Equation of a graph problem

Use the chain rule to differentiate both sides of the given equation with respect to [tex]x[/tex] :

[tex]y = 2 f(g(x))[/tex]

[tex]\dfrac{dy}{dx} = y' = 2 f'(g(x)) g'(x)[/tex]

Differentiate again with the product and chain rules to get the second derivative :

[tex]\dfrac{d^2y}{dx^2} = y'' = \boxed{2 f'(g(x)) g''(x) + 2 f''(g(x)) g'(x)^2}[/tex]

(D)

The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

The equation is given as:

[tex](\frac18)^{-3a} = 512^{3a}[/tex]

Express the equation as a base of 2

[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]

Evaluate the products

[tex]2^{9a} = 2^{27a}[/tex]

Cancel out the common base

9a = 27a

The above equation is not true because [tex]9a \ne 27a[/tex]

Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

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Answer:

2×3.14×r=75

6.28 r=75

r=75/6.28=11.943=12 inch (nearly)

Answer:

n = 7

Explanation:

[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]

simply add the numbers

[tex]\rightarrow \sf 13 + 35n = 258[/tex]

subtract both sides by 13

[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]

simplify the following

[tex]\rightarrow \sf 35n = 245[/tex]

divide both sides by 35

[tex]\rightarrow \sf n = 7[/tex]

Answer:

n = 7

Step-by-step explanation:

1) Subtract 3 from both sides.

5(2 + 7n) = 258 - 3

2) Simplify 258 - 3 to 255.

5(2 + 7n) = 255

3) Divide both sides by 5.

2 + 7n = 255/5

4) Simplify 255/5 to 51.

2 + 7n = 51

5) Subtract 2 from both sides.

7n = 51 - 2

6) Simplify 51 - 2 to 49.

7n = 49

7) Divide both sides by 7.

n = 49/7

8) Simplify 49/7 yo 7.

n = 7

Answer:

30

Step-by-step explanation:

4 cups x 60 hours a min x 2 hours of lunch ÷ 16 cups per gallon = 30 gallons

The answer is 30 gallons.

Firstly, convert the hours to minutes so you know how many minutes you're working with. 2*60=120 minutes.

Then, multiply 120 with 4 to get the number of tea (in cups) that is poured. 120*4=480 cups.

Finally, divide 480 cups with 16 cups to find out the number of gallons poured. 480/16 equals 30 gallons.

Hope this helped.

Answer:

[tex]\fbox {400.41 feet}[/tex]

Step-by-step explanation:

Here we need to take the tan ratio of the angle.

⇒ tan 4° = 28/x = 0.0699268119

⇒ x = 28/0.0699268119

⇒ x = 400.41 feet

Answer:

(2,-3) (3,-3)

Step-by-step explanation:

f(x) is y

x² - 5x + 3 = -3

x² - 5x + 6 = 0

ask yourself

which 2 numbers when multiplied give you

+6 and when added give you -5

they are -3 and -2

(x-3)(x-2)

x=3 x=2

when you put x=3 and x=2

in x² - 5x + 3 it's gives -3 which is y

(3,-3) (2,-3)

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Polygon 3 and 4 are similar to polygon 1.

Polygons will be called similar if they are exactly in the same shape, but can be in different sizes.

Here given, Some of the images are images of the polygon 1 from similarity transformations.

So we have to find the similar polygon from the given picture.

From picture it is clear that Polygon 2 is similar to polygon 1 as the size of polygon 2 has been decreased from polygon 1 but the shape of polygon 2 is the same as polygon 1 as we can their corresponding angles are also equal.

Also, polygon 3 is similar to polygon 1 as the size of polygon 3 has been decreased from polygon 1 but the shape of polygon 2 is the same as polygon 1 and reversed of polygon 1. So polygon 3 is of the same orientation as polygon 1 as we can their corresponding angles are also equal.

So from above, it is clear that Polygon 1 is similar to polygon 3 and 4 as they have the same shape but different sizes.

Therefore Polygon 3 and Polygon 4 are similar to polygon 1.

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Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.

