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3 years ago

8 cubed in standard form and exponential form

Mathematics

1 answer:

masya89 [10]3 years ago

8 0

Answer:

so 8 cubed (8 × 8 × 8) in standard form is: 512

so 8 cubed (8 × 8 × 8) in exponential form is: 8³

Step-by-step explanation:

As we know that

The cube of any given number is that number times itself.

For example, 8 cubed, denoted by 8³ is equal to 8 × 8 × 8.

An exponent basically indicates the number of times we must multiply the base number. For example, to compute 8³, we multiply 3 three times (8×8×8).

so 8 cubed (8 × 8 × 8) in standard form is: 512

so 8 cubed (8 × 8 × 8) in exponential form is: 8³

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Two numbers are in the ratio 7:9. The smaller number is 42. what is the number?

ddd [48]

Answer:

7/9 = 42/n.

7n = 378,

n = 54.

Step-by-step explanation:

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2 years ago

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Topic: The Quadratic Formula

Finger [1]

Answer:

Step-by-step explanation:

The quadratic formula for a equation of form

ax²+bx + c = 0 is

$x= \frac{-b +- \sqrt{b^2-4ac} }{2a}$

For the first equation,

x²+3x-4=0,

we can match that up with the form

ax²+bx + c = 0

to get that

ax² = x²

divide both sides by x²

a=1

3x = bx

divide both sides by x

3 = b

-4 = c

. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.

Plugging our values into the equation, we get

$x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1$

as our possible solutions

Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.

Next, we have

x²+3x+4=0

Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus

$x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\$

Because √-7 is not a real number, this has no real solutions. However,

(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions

Finally, for

4x² + 1= 4x,

we can start by subtracting 4x from both sides to maintain the desired form, resulting in

4x²-4x+1=0

Then, a=4, b=-4, and c=1, making our equation

$x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2$

Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution

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3 years ago

What are the steps to 68 times 49

Anastaziya [24]

so basically what you would have to do is set up your numbers. it would look something like this. 68

× 49

-------------

and would then multiply 9 by 8, 9 by 6. put it down below the line while making sure to carry the numbers if need be. then do the same with the 4 times 8, and 4 by 6.

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3 years ago

Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc

klasskru [66]

Given:
Choose a number between 0 and 20.
If the difference is less than 10 then Eric wins.
Let us x is Eric's number. 0 < x < 20
If Eric wins. |x -7| < 10
|x-7| < 10 → -10 < x-7 < 10 → -10 + 7 < x - 7 + 7 < 10 + 7 → -3 < x < 17

Taking into account that the number must be given between 0 and 20.
0 < x < 20
-3 < x < 17

→ 0 < x < 16

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3 years ago

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