What is the inverse of f(x)=9x-3

Answer:

Zeros: 0, 1, and 7

Step-by-step explanation:

Given function: f(x) = 3x(x - 1)²(x - 7)²

To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.

1. Substitute f(x) = 0:

[tex]\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2[/tex]

2. Divide both sides by 3:

[tex]\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2[/tex]

3. Separate into possible cases:

[tex]\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0[/tex]

4. Simplify:

[tex]\sf a)\ x = 0\ \textsf{[ already simplified ]}[/tex]

[tex]\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1[/tex]

[tex]\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7[/tex]

Therefore, the zeros of this function are: 0, 1, and 7.

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Here is the graph! I hope this helps!

Answer:

^this means graph C.

Step-by-step explanation:

Answer:

x² - 4 = 0

x² = 4

x =± √4

x = +2 or x = -2.

Answer:

2 and -2 (±2)

Step-by-step explanation:

Step 1: Move -4 to the other side of the equal sign; we get x² = 4.

Step 2: A lot of people miss the negative answer! The square root of 4 is equal to both positive 2 and negative 2.

Answer:

3/8

Step-by-step explanation:

probability = wanted outcomes / total outcomes

odds = wanted outcomes / unwanted outcomes

Odds of 3:5 losing means 3 losing outcomes and 5 winning outcomes.

The total outcomes is 8

The probability of losing which is the probability that the event will fail to occur is 3/8.

Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:

1.053x = 30.8.

x = 30.8/1.053

x = 29.2.

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Answer:

69 there hope it helps ;)

Step-by-step explanation:

420

To calculate the distance between two points we use this formula:

[tex] \boxed{ \boxed{{d \: = \: \sqrt{(x_2 \: - \: x_1)^{2} \: + \: (y_2 \: - \: y_1)^{2} } }}}[/tex]

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We apply the values already obtained to the formula to get the distance:

[tex]d \: = \: \sqrt{( - 3 \: - \:( - 5))^{2} \: + \: (0 \: - \: 8)^{2} }[/tex]

[tex]d \: = \: \sqrt{( - 3 \: - \: ( - 5))^{2} \: + \: ( - 8)^{2} }[/tex]

[tex]d \: = \: \sqrt{( - 3 \: + \: 5) ^{2} \: + \: 64 } [/tex]

[tex]d \: = \: \sqrt{ {2}^{2} \: + \: 64 } [/tex]

[tex]d \: = \: \sqrt{4 \: + \: 64} [/tex]

[tex]d \: = \: \sqrt{68} [/tex]

[tex]d \: = \boxed{ \bold{ \: 2 \sqrt{17} \: units}}[/tex]

[tex] \huge{\boxed{ \bold{2 \sqrt{17} \: units }}}[/tex]

Let h represent hamburgers and c represent cheeseburgers

h + c ≤ 100 - The number of burgers sold

3h + 3.5c ≥ 80 - Amount that each burger sells for

Answer:

a)  81π  in³

b)  27  in³

c)  divide the volume of the slice of cake by the volume of the whole cake

d)  10.6%

e)  see explanation

Step-by-step explanation:

The cake can be modeled as a cylinder with:

[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]

Probability is approximately 10.6%  (see above for calculation)

If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found.  So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

Answer:

Step-by-step explanation:

We know that, 252 = 625

And, 262 = 676

Now, 676 - 625 = 51

So, there are 51 - 1 = 50 numbers lying between 252 and 262

The length of the kitchen in the drawing using the scale factor is: B. 5/6.

We are given a scale factor of 1:24.

Let the length of the kitchen in the drawing = x

Actual length of kitchen = 20 ft.

Using the scale factor, we have:

1/24(20) = 20/24

= 5/6

The length of the kitchen in the drawing is: B. 5/6.

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Answer:

really good

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other, so since the slope of the given line is 1, the slope of the line we want to find is -1.

Substituting into point-slope form,

[tex]y+4=-1(x-5)\\\\y+4=-x+5\\\\\boxed{y=-x+1}[/tex]

Answer:

D) 8[tex]\frac{1}{2}[/tex]

Step-by-step explanation:
5[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 8[tex]\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

(xm , ym )  = x1 + x2 / 2               and            y1 + y2 / 2

               = 9 +3 / 2                                      = 10 -10 / 2

               = 12/2                                            = 0/2

                = 6                                                  = 0

                So midpoints are (6 , 0)

Answer:

midpoint =  [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]

Step-by-step explanation:

To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.

• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]

                 = [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]

                 = [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]

                 = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]

Answer:

Liz

Step-by-step explanation:

if the chart is correct only 3 people spent more than 2 1/2 hours on homework when 9 people spent less than 2 1/2 hours on homework

Answer:

55

Step-by-step explanation:

1+1 = 2

1+2 = 3

2+3 = 5

3+5 = 8

5+8 = 13

8+13 = 21

13+21 = 34

21 +34 = 55

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Answer:

x≥11

Step-by-step explanation:

4x-3≥41

4x≥41+3   -44

x≥44/4 = 11

1. The value of x in the equilateral triangle is: 12

2. x = 25; y = 14

If a triangle has three sides that are marked congruent, then the triangle is an equilateral triangle.

1. Since triangle ABC is an equilateral triangle and its sides are equal, therefore:

5x - 22 = 3x + 2 [congruent sides]

Solve for x

5x - 3x = 22 + 2

2x = 24

2x/2 = 24/2

x = 12

The value of x is: 12.

2. Base angles of an isosceles triangle are congruent, therefore:

2x = 50

x = 50/2

x = 25

Thus, using the triangle sum theorem, we have:

2x + 50 + 5y + 10 = 180

Plug in the value of x and find y

2(25) + 50 + 5y + 10 = 180

50 + 50 + 5y + 10 = 180

110 + 5y = 180

5y = 180 - 110

5y = 70

y = 70/5

y = 14

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x = -3

[tex]6( {2x}^{2} - 5) \\ \\ 6(2 \times { (- 3)}^{2} - 5) \\ \\ 6(2 \times ( 9) - 5) \\ \\ 6( 18 - 5) \\ \\ 6 \times ( 13) \\ \\ 78.[/tex]

The equivalent interest rate is 4.07%.

The money will be compounded 12 times.

The equivalent interest rate is the actual interest rate that an account earns after accounting for number of compounding.

Effective interest rate = (1 + APR / m ) ^m - 1

M = number of compounding

(1 + 0.04/12)^12 - 1 = 4.07%

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a) 2/8 = 1/4

b) There are 3 females who can speak French and 2 males who can speak French, so the probability is 3/5

The true statements are (A), (B) and (D)

Data is information that has been translated into a form that is efficient for movement or processing.

As, from the given table we can see that

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‐10+35=25 and 25 × 20=300

Answer:

yea that’s right

Step-by-step explanation:

The minimized value is 50 and the maximized value is 130

The objective function is:

P = 10x + 5y

Subject to

2x+3y ≤30

2x+y ≤ 26

-2x+3y ≤ 30

x, y >0

Next, we plot the graph of the constraints (see attachment)

From the graph, the vertices of the feasible regions are:

(0, 10),(12, 2) and (6,14)

Substitute these values in P = 10x + 5y

P = 10(0) + 5(10) = 50

P = 10(12) + 5(2) = 130

P = 10(6) + 5(14) = 130

Hence, the minimized value is 50 and the maximized value is 130

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Answer: y = -x + 7

Step-by-step explanation:

The slope is [tex]\frac{5-6}{2-1}=-1[/tex], so we know the equation is of the form [tex]y=-x+b[/tex].

Substituting in the coordinates (1,6) to find b,

[tex]6=-1+b\\\\b=7[/tex]

Thus, the equation is y = -x + 7

Step-by-step explanation:

[tex] \sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2} [/tex]

[tex] \sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )[/tex]

Sin is odd function, so if you add pi to it, it would become switch it sign.

[tex] - \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]

Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.

[tex] \sin(x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]

Cosine is basically a sine function translated pi/2 units to the right or left so

[tex] \sin(x) + \tan(x) \sin(x) [/tex]

[tex] \sin(x) ( 1 + \tan(x) )[/tex]

Answer:

z = -2

Step-by-step explanation:

Answer:

[tex]\boxed{\bf z = - 2}[/tex]

Step-by-step explanation:

[tex]\bf 6z + 10 = - 2[/tex]

Subtract 10 from both sides.

Simplify.

Divide both sides by 6.

Simplify.

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