It is defined as the difference between the maximum value in the data set to the minimum value in the data set.

We have:

The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets:

Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}

Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}

Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}

Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}

The IQR for Alyssa:

IQR = Q3 - Q1

IQR = 8 - 5 = 3

The IQR for Bryant:

IQR = Q3 - Q1

IQR = 8 - 2 = 6

The IQR for Camila:

IQR = Q3 - Q1

IQR = 10 - 2 = 8

The IQR for Devon:

IQR = Q3 - Q1

IQR = 8 - 2 = 6

Thus, Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.

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A percentage is a way to describe a part of a whole. The percentage increase of Magikarps is 100%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps. Therefore, The percentage increase of Magikarps is,

Percentage increase = (16-8)/8 × 100% = 100%

Hence, The percentage increase of Magikarps is 100%.

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Answer:

y = -0.5x - 3.5

Explanation:

Take two points: (1, -4), (3, -5)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}[/tex]

Equation:

[tex]\sf y- y_1 = m (x - x_1)[/tex]

[tex]\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)[/tex]

[tex]\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4[/tex]

[tex]\rightarrow \sf y = -0.5 x -3.5[/tex]

The formula of a line is:

[tex]f(x) = kx + b[/tex]

k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.

We can see 2 points:
A (1, -4)
B (3, -5)

We can make a system of equations:

[tex]k*1+b=-4\\k*3+b=-5\\[/tex]

From second equation:

[tex]b = -5 - 3k[/tex]

Let's put b in first equation:

[tex]k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}[/tex]

Now we can find b:

[tex]b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5[/tex]

The answer is:
-0.5x -3.5

Answer:

[tex]\large {\textsf{B and E}}\ \implies x_1=-2\sqrt{5}-3,\ x_2=+2\sqrt{5}-3[/tex]

Step-by-step explanation:

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Quadratic Equation: ax² + bx + x = 0, where a ≠ 0

Given equation: x² + 6x + 9 = 20

Step 1: Subtract 20 from both sides.

x² + 6x + 9 - 20 = 20 - 20

⇒ x² + 6x - 11 = 0

Step 2: Identify the values of a, b, and c and substitute them in the formula.

⇒ a = 1, b = 6, c = -11

[tex]x=\dfrac{-6\pm\sqrt{\bold{6^2}-4(1)(-11)}}{\bold{2(1)}}\\\\x=\dfrac{-6\pm\sqrt{36\bold{\ - \ 4(-11)}}}{2}\\\\x=\dfrac{-6\pm\sqrt{\bold{36+44}}}{2}\\\\x=\dfrac{-6\pm\sqrt{80}}{2}\\\\x=\dfrac{-6\pm\sqrt{16\times5}}{2}\implies \dfrac{-6\pm\sqrt{\bold{16}}\times\sqrt{5}}{2} \\\\x=\dfrac{-6\pm4\sqrt{5}}{2}[/tex]

Step 3: Separate into possible cases.

[tex]x_1=\dfrac{-6-4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{-4\sqrt{5}}{2}\implies \boxed{-3-2\sqrt{5}\ \ \textsf{or}\ -2\sqrt{5}-3}\\\\x_2=\dfrac{-6+4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{4\sqrt{5}}{2}\implies \boxed{-3+2\sqrt{5}\ \ \textsf{or}\ \ 2\sqrt{5}-3}[/tex]

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Answer:

[tex]x=\dfrac{11}{4}[/tex]

Step-by-step explanation:

Given:

[tex]9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

Rewrite 9 as 3² and 27 as 3³:

[tex]\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}[/tex]

Multiply both sides by [tex]3^{(x-1)}[/tex] :

[tex]\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}[/tex]

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

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x-2=\dfrac{3}{4}[/tex]

[tex]\implies 4(x-2)=3[/tex]

[tex]\implies 4x-8=3[/tex]

[tex]\implies 4x=11[/tex]

[tex]\implies x=\dfrac{11}{4}[/tex]

Answer:

134

Step-by-step explanation:

the "nth" term of a sequence means that you can plug in the term number to get the term value

so, if

  11n + 2 is the sequence

  11(12) + 2 is the 12th term

  132 + 2 is the 12th term

  134 is the 12th term

By plugging in the term "place" (1st, 2nd, 3rd, 4th, etc.) for the variable "n", we get a term value.

hope this helps!!

