If the expression (2+ 3+ 2i) is a factor of a polynomial, which expression below
must also be a factor?

A: -(x+3+2i)
B: (x-3-2i)
C:(x-3+2i)
D:(x+3-2i)

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate [tex]x^4[/tex].

We have

[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h[/tex]

Expand the numerator using the binomial theorem, then simplify and compute the limit.

[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}[/tex]

In general, the derivative of a power function [tex]f(x) = x^n[/tex] is [tex]\frac{df}{dx} = nx^{n-1}[/tex]. (This is the aptly-named "power rule" for differentiation.)

The value of x when (f o g)(x) = -8 is 3

The composite function is given as:

(f o g)(x) = -8

The above is calculated as:

(f o g)(x) = f(g(x))

So, we have:

f(g(x)) = -8

From the table, we have:

f(-4) = -8

This means that:

g(x) = -4

From the ordered pair, we have:

g(x) = -4 when x = 3

Hence, the value of x is 3

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The value of x when (f o g)(x) = -8 is 3

How to solve for x?

The composite function is given as:

(f o g)(x) = -8

The above is calculated as:

(f o g)(x) = f(g(x))

So, we have:

f(g(x)) = -8

From the table, we have:

f(-4) = -8

This means that:

g(x) = -4

From the ordered pair, we have:

g(x) = -4 when x = 3

Hence, the value of x is 3

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Explanation:

First factor out the GCF 2x

2x^4+2x^3-4x^2-4x

2x*x^3+2x*x^2-2x*2x-2x*2

2x(x^3 + x^2 - 2x - 2)

Then let's factor the expression inside the parenthesis using the factor by grouping method

x^3 + x^2 - 2x - 2

(x^3 + x^2) + (- 2x - 2)

x^2(x + 1) - 2(x + 1)

(x^2 - 2)(x+1)

We see that x^3 + x^2 - 2x - 2 factors to (x^2-2)(x+1)

Overall, the original expression fully factors to 2x(x^2-2)(x+1)

length = 2x

width = x^2-2

height = x+1

The order of length, width, and height doesn't matter.

The  volume as the product its dimensions 2x*( x²-2)*(x+1).

Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given:

volume of a rectangular prism is given by the expression 2x^4+2x³-4x²-4x

=2x*x^3+2x*x^2-2x*2x-2x*2

=2x(x³ + x² - 2x - 2)

Now, we get the factor 2x(x³ + x² - 2x - 2).

Keeping aside 2x we will now focus on (x³ + x² - 2x - 2)

We already get the one factor 2x and now using (x³ + x² - 2x - 2) to get the other two factors.

Now solving x³ + x² - 2x - 2

=(x³ +  x²) + (- 2x - 2)

= x²(x + 1) - 2(x + 1)

=( x² - 2)(x+1)

Now we get the two factors  ( x² - 2)(x+1).

The expression  for  volume as the product its dimensions is 2x*( x²-2)*(x+1)

Hence,   volume as the product its dimensions is 2x*( x²-2)*(x+1).

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If [tex]A[/tex] is the set of positive divisors of [tex]m[/tex] and [tex]B[/tex] the set of positive divisors of [tex]n[/tex], then [tex]A\cup B[/tex] is the set of positive divisors of [tex]mn[/tex].

Use the inclusion/exclusion principle:

[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]

where [tex]|\cdot|[/tex] denotes set cardinality (the number of elements the set contains). The set [tex]A\cap B[/tex] is the set of common divisors of [tex]m[/tex] and [tex]n[/tex]. Then

[tex]14 = 5 + 6 - |A\cap B| \implies |A\cap B| = 3[/tex]

so that [tex]m[/tex] and [tex]n[/tex] share 3 divisors [tex]d_1,d_2,d_3[/tex]; let [tex]k=d_1d_2d_3[/tex] be their product. They must be prime

This means we can write

[tex]m = p_1 p_2 k[/tex]

[tex]n = p_3 p_4 p_5 k[/tex]

[tex]\implies mn = p_1 p_2 p_3 p_4 p_5 k^2 = p_1 p_2 p_3 p_4 p_5 {d_1}^2 {d_2}^2 {d_3}^2[/tex]

so that [tex]mn[/tex] has up to 8 distinct prime factors.

The probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches is 39.54%.

Given mean diameter of 207, variance=9, sample size of 72.

We have to calculate the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches.

The sample mean may be greater than or less than from population mean than 0.3 inches.

Either greater than 207+0.3=207.3 inches,

Smaller =207-0.3=206.7

Since the normal distribution is symmetric these probabilities are equal. So we find one of them and multiply by 2.

