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3 years ago

State the degree and end behavior of f(x) = 2x3 – 3x – x2 + 1. Explain or show your reasoning

Mathematics

2 answers:

Olin [163]3 years ago

6 0

Answer:

Answer:

As x→∞ , f(x)→-∞

x→-∞ , f(x)→∞

Step-by-step explanation:

End behavior is determined by the degree of the polynomial and the leading coefficient (LC).

The degree of this polynomial is the greatest exponent, or

The leading coefficient is the coefficient of the term with the greatest exponent, or

For polynomials of even degree, the "ends" of the polynomial graph point in the same direction as follows.

Even degree and positive LC:

As x→∞ , f(x)→∞ As x→∞, f(x)→∞

Even degree and negative LC:

As x→−∞ , f(x)→−∞

x→∞ , f(x)→−∞

torisob [31]3 years ago

5 0

Answer:

As x→∞ , f(x)→-∞

x→-∞ , f(x)→∞

DO NOT REPORT ME

Step-by-step explanation:

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Help plis 17. Find the sum of (10x + 3) and (- 4x - 2).

OLEGan [10]

Answer:

6x + 1

Step-by-step explanation:

1. (10x + 3) + (-4x -2) --> sum means to add.

2. Combine like terms --> 10x - 4x = 6x; 3 - 2 = 1.

3. 6x + 1

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3 years ago

Read 2 more answers

55% of what number is 70? Round to the nearest tenth.

umka2103 [35]

55% of x is 70
0.55 times x=70
divide both sides by 0.55
127.27272727
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3 years ago

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Neil drives at an average speed of 60 miles/hour to reach his destination 480 miles away. On the way back, he decides to increas

daser333 [38]

Answer:

480/(x+60) ≤ 7

Step-by-step explanation:

We can use the relations ...

time = distance/speed

distance = speed×time

speed = distance/time

to write the required inequality any of several ways.

Since the problem is posed in terms of time (7 hours) and an increase in speed (x), we can write the time inequality as ...

480/(60+x) ≤ 7

Multiplying this by the denominator gives us a distance inequality:

7(60+x) ≥ 480 . . . . . . at his desired speed, Neil will go no less than 480 miles in 7 hours

Or, we can write an inequality for the increase in speed directly:

480/7 -60 ≤ x . . . . . . x is at least the difference between the speed of 480 miles in 7 hours and the speed of 60 miles per hour

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Any of the above inequalities will give the desired value of x.

4 0

3 years ago

Y=1/2x-3 and 9x-2y=-74 substitution

Luba_88 [7]

x=2(y+3)x=92(y−37)

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3 years ago

Read 2 more answers

write an equation for the perpendicular bisector of the line joining the two points. PLEASE do 4,5 and 6

myrzilka [38]

Answer:

4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5. The equation of the perpendicular bisector is y = - 2x + 16

6. The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

Step-by-step explanation:

Lets revise some important rules

The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ (reciprocal m and change its sign)
The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

∵ The line passes through (8 , 5) and (4 , 3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

∵ $y_{1}$ = 5 and $y_{2}$ = 3

∴ $m=\frac{3-5}{4-8}=\frac{-2}{-4}=\frac{1}{2}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = -2

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{8+4}{2},\frac{5+3}{2})$

∴ The mid-point = $(\frac{12}{2},\frac{8}{2})$

∴ The mid-point = (6 , 4)

- Substitute the value of the slope in the form of the equation

∵ y = - 2x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = -2 × 6 + b

∴ 4 = -12 + b

- Add 12 to both sides

∴ 16 = b

∴ y = - 2x + 16

∴ The equation of the perpendicular bisector is y = - 2x + 16

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 6 and $x_{2}$ = 0

∵ $y_{1}$ = 1 and $y_{2}$ = -3

∴ $m=\frac{-3-1}{0-6}=\frac{-4}{-6}=\frac{2}{3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $-\frac{3}{2}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{6+0}{2},\frac{1+-3}{2})$

∴ The mid-point = $(\frac{6}{2},\frac{-2}{2})$

∴ The mid-point = (3 , -1)

- Substitute the value of the slope in the form of the equation

∵ y = $-\frac{3}{2}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ -1 = $-\frac{3}{2}$ × 3 + b

∴ -1 = $-\frac{9}{2}$ + b

- Add $\frac{9}{2}$ to both sides

∴ $\frac{7}{2}$ = b

∴ y = $-\frac{3}{2}$ x + $\frac{7}{2}$

∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

8 0

3 years ago