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3 years ago

7

Francesca tried to evaluate an expression. Here is her work: 3(5)2–18÷3 = 3(25)–18÷3 = 75–18÷3 = 57÷3 = 19 Is Francesca's work c

orrect?

1 answer:

hram777 [196]3 years ago

5 0

Answer:

Nope. Moltiplication (and thus divisions) has to be done before any addition or subtractions, unless parenthesis indicate otherwise.

$3(5)^2 - 18\div 3 = 3(25) - 6 = 75-6=69$

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If y= 1-x+x²/1+x-x² than how about y'=? <br> This question is about derived function.

zavuch27 [327]

Answer:

as

$\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0$

so

$y'=0$

Step-by-step explanation:

Given the function

$y=\:1-x+\frac{x^2}{1}+x-x^2$

Taking derivative

$\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)$

as

$\frac{d}{dx}\left(1\right)=0$ ∵ $\mathrm{Derivative\:of\:a\:constant}:\quad \frac{d}{dx}\left(a\right)=0$

$\frac{d}{dx}\left(x\right)=1$ ∵ $\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x$ ∵ $\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$\frac{d}{dx}\left(x\right)=1$ ∵ $\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x$ ∵ $\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

substituting all the values in the expression

$=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)$

$=0-1+2x+1-2x$

$=0$

Hence,

$\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0$

Therefore,

$y'=0$

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3 years ago

Following the recommended steps for solving equations, what should be your first step in solving the given equation?

Free_Kalibri [48]

To solve equations, you isolate the variable you are solving for on one side and everything else on the other side.

The first step to solving this equation is to combine like terms.
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If no exponent is shown, then a 1 exponent is implied. The reason why we don't show a term raised to the first power is that it doesn't have any effect on the term.

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I'll rearrange the left-hand side to combine all the terms with the x variable.

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Combine all terms that have the x variable.

-3 + 2x - 4x - 2x = -6
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Now we have -3 - 4x = -6
What can we do now to isolate the x variable on the left-hand side?
For starters, we can add 3 to each side of the equation.
That way the -3 term will disappear.

-3 - 4x + 3 = -6 + 3
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Last step.
The x variable is being multiplied by the -4. If we reverse that operation
we can get the value of x.

-4x / -4 = 3 / -4
x = 3/-4 or x = -0.75

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