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Liula [17]
3 years ago
6

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

6 0
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
368/16=23 miles per gallon
3 0
3 years ago
marcy guessed the number of hershey kisses in the school jar. since she guessed correctly, she got to keep all of the candy. she
zaharov [31]

Answer:

118.............................

6 0
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.

6 0
3 years ago
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