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melisa1 [442]
3 years ago
9

. Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and pro

vide the leading term.
-3x5 + 9x4 + 5x3 + 3
Mathematics
1 answer:
QveST [7]3 years ago
3 0
Because this is a fifth degree polynomial, it's an odd function.  Odd functions have one tail go up and the other down.  Because the leading coefficient is a negative number, 3 to be exact, the left one goes up and the right goes down.
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Six less than five times a number is at least 29.
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3 years ago
Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 m
weqwewe [10]

Given Information:

Distance = 160 miles

Required Information:

Rate = r = ?

Answer:

Rate = r = 20 mph

Step-by-step explanation:

Recall that the rate is given by

Rate = distance/time

r = \frac{d}{t} \\\\t = \frac{d}{r} \\\\t = \frac{160}{r} \\\\

It is given that the same trip would have taken 2 hours longer if he had decreased his speed by 4 mph.

Mathematically,

\frac{160}{(r-4)} = \frac{160}{r} + 2 \\\\

Simplify the equation

\frac{160}{(r-4)} - \frac{160}{r} = 2 \\\\\frac{160r - 160(r-4)}{r(r-4)} = 2 \\\\\frac{160r - 160r+640)}{r(r-4)} = 2 \\\\160r - 160r+640 = r(r-4) (2) \\\\640 = r(r-4) (2) \\\\640 = (r^2 - 4r) (2) \\\\640 = 2r^2 - 8r \\\\2r^2 - 8r-640 =0 \\\\2(r^2 - 4r-320) =0 \\\\r^2 - 4r-320 =0 \\\\

Now we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method  

r^2 - 4r-320 =0 \\\\r^2-20r+16r-320=0 \\\\r(r-20)+16(r-20)=0 \\\\(r-20) (r+16)=0 \\\\

So,

(r-20) = 0 \\\\r = 20 \\\\

OR

(r+16)=0 \\\\r = -16 \\\\

Since rate cannot be negative, discard the negative value of r

Therefore, the rate is

r = 20 \: mph

3 0
4 years ago
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Angelina_Jolie [31]

Answer:

Group A, because seven children have a forearm length longer than 10 inches

Step-by-step explanation:

Create the dot plots based on the given information (please see attached images).

Group A = blue dots

Group B = red dots

From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length.  This is because 7 children have a forearm length of longer than 10 inches.

To calculate the average forearm length, sum all data values and divide by the total number of data values.

\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11

\textsf{Average of Group B}=\dfrac{ 3 \times 9 + 5\times 10+ 2\times 11}{10}=9.9

Thus proving that Group A has the longer average former length.

7 0
2 years ago
Read 2 more answers
The table below represents the velocity of a car as a function of time:
Naddik [55]
A)The y-intercept is 50 because when X=0, y=50. This shows that the car was moving at 50 mph as an initial speed.

B) in two hours (from 1 to 3) the speed increased by 4 miles per 2hours. (from 52 to 56). 4/2 = 2 mph, which is the average rate of change. This represents the amount of speed increased each hour.

C) y=2x+50, and y=60 in this case, so 60=2x+50
60=2x+50
-50 -50
-----------------
10=2x
5=x, so the domain is X<=5 (less than or equal to 5)
7 0
4 years ago
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The following is the graph of f(x) = tan (x)<br> True or False
SIZIF [17.4K]
That is false.  This is the graph of -tan (x).
4 0
3 years ago
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