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3 years ago

Using remainder theorem find the remainder when p(x) = 3x^3 - 4x^2 - 5x +11 divided by ( x + 1)

Mathematics

2 answers:

Natali5045456 [20]3 years ago

6 0

The answer would be 9

DedPeter [7]3 years ago

3 0

Answer:

Step-by-step explanation:

The remainder is given by the value of f(-1):

Remainder = 3(-1)^3 - 4(-1)^2 - 5(-1) + 11

= -3 - 4 + 5 + 11

= -7 + 16

= 9.

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which statements are true about the graph of the function f(x) = 6x – 4 x2? check all that apply. the vertex form of the functio

Brut [27]

Answer:

The vertex of the function is the point $(-3,-13)$

The graph increase over the interval--------> (-3,∞)

Step-by-step explanation:

we have

$f(x)=6x-4+x^{2}$

1) Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+4=x^{2}+6x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+4+9=x^{2}+6x+9$

$f(x)+13=x^{2}+6x+9$

Rewrite as perfect squares

$f(x)+13=(x+3)^{2}$

$f(x)=(x+3)^{2}-13$ -----> function in vertex form

2) Find the vertex

The vertex of the function is the point $(-3,-13)$

3) Find the axis of symmetry

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

The x-coordinate of the vertex in this problem is equal to $x=-3$

therefore

the equation of the axis of symmetry is $x=-3$

4) Find the increase-decrease intervals

The graph increase over the interval--------> (-3,∞)

The graph decrease over the interval--------> (-∞,-3)

see the attached figure to better understand the problem

5) Find the x-intercepts of the function

we know that

the x-intercepts are the values of x when the value of the function is equal to zero

In this problem the x-intercepts are

$(-6.61,0)$ and $(0.61,0)$

The function cross the x-axis twice

see the attached figure

5 0

3 years ago

Read 2 more answers

What names apply to 50

sammy [17]

Do u mean like other names for it

5 0

2 years ago

What type of association does there appear to be between the variables? explain

Nataliya [291]

Where are the variables for the equation?

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3 years ago

In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for

Veronika [31]

The general formula for the margin of error would be:

z * √[p (1-p) ÷ n]

where:
z = values for selected confidence level
p = sample proportion
n = sample size

Since the confidence level is not given, we can only solve for the
√[p (1-p) ÷ n] part.

p = 44/70
n = 70

√[44/70 (1 - (44/70) ÷ 70]

√[0.6286 (0.3714)] ÷ 70

√0.2335 ÷ 70

√0.0033357 = 0.05775 or 0.058 Choice B.

7 0

3 years ago

In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many rig

horrorfan [7]

Answer:

(b) 24

Step-by-step explanation:

The given variable definitions and the given relationships let us write these statements:

LH males = 4 × LH females = 4x

RH females = 3 × RH males = 3y

LH males + RH males = 204 = 4x +y

RH females + LH females = 348 = 3y +x

Your favorite method of solving equations of this sort can tell you ...

(x, y) = (24, 108)

There are 24 left-handed females.

Additional comment

Other numbers involved here are ...

y = 108 . . . . right-handed males

204-108 = 96 . . . . left-handed males (=4×24)

348-24 = 324 . . . . right-handed females (=3×108)

If you want to solve the equations by hand, you can use substitution for y to get an equation in x:

3(204 -4x) +x = 348 ⇒ -11x = -264 ⇒ x = 24

3 0

1 year ago