Factoring area models x2 + 6x + 5

Victor's Video Arcade pays its employees $7.95 per hour for weekday hours and $9.25 per hour for weekend hours. How much will an

Ivan

Answer:

i can't understand ur question

3 0

2 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

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Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0

1 year ago

Which one is true show work for all

Nataly [62]

C and D is true and others are false

7 0

2 years ago

The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.

Zepler [3.9K]

Answer:

option-C

Step-by-step explanation:

We are given row-echelon form

So, we can write equation from matrix as

$x-5z=-3$

$y-4z=-5$

Let's assume

$z=t$

now, we can find x and y

$x-5t=-3$

$x=5t-3$

$y-4t=-5$

$y=4t-5$

so, we get solutions as

$x=5t-3$

$y=4t-5$

$z=t$

where t can be any real numbers

6 0

3 years ago

Read 2 more answers

Find the area of an equilateral triangle that has perimeter of 24 m.

mafiozo [28]

we know the perimeter is 24, and is an equilateral triangle, so it has three equal sides, so each side is 24 ÷ 3 = 8.

$\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=side's\\ \qquad length\\ \cline{1-1} s = 8 \end{cases}\implies A=\cfrac{8^2\sqrt{3}}{4}\\\\\\ A=16\sqrt{3}\implies A\approx 24.71$

6 0

3 years ago