Probability of being less than 206.7

P value of z when X=206.7. So

Z=(X-μ)/s

=(206.7-207)/0.35

=-0.3/0.35

=-0.857

p value =0.1977

Probability of differing from population mean greater than 0.3 inches=2*0.1977

=0.3954

=39.54%

Hence the probability that the mean diameter of the sample shafts would differ from the population mean  by greater than 0.3 inches is 39.54%.

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Answer: 24 - 100, 12 - 5 - 22, -4, 37

Step-by-step explanation:

Simplificar:

-4 = -4

12 - 5 - 22 = -15

24 - 100 = -76

37 = 37

Ordenar de menor a mayor:

-76, -15, -4, 37

       \/

24 - 100, 12 - 5 - 22, -4, 37

Answer:  [tex]\boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}[/tex]  (choice D)

You have the correct answer.

=====================================================

Work Shown:

[tex]\frac{2}{\text{x}} + \frac{3}{\text{x}-1}\\\\\frac{2(\text{x}-1)}{\text{x}(\text{x}-1)} + \frac{3\text{x}}{\text{x}(\text{x}-1)}\\\\\frac{2\text{x}-2}{\text{x}^2-\text{x}} + \frac{3\text{x}}{\text{x}^2-\text{x}}\\\\\frac{2\text{x}-2+3\text{x}}{\text{x}^2-\text{x}}\\\\ \boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}\\\\[/tex]

--------

Explanation:

The idea I used is that we cannot add the fractions unless the denominators are the same. The denominators x and (x-1) lead to the lowest common denominator, aka LCD, of [tex]\text{x}(\text{x}-1) = \text{x}^2 - \text{x}[/tex]. We multiply the denominators together to get the LCD.

The first original fraction [tex]\frac{2}{\text{x}}[/tex] is missing (x-1) in the denominator. This is why I multiplied top and bottom by (x-1) in the 2nd step. Similarly, the fraction [tex]\frac{3}{\text{x}-1}[/tex] is missing an x out front to get to x(x-1). This is why I multiplied top and bottom of that fraction by x.

After we get the denominators to be the same, we can then add the numerators like any other algebraic expression. The denominator stays the same the entire time.

It's similar to how [tex]\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7} = \frac{5}{7}[/tex] has the numerators add like you'd expect while the denominator stays at 7 the entire time.

You can think of it like this: "2 sevenths + 3 sevenths = 5 sevenths" or "2s+3s = 5s" for short. The term "sevenths" is effectively a unit such as cm or meters. We must have common units if we want to add them.

Answer:

$54.30

Step-by-step explanation:

Given Total Donations already raised

= $30.20 + $10.50 + $5.00

= $45.70

Donations still required = Total Donations needed - Donations already raised

= $100 - $45.70 = $54.30

The length of the blue ribbon given the length of red ribbon is 8 inches

length of blue ribbon = 2/3 of red ribbon

= 2/3 × 12

= (2×12)/3

= 24/3

= 8 inches

Let

3x = 15

x = 15/3

x = 5 books

Therefore, the number of books Mai has is 5 books

Complete question:

The length of the blue ribbon is two-thirds the length of the red ribbon. How long is the blue ribbon if the red ribbon is 12 inches?

Tyler has 3 times as many books as Mai. How many books does Mai have if Tyler has 15 books?

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Answer:

No solutions.

Step-by-step explanation:

Problem:

Solve y−4x=−3;y=4x+7

Steps:

I will solve your system by substitution.

y=4x+7;−4x+y=−3

Step: Solve y=4x+7 for y:

Step: Substitute 4x+7 for y in −4x+y=−3:

−4x+y=−3

−4x+4x+7=−3

7=−3(Simplify both sides of the equation)

7+−7=−3+−7(Add -7 to both sides)

0=−10

Answer:

No solutions.

Answer:

  No solutions

Step-by-step explanation:

It is easiest to determine whether the equations are consistent by putting both of them in the same form.

The equation on the left is in "standard form." The one on the right is in "slope-intercept form." We can rewrite either one of them to put it into the other form.

Rewriting the left equation to slope-intercept form, we have ...

  y = 4x -3 . . . . . . . add 4x to both sides

Comparing this to the right equation ...

  y = 4x +7

we see that the slopes are the same, and the intercepts are different. These equations describe parallel lines. Parallel lines can never meet, so cannot have any point in common. The equations are inconsistent and have no solution.

Rewriting the right equation to standard form, we have ...

  y -4x = 7 . . . . . . . subtract 4x from both sides

Comparing this to the left equation ...

  y -4x = -3

we see that the coefficients are the same, but the constants are different. There can be no values of x and y that will satisfy both equations. Any values that make the terms have one sum cannot also make them have a different sum.

There are no solutions.

By definition, when a test or technique measures what it intends to, it is valid.

The answer is option A.

