Can you find the inverse of the function y = 4x^2 + 12x + 9? Why or why not?
What domain restrictions are necessary to allow the function to have an inverse?
Find the inverse of the domain restricted function.

a) The average wait time in the line = 13.33 minutes.

b) The average number of customer waiting on line = 4.67 minutes

What do you mean by average?

The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

a) Values:

Arrival rate = 9 per hour

Service rate [tex]= \frac{60}{Service\ time}[/tex]

Service rate [tex]= \frac{60}{4.5} = 13.33[/tex]  minutes

b) Queue:

units in queue(LQ) = Arrival Time^2 / (Service rate* (Service rate - Arrival rate))

unit in queue(LQ) [tex]= \frac{ 9^2}{(13.33\times (13.33 - 9))}[/tex]

unit in queue(LQ) = 0.70

Time in Queue(WQ) = Arrival rate / (Service rate * (Service rate - Arrival rate))

time in queue (WQ) [tex]= \frac{9}{ (13.33 \times (13.33 - 9)}[/tex]

time in queue (WQ) = 4.67 minutes

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Answer:

y=10x-15

Step-by-step explanation:

Use slope-intercept form: y=mx+b

M is your slope and B is your Y intercept

since your Y-intercept is negative, and adding a negative is just subtracting, you can just put -15 instead of +-15

Answer:

[tex]z \in \left[-\frac{3}{16}, \frac{3}{16} \right][/tex]

Step-by-step explanation:

[tex]-9 \leq 32z-3 \leq 3 \\ \\ -6 \leq 32z \leq 6 \\ \\ -\frac{3}{16} \leq z \leq \frac{3}{16} \\ \\ \therefore z \in \left[-\frac{3}{16}, \frac{3}{16} \right][/tex]

The solutions to each of the given exponential functions are;

1) g = 1.356

2) u = 1.725

3) x = 3

4) k = -5.288

5)  a = 4/3

6) z = 1.295

7) x = 13/2

8) v = -1.5286

9) y = 4.17

10) b = 1.2648

Exponential equations are usually in the form a^(x) = b^(y) . To solve exponential equations with same base, we normally make use of the property of equality of exponential functions .

1) 7^(g) = 14

gIn 7 = In 14

g = In 14/In 7

g = 1.356

2) 6^(u) = 22

u In 6 = In 22

u = In 22/In 6

u = 1.725

3) 7^(x - 2) = 7

7^(x - 2) = 7¹

Equating the exponents gives;

x - 2 = 1

x = 3

4) (0.66)^k = 9

k In 0.66 = In 9

k = In 9/In 0.66

k = -5.288

5) Exponential equation 8^a = 16

2^(3a) = 2⁴

Equating the exponents gives;

3a = 4

a = 4/3

6) The exponential equation 12^z = 25;

z In 12 = In 25

z = In 25/In 12

z = 1.295

7) The exponential equation 4^(x-5) = 8

2^(2(x - 5)) = 2^(3)

2x - 10 = 3

2x = 13

x = 13/2

8) (0.28)^v = 7

vIn 0.28 = In 7

v = In 7/In 0.28

v = -1.5286

9) 2^y = 18

y In 2 = In 18

y = In 18/In 2

y = 4.17

10) 17^b = 36

b In 17 = In 36

b = In 36/In 17

b = 1.2648

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After solving the expression we get the answer as the equation does not have a solution.

Given, we have:

(x+10)²-7=5

Open the brackets.

⇒ (x²+20x+100)-7=5

⇒ x²+20x+100-7=5

Calculate the difference.

⇒ x²+20x+93=5

Arrange the like terms:

⇒ x²+20x+93-5=0

⇒ x²+20x+88=0

Factorize the a²ove expression.

⇒ x²+20x+88

can't be factorize, as it does not have factors to reduce the expression.

Hence the expression does not have a solution.

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The percentages are given as follows:

a) Failed, given that they completed the review: 15.38%.

b) Failed, given that they did not complete the review: 42.86%.

Considering these percentages, for item c, there is an inverse association between failing the exam and completing the exam review, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.

A proportion represents a fraction relative to a total amount, and this fraction, which is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

A percentage is one example of application of proportions, as it is the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.

For item a, we have that:

Hence the percentage is:

p = 10/65 x 100% = 15.38%.

For item b, we have that:

Hence the percentage is:

p = 15/35 x 100% = 42.86%.

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The variable y represents the range or output values of the function.

The range of a function is the set of output values of the function.

The given equation is y = mx + b.

Note that x is an independent variable, therefore, we substitute the values for x and calculate the value of y to that value of x.

