Wharton how many times have you taken the gmat

Write two different rational functions whose graphs have the same end behaviour as the graph of y=3x^2

baherus [9]

Answer:

$y=x^2+5x+20\\ \\ y=8x^2+35$

Explanation:

The <em>end behavior</em> of a <em>rational function</em> is the limit of the function as x approaches negative infinity and infinity.

Note that the the values of even functions are the same for ± x. That implies that their limits for ± ∞ are equal.

The limits of the quadratic function of general form $y=ax^2+bx+c$ as x approaches negative infinity or infinity, when $a$ is positive, are infinity.

That is because as the absolute value of x gets bigger y becomes bigger too.

In mathematical symbols, that is:

$\lim_{x \to -\infty}3x^2=\infty\\ \\ \lim_{x \to \infty}3x^2=\infty$

Hence, the graphs of any quadratic function with positive coefficient of the quadratic term will have the same end behavior as the graph of y = 3x².

Two examples are:

$y=x^2+5x+20\\ \\ y=8x^2+35$

5 0

3 years ago

The diagram shows a track composed with a semicircle on each end. The area of the rectangle is 8,400 square meters. What is the

MrRa [10]

Answer:

468.4 meters

Step-by-step explanation:

Find the width of the rectangle.

The area of a rectangle is A=length*width. Substitute the values of length and area and solve for width.

A=length*width

8,400=140*width

60= width

Use the width of the rectangle to find the circumference of the semicircles. Since each semicircle is half of a circle, the perimeter of the two semicircles is equal to the circumference of one circle.

The circumference of a circle is equal to pid, where d is the diameter. The diameter of the semicircle is the same as the width of the rectangle.

So, the diameter is 60 meters. Substitute the diameter into the formula for the circumference and simplify using 3.14 for pi.

≈188.4

(2 times 140)+ 188.4

So, the perimeter of the track is 468.4 meters.

7 0

2 years ago

Nate has $50 to spend at the grocery store. he fills his shopping cart with items totaling $46. At checkout he will have to pay

Akimi4 [234]

Answer:

yes he can

Step-by-step explanation:

he has to pay total is : 46+46x6%=48.76$

so he can pay that

8 0

3 years ago

Read 2 more answers

brooke found the equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form as follows

Goryan [66]

Answer:

The equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form is $\mathbf{y=-4x-3}$

Step-by-step explanation:

Equation of line passing through the points (-7,25) and (-4,13) in slope-intercept form.

The general equation of slope-intercept form is: $y=mx+b$

First we need to find slope

The formula used for finding slope is: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We are given: $x_1=-7, y_1=25, x_2=-4, y_2=13$

Putting values in formula and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{13-25}{-4-(-7)}\\Slope=\frac{13-25}{-4+7}\\Slope=\frac{-12}{3}\\Slope=-4$

So, slope m= -4

Now finding y-intercept

Using slope m=-4 and point (-7,25) we can find y-intercept

$y=mx+b\\25=-4(-7)+b\\25=28+b\\b=25-28\\b=-3$

So, y-intercept b =-3

Now, the equation of required line having slope m=-4 and y-intercept b=-3 is:

$y=mx+b\\y=-4x-3$

So, the equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form is $\mathbf{y=-4x-3}$

3 0

2 years ago

Verify that a+b=b+a by taking a=6 and b=3/6

Klio2033 [76]

Answer:

13

Step-by-step explanation:

substitute all the numbers in

6+3/6+3/6+6=13

4 0

3 years ago