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3 years ago

Which graph represents the piecewise-defined function? y={−45x−3 if x<03x−10 if x≥2

Mathematics

1 answer:

Nikitich [7]3 years ago

3 0

Step-by-step explanation:

$y=\left \Bigg\{ {\big{-45x-3 \qquad x < 0} \atop \big{3x - 10 \qquad x \geq2 }} \right.$

$\begin {array}{c|c}{ x&y}}\\ -\infty&-\infty\\-2&-93\\-1&-48\\ 0 &-3^*\\1&nothing\\2&-4\\3&-1\\4&2\\ \infty&\infty\\\end{array}$

* open dot

You did not provide the graphs to choose from so use the table above to determine which graph fits those coordinates.

Make sure that:

(0, -3) has an open dot
nothing is plotted between x = 0 and x = 2
(2, -4) has a closed dot

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I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful

Bingel [31]

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let $f(x)=\sqrt{x}$ and $g(x)=7x^2+4x+1$ . Then, the given equation is essentially $f(g(x))=\sqrt{7x^2+4x+1}$ . Thus, we can use the chain rule.

Recall the chain rule: $\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)$ . So, let's find the derivative of each function:

$f(x)=\sqrt{x}=x^\frac{1}{2}$

We can use the Power Rule here:

$f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}$

Now:

$g(x)=7x^2+4x+1$

Again, use the Power Rule and Sum Rule

$g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4$

Now, we can put them together:

$y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)$

$y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }$

5 0

3 years ago

What function corresponds to the ordered pairs shown in the table?

Anettt [7]

well, we know it's a line, and to get the equation of any line all we need is two points, let's pick two from the table hmmmm say let's use (-3 , -7) and (3 , 11)

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{11}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}}\implies \cfrac{11+7}{3+3}\implies \cfrac{18}{6}\implies 3$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{3}(x-\stackrel{x_1}{(-3)}) \\\\\\ y+7=3(x+3)\implies y+7=3x+9\implies y = 3x+2$

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3 years ago

Fred's car can travel 368 miles on one tank of gas. His gas tank holds 16 gallons.What is the unit rate for miles per gallon ple

julia-pushkina [17]

368 miles / 16 gallons
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3 years ago

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zaharov [31]

Answer:

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3 years ago

A mechanic charged $220.28 to repair a car. The price included charges for 3 hours of labor and $126.53 for parts. How much does

Assoli18 [71]

Answer:

$31.25

Step-by-step explanation:

Let's set up an equation.

$220. 28 - total

$126.53 - cost for parts

3 - # of hours

? - price per hour

3h + $126.53 = $220.28

Subtract $126.53 from both sides.

3h = $93.75

Divide by 3.

h = $31.25

The mechanic charges $31.25 per hour for labor.

Hope that helps.

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3 years ago