constant function) if it always assumes the same value independent of how its parameters are varied.

6 0

3 years ago