the degree of the polynomial -5 + 3x^6 + 2x^5 + 6x^3 is

Answer:

[tex]f'(x)=1+\ln x[/tex]

Step-by-step explanation:

[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

Therefore, we have:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]

Simplify:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]

The derivative is:

[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]

[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]

[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]

Answer:

Ada is correct.

Step-by-step explanation:

Problems with Naman:

Naman is supposed to follow PEMDAS, which is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Division

Addition

Subtraction

~

The mistake: Naman moved +6 to the left and added it to the 2 located on the left side of the expression. You cannot do that, as it breaks the law of PEMDAS. On the other hand, Ada did the correct thing, which was to distribute 2 to all terms within the parenthesis (as one term in the parenthesis has a variable, and the other is a constant, meaning that they cannot be combined). This leads to Naman not doing the rest of the question correct.

Next, Ada correctly combined the two constants, which resulted in 0. 0 means nothing, therefore the placeholder is not needed. Therefore, 8x is the final answer.

Answer:

-7

Step-by-step explanation:

The line (y-1)=(2/3)(x+1) contains point (a,-3)

=> (-3-1) = (⅔)(a+1)

-4 = (⅔)(a+1(

(a+1)= -4 ÷ ⅔

a + 1 = -4 × 3/2

a+ 1 = -6

a = -6-1

a = -7

The value of 'a' will be;

⇒ a = - 7.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation of line is,

⇒ (y - 1) = (2/3) (x + 1)

And, The point on the line = (a, - 3)

Now,

Since, The point on the line = (a, - 3)

Hence, It satisfy the equation of line.

Substitute x = a and y = - 3, we get;

⇒ (y - 1) = (2/3) (x + 1)

⇒ (- 3 - 1) = (2/3) (a + 1)

⇒ - 4 × 3 = 2a + 2

⇒ - 12 - 2 = 2a

⇒ 2a = - 14

⇒ a = - 7

Thus, The value of a = - 7

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Answer:

[tex] \sqrt{24} = 4.9[/tex]

[tex] \sqrt{102} = 10.1[/tex]

positive integers = x

4.9 < x < 10.1

x = 5, 6, 7, 8, 9, 10

sum = 5 + 6 + 7 + 8 + 9 + 10

= 45

Answer:

12 miles in a day.

Step-by-step explanation:

Variable x = number of miles

Company A: 120 + 0.20x

Company B: 60 + 0.40x

Set up an equation:

120 + 0.20x = 60 + 0.40x

60 + 0.20x = 0.40x

60 = 0.20x

12 = x

Answer:

4.43

Step-by-step explanation:

4 3/7

~Turn into an improper fraction

31/7

~Divide

4.42885714286...

~Round

4.43

Best of Luck!

Answer:

C

Step-by-step explanation:

y and 67 are alternate exterior angles and are congruent , then

y = 67° → C

Answer:

A

Step-by-step explanation:

-2x-4>8

-2x>12

-x>6

x<-6

Answer:

[tex]x < - 6[/tex] (first option)

Step-by-step explanation:

[tex] - 2x - 4 > 8[/tex]

[tex] - 2x > 8 + 4[/tex]

[tex] - 2x > 12[/tex]

[tex] = x < - 6[/tex]

Answer:

Step-by-step explanation:

1) 7/10 × 2/21

1/15

2) 9/16 × 10/21

90/336

15/56

3) 11/12 × 26/55

13/30

4) 2/6 × 18/12 × 2/3

72/216

1/3

5) ⅚ × 9/10

45/60

3/4

Answer

7, 1

Step-by-step explanation:

do math

Answer:

your answer is F

I hope it's helps you

Answer:

47

Step-by-step explanation:

8(4) + 2(6) + 3 = 47

32 + 12 + 3 = 47

Answer: The correct answer is C

Step-by-step explanation:The graph is horizontally stretched by a factor of 1/5 because you are literally multiplying x by 1/5. So, your answer is C. Hope it makes sense. mark me brainlest

Answer:

x = -11

Step-by-step explanation:

To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.

-11 + 4 = -7

(-7)^2 = 49

Answer:

x = -11

Step-by-step explanation:

To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.

Answer:

1 1/4 =c

Step-by-step explanation:

4 1/6 = 3 1/3c

Change the mixed numbers to improper numbers

4 1/6 = ( 6*4+1)/6 =25/6

3 1/3 = ( 3*3+1)/3 = 10/3

25/6 = 10/3c

Multiply each side by 3/10

25/6 * 3/10 = 10/3c * 3/10

3/6 * 25/10 = c

1/2 * 5/2 =c

5/4 =c

Change back to a mixed number

1 1/4 =c

Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:

The pattern

The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)

The expressions for the number of tiles

The design number and the number of tiles is represented as follows

[tex]1 \to 7[/tex]

[tex]2 \to 12[/tex]

[tex]3 \to 19[/tex]

From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.

Design 1 has 1 tile at the center and 6 tiles at either sides.

So, we have:

[tex]1 \to 1 + 6[/tex]

[tex]2 \to 4 + 8[/tex]

[tex]3 \to 9 + 10[/tex]

Expand

[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]

[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]

[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]

Notice the pattern,

The number of tiles in design n will be:

[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]

Open bracket

[tex]Tiles = n^2 + 2n + 4[/tex]

Hence, the expressions for number of tiles in design n are:

[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]

Technology to prove that both expressions are equivalent

To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared

The table and graph for the first 6 designs

The table entry for the first 6 designs is calculated as follows:

[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]        

[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]        

[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]        

[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]        

[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]        

[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]        

So, we have:

[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]

See attachment for the graph of the above table

All the points on the curve make sense in this scenario because all values are positive.

