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3 years ago

11

Suppose the polynomial f(x) has the following end behavior: as x approaches infinity, f(x) approaches infinity, and as x approac

hes negative infinity, f(x) approaches negative infinity.
Which of the following polynomials could represent f(x)?
There may be more than one correct answer. Select all correct answers.
A. −x3
B. −2x^5−x^3−4x
C. x^3+10x^2−5x+5
D. x^2+x−3
E. 7x^5+4x^2
F. x+8

1 answer:

galina1969 [7]3 years ago

6 0

Answer:

C. x³+10x²−5x+5

E. 7x⁵+4x²

F. x+8

Step-by-step explanation:

The graph they described should look something like the one i drew below.

So all you have to do is look at the number with the highest exponent.

If the exponent is an odd number and the x is positive then that function will have an end behavior like the picture i posted.

x³ is good

-x³ is bad because of the negative sign

x² is bad because exponent is even

x⁷ is good

123x¹ is good

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Can someone please help me!!

Sloan [31]

Answer:

<h2>x = 6</h2>

Step-by-step explanation:

Use Angle Bisector theorem (look at the picture).

We have the equation:

$\dfrac{3}{x}=\dfrac{x-4}{4}$ <em>cross multiply</em>

$x(x-4)=(3)(4)$ <em>use the distributive property</em>

$x^2-4x=12$ <em>subtract 12 from both sides</em>

$x^2-4x-12=0\\\\x^2+2x-6x-12=0\\\\x(x+2)-6(x+2)=0\\\\(x+2)(x-6)=0\iff x+2=0\ \vee\ x-6=0$

$x+2=0$ <em>subtract 2 from both sides</em>

$x=-2$

$x-6=0$ <em>add 6 to both sides</em>

$x=6$

4 0

2 years ago

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river

inn [45]

Answer:

The length and width of plot is $L=300\:ft$ , $W=150\:ft$

Largest area of the plot is $A=45000 ft^{2}$

Step-by-step explanation:

Assume width as x and length as y. Given that length of fencing is 600 feet and fencing is enclosed on 3 sides. So perimeter is given as,

Perimeter = width + length + width

Substituting the value,

$600=x+y+x$

$600= 2x+y$ ….1

Now area of fence of rectangular box is given as follows,

$A=xy$ ….2

Solving equation 1 for y, subtracting 2x from both sides,

$600-2x= y$

Substituting the value in equation 2,

$A=x\left (600-2x \right )$

Simplifying

$A=600x-2x^{2}$

Rewriting,

$A=-2x^{2}+600x$

Above equation looks like quadratic equation $f\left ( x \right )=ax^{2}+bx+c$ whose graph looks like parabola.

Comparing equation f(x) and A values of a, b and c are, $a=-2,b=600$ and $c=0$ .

Now maximum of $f\left ( x \right )$ occurs at vertex.

The x coordinate of the vertex is given as $-\dfrac{b}{2a}$

Substituting the values,

$x=-\dfrac{600}{2\left (-2 \right )}$

Simplifying,

$x=\dfrac{600}{4}$

$x=150$

So width of plot is 150 feet.

Now to calculate value of length by using equation 1,

$600= 2x+y$

Substituting the values,

$600= 2\left (150 \right )+y$

$600= 300+y$

Subtracting 300 from both sides,

$300= y$

So length of plot is 300 ft.

The y coordinate of the vertex is given as $y=f\left ( -\dfrac{b}{2a} \right )$ which also means, $y=f\left ( 150 \right )$

$\therefore A=-2\left (150 \right )^{2}+600\left (150 \right )$

Simplifying,

$\therefore A=-2\left (22500 \right )^{2}+600\left (150 \right )$

$\therefore A=-45000+90000$

$\therefore A=45000$

So, area of the plot will be $A=45000 ft^{2}$

7 0

3 years ago

Solve & Discuss It!

agasfer [191]

Answer:

<u>There were 6, 9, 12 and 15 children if the number of adults at the beach were 8, 12, 16 and 20.</u>

Step-by-step explanation:

After reviewing the information given for solving the question, we notice that the ratio of adults in relation with the number of children at the beach is 4:3. In that case, for finding the number of children for every specific number of adults, we do the following calculations:

1. For 8 adults: 8/4 = 2 and using the ratio 4:3, we multiply by 2 and we get that the number of children is 6.

2. For 12 adults: 12/4 = 3 and using the ratio 4:3, we multiply by 3 and we get that the number of children is 9.

3. For 16 adults: 16/4 = 4 and using the ratio 4:3, we multiply by 4 and we get that the number of children is 12.

4. For 20 adults: 20/4 = 5 and using the ratio 4:3, we multiply by 5 and we get that the number of children is 15.

<u>There were 6, 9, 12 and 15 children if the number of adults at the beach were 8, 12, 16 and 20.</u>

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3 years ago

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natta225 [31]

Answer:

$a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}$

Step-by-step explanation:

The function is $a(m)=0.6735e^{0.423m}$

Changing functional notation of a(m) to y:

$y=0.6735e^{0.423m}$

Now, interchanging m and y:

$m=0.6735e^{0.423y}\\$

Now, solving for y:

$e^{0.423y}=\frac{m}{0.6735}\\ln[e^{0.423y}]=ln[\frac{m}{0.6735}]\\0.423y=ln(\frac{m}{0.6735})\\y=\frac{ln(\frac{m}{0.6735})}{0.423}$

Thus, the inverse function is:

$a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}$

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Neporo4naja [7]

Answer:

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