The criterion-related validity of a take-a-look is measured by the validity coefficient. Its miles said as a number between zero and 1.00 that indicates the significance of the relationship, "r," among the take a look at and a measure of task overall performance (criterion).

Reliability and validity are both approximately how nicely a technique measures something: Reliability refers to the consistency of a measure (whether or not the consequences can be reproduced below identical situations).

Validity refers back to the accuracy of a measure (whether or not the results really do constitute what they may be speculated to a degree).

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Answer:

x = 9

Step-by-step explanation:

[tex]\sf \dfrac{(x +7)(x+8)}{(x -9(x + 6)} \ \div \ \dfrac{(x+8)(x - 2)}{(x+ 6)(x - 2)} =\dfrac{(x +7)(x+8)}{(x -9)*(x +6)}*\dfrac{(x + 6)(x - 2)}{(x +8 )(x - 2)}[/tex]

                                                   [tex]\sf =\dfrac{x +7}{x - 9}[/tex]

x - 9 = 0

   x = 9

If we plugin x = 9, then the denominator would become 0 and hence the expression will become undefined.

So, x = 9 is the restricted value of the expression.

Answer:

Option 1

Step-by-step explanation:

The equations in the options are in the slope-intercept form (y= mx +c, where m is the slope and c is the y-intercept).

In the graph, the line cuts through the y-axis at y= -2. Thus, c= -2 and the 2nd option can be eliminated.

The slope can be found using the formula below.

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Let's choose 2 points on the line: (0, -2) and (-2, 4)

Slope

[tex]=\frac{4-(-2)}{-2-0}[/tex]

[tex]=\frac{4+2}{-2}[/tex]

[tex]=\frac{6}{-2}[/tex]

= -3

The equation of the line is thus y= -3x -2.

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Answer:

The answer is C

Step-by-step explanation:

it is C because parallel lines don't intercept the go up or across but they don't touch, just imagine it isn't graphed.

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a translation followed by a rotation.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a translation followed by a rotation.

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Answer:

x = 10

Step-by-step explanation:

BF   is two times AX   so

2 ( 2x+10) = 5x+10

4x + 20 = 5x + 10

x = 10

The unit vectors are u = {1, 1}. Option C

Unit vectors can be defined as vector with magnitude of 1.

It is important to note that a unit vector is a vector quantity. Vector quantities are known to have magnitude and direction.

They are represented with the sign 'u'

Thus, the unit vectors are u = {1, 1}. Option C

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Hello,

Answer:

S = { -0,42 ; 2,71 }

Step-by-step explanation:

7x² - 16x = 8 ⇔ 7x² - 16x - 8 = 0

a = 7 ; b = -16 ; c = -8

Δ = b² - 4ac = (-16)² - 4 × 7 × (-8) = 480 > 0

x₁ = (-b - √Δ)/2a = (16 - √480)/14 ≈ -0,42

x₂ =  (-b + √Δ)/2a = (16 + √480)/14 ≈ 2,71

Answer:

The two answers:

2.707778736

0.42206445

Step-by-step explanation:

Here is the equation:

[tex] {7x}^{2} - 16x = 8[/tex]

Take away the 8 from the right hand side, so that we are left with this quadratic equation:

[tex] {7x}^{2} - 16x - 8 = 0[/tex]

This equation is too complex to solve with the factorizing method, so let's use the quadratic formula, which is as follows:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

In this equation, a = 7, b = -16, and c = -8. So let's substitute in:

[tex]x = \frac{-( - 16) \pm \sqrt{ { - 16}^{2} - 4 \times 7 \times - 8}}{2 \times 7}[/tex]

[tex]x = \frac{ - ( - 16) \pm \sqrt{256 + 224} }{14}[/tex]

[tex]x = \frac{ 16 \pm \sqrt{480}}{14}[/tex]

And let's work out the two possible answers:.

2.707778736

0.42206445

Answer:

4√3.

Step-by-step explanation:

If the height is h then

tan 60 = h / (1/2*8)

tan 60 = h/4

h = 4 tan 60

   = 4 * √3.

Step-by-step explanation:

here a= 7 ,d=4

then S31= 31/2(7+7+30*4)= 31/2(14+120)= 31/2(134)= 31*67= 2077

hope it helps

The sum of the first 31 terms is 2077.

An arithmetic sequence is one in which each phrase grows by adding or subtracting some constant k. In contrast, in a geometric sequence, each term grows by dividing/multiplying some constant k.

