All categories

3 years ago

Need help please with end behavior!

Mathematics

1 answer:

Contact [7]3 years ago

6 0

I'll focus on problem 2.

For these types of problems, I recommend graphing the functions to see how the end behavior looks.

The graph of y = x^2 has a parabola where both endpoints aim upward. So each end goes to positive infinity (regardless if x is going to positive or negative infinity).

In short, the graph rises to the left and it rises to the right.

Increasing the leading coefficient will not change this fact. We can pick any leading coefficient we want and the end behavior will stay the same. All that matters is the leading coefficient is positive.

If the leading coefficient becomes negative, then everything flips: the endpoints will aim down. The other terms we add on (such as a 3x+3) will not change the end behavior. The leading term, with the largest exponent, is what directly and solely determines the end behavior.

The graph is shown below. I used GeoGebra to make the graph. Desmos is another handy tool you could use.

You might be interested in

I need answer on this graphing va substitution.Problem 7 I tried to solve it but not sure that’s correct

Bond [772]

Given the system of equations:

$\begin{gathered} 2x+9y=27 \\ x-3y=-24 \end{gathered}$

To solve it by substitution, follow the steps below.

Step 1: Solve one linear equation for x in terms of y.

Let's choose the second equation. To solve it for x, add 3y to each side of the equations.

$\begin{gathered} x-3y=-24 \\ x-3y+3y=-24+3y \\ x=-24+3y \end{gathered}$

Step 2: Substitute the expression found for x in the first equation.

$\begin{gathered} 2x+9y=27 \\ 2\cdot(-24+3y)+9y=27 \\ -48+6y+9y=27 \\ -48+15y=27 \end{gathered}$

Step 3: Isolate y in the equation found in step 2.

To do it, first, add 48 to both sides.

$\begin{gathered} -48+15y=27 \\ -48+15y+48=27+48 \\ 15y=75 \end{gathered}$

Then, divide both sides by 15.

$\begin{gathered} \frac{15y}{15}=\frac{75}{15} \\ y=5 \end{gathered}$

Step 4: Substitute y by 5 in the relation found in step 1 to find x.

$\begin{gathered} x=-24+3y \\ x=-24+3\cdot5 \\ x=-24+15 \\ x=-9 \end{gathered}$

Answer:

x = -9

y = 5

or (-9, 5)

Also, you can graph the lines by choosing two points from each equation, according to the picture below.

7 0

1 year ago

Verna shipped three packages to chicago. If the packages weighed 12 1/2, 35 1/4, and 41 7/20 pounds, what was the total weight?

stiv31 [10]

Answer:

Step-by-step explanation:

1st package weighs $12\dfrac{1}{2}$ pounds;

2nd package weighs $35\dfrac{1}{4}$ pounds;

3rd package weighs $41\dfrac{7}{20}$ pounds;

First, add whole numbers:

$12+35+41=88$

Now add fractions:

$\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{7}{20}=\dfrac{10}{20}+\dfrac{5}{20}+\dfrac{7}{20}=\dfrac{10+5+7}{20}=\dfrac{22}{20}=\dfrac{11}{10}=1\dfrac{1}{10}$

So, the total weight is

$88+1\dfrac{1}{10}=89\dfrac{1}{10}\ pounds$

3 0

4 years ago

8% of the employees at a shop work part time. If there are 4 part time employees at the shop, how many employees are there in to

Murljashka [212]

Answer:

50 employees

Step-by-step explanation:

We can set up a proportion which would be

4/x = 8/100

This shows 4 out of x people is the same as 8% of 100.

We divide 100 by 8, and then multiply by 4 to get 50.

We can check this by plugging 50 into the proportion.

4/50 = 0.08

8/100= 0.08

There are 50 total employees at the shop.

4 0

4 years ago

Ex Cash price of a TV is $1200-you agree to pay $200

nika2105 [10]

Answer:

$140 extra

Step-by-step explanation:

you answered it you self

5 0

3 years ago

Worth a 100 points.....

EleoNora [17]

It would be A. Since the both equations adding would be correct.

6 0

3 years ago

Read 2 more answers