Therefore, y denotes the range or output values of the function.

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The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.

Given that,

The table is

Input        Output

X               Y

1                 0

3                4

4                6

7                 p

20              q

We have to find the p and q values.

Take the points as

(x,y)=(1,0),(3,4),(4,6),(7,p) and (20,q)

Take the points (1,0) and (3,4)

Equation of the line is

y=mx+b

Where

The slope of the line is m, and the intercept is b.

Slope of the line is rise/run

m=4-0/3-1

m=4/2

m=2

Now,

y=mx+b

0=2(1)+b

2+b=0

b=-2

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

Take the point(7,p)

p=2(7)-2

p=14-2

p=12

Take the point (20,q)

q=2(20)-2

q=40-2

q=38

Therefore, The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.

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x + y + 5 = 0 is the equation of the line that passes through the points (-5,0) and (-2,-3).

Given, two points (-5,0) and (-2,-3).

We are asked to find an equation of the line that passes through the given points.

As, we know

the equation of a line is

(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)

(y - 0)/(x - (-5)) = (0 - (-3))/(-5 - (-2))

y/(x + 5) = 3/-3

y/(x + 5) = -1

y = -(x + 5)

y = -x - 5

x + y + 5 = 0

Hence, x + y + 5 = 0 is the equation of the line that passes through the points (-5,0) and (-2,-3).

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{0})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 4}(x-\stackrel{x_1}{(-8)}) \implies y -0= -4 (x +8) \\\\\\ y=-4x-32\implies {\Large \begin{array}{llll} 4x+y=-32 \end{array}}[/tex]

Answer:

[tex]\text{cosw}(\frac{1}{1-tanw} +\frac{sinw}{sinw-cosw} )[/tex]

Step-by-step explanation:

Assuming we're factoring.

1) Find the Greatest Common Factor (GCF).

GCF = [tex]\text{cosw}[/tex]

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]\text{cosw}(\frac{\frac{cosw}{1-tanw} }{cosw} +\frac{\frac{sinwcosw}{sinw-cosw} }{cosw} )[/tex]

3)  Simplify each term in parentheses.

[tex]\text{cosw}(\frac{1}{1-tanw} +\frac{sinw}{sinw-cosw} )[/tex]

Thanks.

Answer: 870

Step-by-step explanation:

The tickets will sell until there is a day when a non-positive number of tickets will be sold.

[tex]\lfloor 133/11 \rfloor=12[/tex], so this will be after 12 days.

Thus, we can interpret this as an arithmetic series with 12 terms, a first term of 133, and a common difference of -11.

The sum of this series is [tex]\frac{12}{2}[2(133)+(12-1)(-11)]=870[/tex].

Answer:

21

Step-by-step explanation:

Do long division of 378 and 18.
The result of the division will be 21.
There will be 21 seashells on reach row for the science display.

Answer:

Step-by-step explanation:

Cube Surface Area = 150 cm2

Cube Volume = ?

Ac = 6 a2

150 = 6a2

150/6 = a2

25 = a2

5 = a

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

Vc = a3

Vc = (5)3

Vc = 125 cm3

Answer:

Step-by-step explanation:

divide 150 by 6 and find the area of ​​one face of the cube, take the square root and find the side, side^3 and find the volume

150 : 6 = 25 cm² (area of ​​one face of the cube)

√25 = 5 (side of the cube)

5³ = 125 cm³ (volume of the cube)

To work to pay for the refurbished computer exists 89 hours.

Tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers are paying the right amount of tax at the right time and securing the correct tax allowances and tax reliefs.

Tax is defined as a mandatory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or national).

First estimate all the deduction

FICA = $10 per hour × 0.0765 = $0.77 per hr

Fed tax = $10 per hr × 0.12 = $1.2 per hr

State tax = $10 per hr × 0.08 = $0.8 per hr

Remaining pay = 10 – 0.77 – 1.2 – 0.8 = $7.23 per hour

Time required = $640 / $7.23 per hr

Time required = 89 hours

Therefore, the correct answer is option c) 89 hours.

The complete question is:

You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the refurbished computer?

a) 111 hours

b) 98 hours

c) 89 hours

d) 87 hours

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Answer:

200

Step-by-step explanation:

For x =  12°, line m and line n will be parallel to each other.

Option (C) is correct.

What are angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

In the given figure, the line m and line n will be parallel, if and only if the both angles are in a linear pair,

So by using the property of the angles in a linear pair, we get

             11x° + 4x° = 180°

             15x° = 180°

              x° = 180°/15°

              x = 12°

Hence for x =  12°, line m and line n will be parallel to each other.