The 12th term of the sequence is 133

The nth term is given as:

Tn = 11n + 1

The 12th term is calculated as:

T(12) = 11(12) + 1

Evaluate

T(12) = 133

Hence, the 12th term of the sequence is 133

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Answer:

opotion has not correct answer

answer is 15.

Answer:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

Step-by-step explanation:

[tex]\left(\sqrt{3}\right)\left(\sqrt[5]{3}\right)=\sqrt[10]{3^7}\quad[/tex]

(√3)([tex]\sqrt[5]{3}[/tex]) = √3 · [tex]\sqrt[5]{3}[/tex]

{√3 = [tex]3^{\frac{1}{2}}[/tex]}                 {radical rule: [tex]\sqrt{x}=x^1^/^2[/tex]}

[tex]\sqrt3[/tex][tex]\sqrt[5]{3}[/tex] =  [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex]

{[tex]\sqrt[5]{3}[/tex] = [tex]3^{\frac{1}{5}}[/tex]}                  {radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex]}

 [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex] =   [tex]3^{\frac{1}{2}}[/tex] · [tex]3^{\frac{1}{5}}[/tex]     {exponent rule:  [tex]a^x*a^y=a^x^+^y[/tex]}

                (1/2 + 1/5 = 5/10 + 2/10 = 7/10)

              [tex]=3^\frac{7}{10}[/tex]        {opposite of radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex] ;  [tex]x^\frac{a}{b}=\sqrt[b]{x^a}[/tex]}

             = [tex]\sqrt[10]{3^7}[/tex]

so, the simplified version of this equation can either be written as:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

hope this helps!!

(I can't clearly see the last option, but if it's either of these, then it's correct)

Answer:

  85,999,999.999 999 909

Step-by-step explanation:

The expression represents the difference of a relatively large number and one that is relatively small. That difference is approximately the value of the large number. The exact value requires 17 digits for its proper expression. Most calculators and spreadsheets cannot display this many digits.

The numbers in standard form are ...

  86,000,000 = 8.6×10^7

  0.000000091 = 9.1×10^-8

Their difference is ...

  86,000,000 -0.000000091 = 85,999,999.999 999 909

In scientific notation, this is ...

  8.599 999 999 999 990 9×10^7

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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Answer:

You can make 10 tortillas with one and a half kilograms of ground meat

Step-by-step explanation:

one and a half kilograms to grams

1.5kg x 1000 = 1500g

150 grams prepared to make 1 hamburger

than, 150 x h = 1500

h = 1500 / 150

h = 10

Answer:

10 tortillas

Step-by-step explanation:

First convert kilograms to grams:

   1 kg = 1000 g

⇒ 1.5 kg = 1500 g

Let x = number of tortillas made with 1500 g of meat

Set up a ratio of tortillas and meat and solve for x:

⇒ 1 tortilla : x tortillas = 150 g meat : 1500 g meat

[tex]\sf \implies \dfrac{1}{x}=\dfrac{150}{1500}[/tex]

[tex]\sf \implies 1 \cdot 1500= 150 \cdot x[/tex]

[tex]\sf \implies 1500=150x[/tex]

[tex]\implies \sf x=\dfrac{1500}{150}[/tex]

[tex]\implies \sf x=10[/tex]

Therefore, 10 tortillas can be made with 1.5 kg of ground meat.

Answer:

9

Step-by-step explanation:

√x+5-2=0

√x+3=0

√x= -3

x=9   [(-3)*(-3) = 9]

2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.

3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]

4) [tex]X[/tex]

Answer:

Step-by-step explanation:

what is the question?

Answer:

Median = A

Mean = B

Step-by-step explanation:

Khan Academy

Here's your answer down here↓:

Step-by-step explanation:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)

Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.

