Are the following proportional? Explain or show
your reasoning
3/5 and 18/25

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:

3.2×10^-7 hope this will be of help

[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:

The answer is 8.8

Step-by-step explanation:

4/5 x 20/20 = 80/100

80/100 = .8

Step-by-step explanation:

[tex]8 + \frac{4}{5} = \frac{40 + 4}{5} \\ = \frac{44}{5} = 8.8 \\ thank \: you[/tex]

Answer:

Step-by-step explanation:

4+x-3*z(7+3+6)

4+x-3*z*16

4+x-3*16z

4+x-48z

x-48z+4

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:

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:

Step-by-step explanation:

[tex] \frac{ - 216}{144} \\ \\ = \frac{ - 3}{2} [/tex]

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

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:

11. [tex]x^{5}[/tex]

12. 5*[tex]x^{2}[/tex]

13. x+21

14. 2x-8

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

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

32 + 12 + 3 = 47

Answer:

He paid $9 twelve times

12× 2= 24 days

Step-by-step explanation:

1st day = $16.60

3rd day=$ 9 (i.e for every 2days afterwards)

5th day=$ 9

Yuri pays : 124.60

124.60-16.60

= $108.00

After paying the first day he paid 108.00

108.00÷ 9 = 12

He paid $9 twelve times

12× 2= 24 days

Answer:

4*3+X

IGNORE THIS JWINFWONDIWJFIENFIWKQPXK

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

Read more about patterns at:

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Answer:

Option 1 is the correct equation.

Step-by-step explanation:

x = price of the student ticket.

One half price of x + $8 = adult ticket price ($15)

Answer:

The correct answer is A

Because taking the student ticket to be x

one half of x + 8 =15

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: Square root of negative 7 is greater than -3.12345

Step-by-step explanation: Since the square root of -7= 2.64575131 i (A positive number) Then it's greater, since the positive number is always greater than the negative numbers, because the negative numbers are further below zero than the positive number, if there is a number below the zero and a number above the zero, the one above the zero is greater,  because it's a positive number, the one below 0 is negative.

Answer:

Step-by-step explanation:

Answer:

5 * sqrt(3)

Step-by-step explanation:

The sine of 60 degrees is equal to x/10 because x is opposite to it and 10 is the hypotenuse. Since the sine of 60 degrees is equal to sqrt(3)/2, sqrt(3)/2 = x/10. Because 5sqrt(3)/10 = sqrt(3)/2, 5sqrt(3)/10 = x/10 and therefore 5sqrt(3) = x.

Answer:

5.82

Step-by-step explanation:

0.582 x 10

=> Shift the decimal place by 1

=> 5.82

The required simplified value of the product is 5.82 and the value of 2 in the expression is 0.01 times.

To determine the value of 2 in the product of 0.582 times 10.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
Product = 10 * 0.582
Product = 5.82,
Where 2 is located at the thousandth place,
So, the value of 2 in 5.82 is 0.01 times of 2.

Thus, the required simplified value of the product is 5.82 and the value of 2 in the expression is 0.01 times.

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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

Step-by-step explanation:

3x²+1+8=27

3x²+9=2

3x²=27-9

3x²=19

x²=19/3

[tex]x = \frac{ \sqrt[]{19} }{ \sqrt{3} } [/tex]

Answer:

[tex]3^{2x} + 1 + 18 = 27\\ 3^{2x} = 18\\2x = log_{3} 18[/tex]

Step-by-step explanation:

[tex]\\ \sf\longmapsto -7\dfrac{8}{45}[/tex]

[tex]\\ \sf\longmapsto \dfrac{45(-7)+8}{45}[/tex]

[tex]\\ \sf\longmapsto \dfrac{315+8}{45}[/tex]

[tex]\\ \sf\longmapsto \dfrac{323}{45}[/tex]

[tex]\\ \sf\longmapsto 7.1[/tex]

Answer:

since there is no value for the dimensions of the tennis ball. The tennis ball is a sphere with a Surface Area 4pir²

Answer:

10

Step-by-step explanation:

By using intersecting chord theorem:

NH.HT=MH.HY

(x+20)*8=12*20

x+20=12*20/8

x+20=240/8

x+20=30

x=30-20

x=10

Answer:

C

Step-by-step explanation:

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

y = 67° → C