We have,

Sequence:  {7, 11, 15, 19, 23 ...}

First term = 7

Common difference, d= 11- 7 = 4

Now, the sum of first 31 st term of sequence

= 31/2 [ 2(7) + (31-1)4]

= 31/2 [ 14 + 120]

= 31/2 x 134

= 31 x 67

= 2077

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Answer:

6 pounds

Step-by-step explanation:

Let the can weigh x pounds

Let the milk weigh y when full, therefore half is [tex]\frac{y}{2}[/tex]

Now we for 2 simultaneous equations:

[tex]x + y =70[/tex] ....(i)

[tex]x+ \frac{y}{2}= 38[/tex] .... (ii)

we solve by eliminating the x in both equation throug subtraction

[tex]x - x + y- \frac{y}{2} =70-38\\y- \frac{y}{2} = 32\\\frac{y}{2} = 32\\y=2(32)\\y=64\\x+y=70\\x+64=70\\x=6[/tex]

Step-by-step explanation:

[tex] = \frac{ \frac{3}{x - 2} - 5 }{2 - \frac{4}{x - 2} } [/tex]

[tex] = \frac{ \frac{3 - 5.(x - 2)}{x - 2} }{ \frac{2.(x - 2) - 4}{x - 2} } [/tex]

[tex] = \frac{ \frac{3 - 5.(x - 2)}{ \cancel{x - 2}} }{ \frac{2.(x - 2) - 4}{ \cancel{x - 2} }} [/tex]

[tex] = \frac{3 - 5.(x - 2)}{2.(x - 2) - 4} [/tex]

[tex] = \frac{3 - 5x + 10}{2x - 4 - 4} [/tex]

[tex] = \frac{ - 5x + 13}{2x - 8} [/tex]

[tex] = \frac{13 - 5x}{2x - 8} [/tex]

The answer is D.

The equivalent value of the expression is A = ( 13 - 5x ) / ( 2x - 8 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the equation be represented as A

Now , the value of A is

[tex]A = \frac{\frac{3}{x-2}-5}{2\:-\:\frac{4}{x-2}}[/tex]

On simplifying , we get

[tex]A = =\frac{\frac{-5x+13}{x-2}}{2-\frac{4}{x-2}}[/tex]

On further simplification , we get

[tex]A = =\frac{\frac{-5x+13}{x-2}}{\frac{2x-8}{x-2}}[/tex]

Therefore , the value of A is A = ( 13 - 5x ) / ( 2x - 8 )

Hence , the equation is A = ( 13 - 5x ) / ( 2x - 8 )

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Answer:

96 students

Step-by-step explanation:

I am not exactly sure if this question is talking about a 1:5 ratio, but that's what I am assuming. To get 96, you need to replace the 5 with 480 because the problem seems to mean 1 to every 5 people wear glasses. Next, you do 480/5 to get the number on the left side of the ratio. You get 96 when you do that. I am a little confused with the question because it isn't exactly formatted correctly, but this is what I am guessing. Hope this helps!

Answer:

A

Step-by-step explanation:

calculate the ratios AB/DE BC/EF AND AC/DF。their ratios are 1/2

Answer:

Step-by-step explanation:

the first because the ratio is always from a small to a large triangle, and it is right, the second is wrong, the sides are not congruent, the third is also wrong, the last ratio is wrong

Answer:

AB = 4

BC = 4

AC = 8

Step-by-step explanation:

Given, B is the midpoint of AC which means it divided the AC into two equal parts. Using this information we can write the following equation:

5x - 6 = 2x add 6 to both sides

5x = 2x + 6 subtract 2x from both sides

3x = 6 divide both sides by 3

x = 2 to find the length of AB, AC, and BC replace x with 2

AB = 5*2 - 6

BC = 2*2

AC = 8 (sum of AB and BC)

[tex]\huge \boxed{\sf x=2}\\\\\huge \boxed{\sf AB=4}\\\\\huge \boxed{\sf BC=4}\\\\\huge \boxed{\sf AC=8}[/tex]

[tex]\displaystyle \sf AB=BC\\\\5x-6=2x\\\\Subtracting\ 2x\ and\ adding\ 6\ to\ each\ side \\\\5x-6+6-2x=2x-2x+6\\\\5x-2x=6\\\\3x=6\\\\Divide\ each\ side\ by\ 3\\\\\frac{3x}{3} =\frac{6}{3} \\\\x=2[/tex]

[tex]\sf Substituting\ x=2\\\\AB=5(2)-6=10-6=4 \\\\BC=2(2)=4\\\\AC=AB+BC=4+4=8[/tex]

Answer:

It will triple in approximately 48 years.

Step-by-step explanation:

t=30*ln3/ln2=30*1.5849= 48 years (approx.)

Using it's concept, it is found that the graph has no horizontal asymptote.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, we have that:

Thus, the graph has no horizontal asymptote.

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Probability helps us to know the chances of an event occurring. There are 8 different scenarios possible.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

For the given word SANDWICH, there are 8 different scenarios possible, which can be represented as shown below.

Hence, there are 8 different scenarios possible.

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