So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)

And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)

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Answer:  [tex]\textsf{Option A, (-2, 4)}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{f(x) = x + 6}[/tex]

Find:  [tex]\textsf{f(-2)}[/tex]

Solution:  We need to plug in the value -2 into every variable x that we have in the expression and simplify to get the solution.

Plug in the values

Simplify

Therefore, the ordered pair that would match would have a x-coordinate of -2 and a y-coordinate of 4 producing (-2, 4) which matches option A.

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:

y = m · x + b     (1)

Slope

m = (7 - 0)/[9 - (- 6)]

m = 7/15

Intercept

b = 4

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

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Answer = #2 - 1/3^3

Step-by-step explanation:

[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

[tex] \sf \dfrac{2}{15} \div \dfrac{3}{20} = \dfrac{2 \times 20}{15 \times 3} = \dfrac{40}{45} = \dfrac{8}{9} [/tex]

Answer :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \Rrightarrow \dfrac{8}{9} [/tex]

I hope I've helped : )

[tex]\dfrac{1}{50}[/tex]

[tex] \cfrac{2}{15} \times \cfrac{3}{20} [/tex]

[tex] \cfrac{2 \times 3}{15 \times 20} [/tex]

[tex] \cfrac{6}{15 \times 20} [/tex]

[tex] \cfrac{6}{300} [/tex]

[tex] \cfrac{1}{50} [/tex]

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Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.

What is the range of the function?

The equation of the function is f(x) = x(x + 2)(x -1)(x -3)

From the graph, we have the following highlight:

The above means that:

f(x) approaches positive infinity irrespective of the x value

Hence, the end behavior of the function is:

[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]

Since, the function opens upward.

Then the sign of the leading coefficient is positive

This is the point, where the graph crosses the x-axis.

From the graph, we have the zeros to be:

x = -2, x = 0, x = 1 and x = 3

Since the graph crosses the x-axis at this point, then the multiplicity of the zeros is 1

In (c), we have:

x = -2, x = 0, x = 1 and x = 3

Rewrite as:

x + 2= 0, x = 0, x - 1 = 0 and x - 3 = 0

Multiply these values

f(x) = x(x + 2)(x -1)(x -3)

Hence, the equation of the function is f(x) = x(x + 2)(x -1)(x -3)

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Answer:

Step-by-step explanation:

Declaration

Let Brand A number of 2.00 socks= x

Let Brand B number of 3.00 socks = y

Equations

Number of socks : x + y = 5

Cost of socks: 2x + 3y = 13

Solution

Multiply top equation by 2

2(x+ y = 5)

2x + 2y = 10

Write the new equation under the cost of socks equation

2x + 3y = 13

2x + 2y = 10       Subtract.

y = 3

She spent 3 dollars on 1 pair of socks.

Now she needs to calculate the number of 2.00 dollar socks

2x + 3y = 13

2x + 3*3 = 13                Combine the left

2x + 9 = 13                   Subtract 9 from both sides.

2x +9-9 = 13-9             Combine

2x = 4                          Divide by 2

2x/2 = 4/2

x = 2

Answer

#2 dollar socks = 2

#3 dollar socks = 3

If the first inequality is written as:

3x ≤ -12

Then the correct option is D.

If it is written as it is in the problem, then neither of the graphs is the correct option.

Here we have the inequalities:

3x ≤ 12

2x + 3 > 11

(notice that in all the options, the first inequality has a negative sign, while in the two given inequalities there are no negative sign. This means that you will never get the correct answer if you use the given information, as the problem is incorrectly written).

First, we need to isolate x on both inequalities, we will get:

3x ≤ 12

x ≤ 12/3

x ≤ 4

(As you can see, because we don't have the negative sign, this inequality is different to all the ones in the options).

And for the other:

2x + 3 > 11

2x > 11 - 3

x > 8/2

x > 4

So neither of the options is actually correct.

If we instead write the first inequality as:

3x ≤ -12

We would solve this as:

x ≤ -4

And in that case, our two inequalities are:

x ≤ -4

x > 4

So the correct graph is graph D.

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