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LenKa [72]
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

Mathematics
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 &amp; 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>

7 0
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}

5 0
3 years ago
if there are 13 cookies birthday party is there any way to divide them equally amongst a group of friends so that each has a who
Neporo4naja [7]

Answer:

yes but it depends on how many friends are in the friend group

8 0
2 years ago
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