The pattern type

We have:

[tex]Tiles = n^2 + 2n + 4[/tex]

When an equation has a degree of 2, the equation is quadratic.

Hence, the pattern is quadratic.

The largest design that an empty sign of 10ft by 12ft can contain.

From the first three designs:

The number of tiles on a complete row and column are always the same.

Design 1 has 3 tiles in its complete row and column

Design 2 has 4 tiles in its complete row and column

Design 3 has 5 tiles in its complete row and column

The relationship between the design number (d) and the number of complete tiles (t) is:

[tex]d = t - 2[/tex]

For the 10ft by 12ft empty sign

[tex]t = 10[/tex] because [tex]10 < 12[/tex]

So, we have:

[tex]d = t - 2[/tex]

[tex]d = 10 - 2[/tex]

[tex]d = 8[/tex]

Hence, the largest design number is design 8

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Answer:

Step-by-step explanation:

Step-by-step explanation:

if I understand the typed information here, we have

(-4 + 8x) + 3 > -4

so, I am looking at that :

-4 + 8x + 3 > -4

let's first add 4 on both sides

8x + 3 > 0

then subtract -3 on both sides

8x > -3

and finally divide both sides by 8

x > -3/8

since we never multiplied or divided by a negative number, the inequality sign stays the same.

so, this inequality is true for all x > -3/8

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Ok, so we know 42 is the number of points added up, and we know that she threw 6 darts all scoring the same. Now, all we have to do is figure out what number(for example x) multiplied by 6 equals 42. Or in the form of an equation:

6x = 42

Now, to finish the equation, all we have to do is divide:

6x/6 = 42/6

42/6 = 7

x = 7

Your answer is in the attachment .

Note: I have only done upto q.n d because you haven't clearly uploaded question of no. e. stay blessed !!!!!!

Answer:

Step-by-step explanation:

The probabilities for each point:

Required probability:

Correct choice is D

Answer:

Reflection is shown in the graph.

Answer:

Hope it helped

Step-by-step explanation:

The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

An inverse function or an anti function is defined as a function, which can reverse into another function.

Now the given quadtratic function is,

f(x) = x² + 2

Now vertex of the given quadratic function is (0,2)

Thus the range of the function is [2,∞)

If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.

Now the inverse function is given as,

y = x² + 2

Upon interchanging x and y, we get:

x = y² + 2

⇒ y² = x - 2

or, y = ±[tex]\sqrt{x-2}[/tex]

Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function  would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be  f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .

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Answer:

B

Step-by-step explanation:

t=4x+c

Since we are looking for x,

t-c=4x

Divide through by the coefficient of x which is 4

4x/4=t-c/4

Therefore, x=t-c/4

A general linear equation is given by:

[tex]y = a*x + b[/tex]

Where a is the slope and b is the y-intercept.

Here we will find that the linear equation that represents the situation is

[tex]y = 0.033*x + 1.269[/tex]

And we can expect that the median salary in 2048 is $2.853 million

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we know that:

in 2007 (x = 7) the median player salary was y = $1.5 million

in 2013 (x = 13) the median player salary was y = $1.7 million.

Then we have two points that we can write as:

(7, 1.5)

(13, 1.7)

Note that the y-value is in millions.

Then the slope of the linear equation will be:

[tex]a = \frac{1.7 - 1.5}{13 - 7} = 0.033[/tex]

So the linear equation is something like:

[tex]y = 0.033*x + b[/tex]

To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:

[tex]1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269[/tex]

Then the linear equation is:

[tex]y = 0.033*x + 1.269[/tex]

b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48

So we just need to evaluate this in the linear equation:

[tex]y = 0.033*48 + 1.269 = 2.853[/tex]

Then the median salary in 2048 will be $2.853 million

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{350 rounded to the nearest hundred is...}[/tex]

[tex]\huge\text{Rounding is basically is the}\\\huge\text{approximation of the given number.}[/tex]

[tex]\huge\bullet\huge\text{ So, when you are looking at 350, you are}\\\huge\text{asking yourself is it closer to 300 or 400.}\\\huge\text{If you are looking at the number correctly}\\\huge\text{you would see it is closer to \underline{\underline{400}} when you}\\\huge\text{rounded to NEAREST HUNDRED.}[/tex]

[tex]\huge\boxed{\textsf{Therefore, your ANSWER/RESULT is: \bf 400}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

You would shade the fourth quadrant (bottom right).

Step-by-step explanation:

Due to the domain and range sets, you're given the facts that x must be greater than or equal to 0, but y is less than or equal to zero. This gives you what quadrant the graph should be in. Since you're not given an equation to follow like y=ax+b, then I can not say that this will give you a line.

Answer:

thequantity in column b is greater

Step-by-step explanation:

7a+b=33......(1)

3a-b=7.........(2)

(1)+(2)

7a+b+3a-b=33+7

10a+b-b=40

10a=40

a=4

in equation (1)

7*4+b=33

28+b=33

b=33-28

b=5

b>a