Option (C) is correct.

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Answer: 24,000 ft.

Step-by-step explanation:

1in.(8)= 8 in.

SO: 3000ft.(8)= 24,000ft.

If one plane can travel 10 miles per hour faster than another. The planes' speeds would be 435 miles per hour.

let s = speed of the slower plane

then

(s+10) = speed of the faster

time = distance /speed

495/s =510 /(s+10)

495s = 510s + 5100

Combine like terms

495 - 510s = 5100

15s = 5100

Divide both side by 15s

s = 5100/15

s = 425 mph  ( speed of the slower plane)

Speed of the fastest plane

(s+10)

425 +10

= 435 mph

Therefore  the speed of the fastest is 435 mph.

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Answer:

cost of each pencil [tex]= \frac{150}{x}[/tex]

In the information provided, cholesterol is high and accounts for 39% of the total. It may have a negative impact on heart health as well.

Cholesterol;-

Any member of the lipid class of chemical compounds is referred to as cholesterol. Sterols are a subclass of lipids.

All animal cells produce cholesterol, which is a structural component of animal cell membranes.

It may result in a number of issues, including obesity, heart disease, and stones. As its level is 39% in the amount provided, this is high.

Therefore, cholesterol looks to be a high-nutrient food.

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Answer:

5.1 units

Step-by-step explanation:

[tex]f(x)=5x-2\\f(3)=5(3)-2=13\\f(4)=5(4)-2=18[/tex]

[tex]\Delta x=1 unit=a\\\Delta y=5 units=b\\a^2+b^2=c^2\\(1)^2+(5)^2=c^2\\\sqrt26=c\\c=5.1 units[/tex]

Answer:

The correct answer is: 204.6

Step-by-step explanation:

(26 * 7.75) + (2/5 * 7.75) = 204.6

Answer:

222-148=74 (people 3-2=1)

296-222=74 (people 4-3=1)

370-296=74 (people 5-4=1)

so 1/74 is the answer

let's say "x" is the original price, now let's reduce it by 25%

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of x}}{\left( \cfrac{25}{100} \right)x}\implies \cfrac{1}{4}x\hspace{5em}x-\stackrel{25\%}{\cfrac{1}{4}x}\implies \stackrel{new~price}{\cfrac{3}{4}x}[/tex]

so the new price after applying a 25% or namely 1/4 of "x" is just 3/4 of "x".

if we apply the same reduction again, we'll  be left with only 3/4 of ( (3/4)x ) and so on, check the picture below which shows the value once we apply the 1/4 four times, we end up with the new price being to 3/4 of whatever it was before, so

[tex]\cfrac{3}{4}\cdot \cfrac{3}{4}\cdot \cfrac{3}{4}\cdot \cfrac{3}{4}x\implies \cfrac{81}{256}x\hspace{5em}\cfrac{81}{256}\cdot 37\implies \cfrac{2997}{256}[/tex]

now, since we know the 100% or original price was 37, what's the new reduced price of 2997/256 off of it in percentage?

[tex]\begin{array}{ccll} amount\%\\ \cline{1-2} 37&100\\[1em] \frac{2997}{256}&p \end{array}\implies \cfrac{37}{~~ \frac{2997 }{256 } ~~}=\cfrac{100}{p}\implies \cfrac{(37)(256)}{2997}=\cfrac{100}{p} \\\\\\ (37)(256)p=299700\implies p=\cfrac{299700}{(37)(256)}\implies p\approx \stackrel{\%}{31.64}~\hfill \underset{savings}{\stackrel{100\%~~ - ~~31.64\%}{\approx\text{\LARGE 68.36\%}}}[/tex]

The icon to view the customary units in 11880 yields is 6.75 mi

Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.

Additionally, rounding and choosing the appropriate number of significant digits may be necessary during the process.

To measure various parameters, various units of conversion are utilized.

Counting Length

Weighing Things

Evaluation of Capacity

Temperature Measurement

To better understand, we convert measurement units in mathematics.

For ease of understanding, the length of a table is measured in inches, whereas the length of a garden is measured in yards.

A finger's length cannot be expressed in kilometers.

Units of measurements are necessary to measure various quantities.

divide 11,880 yards length value by 1760 to get 6.75 miles

Therefore the icon to view the customary units in 11880 yields is 6.75 mi

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The value of y' by implicit differentiation, the value of y is [tex]y = \sqrt{5x +c}[/tex]

We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.

Given

The function is [tex]y^2 + 5 = 5x[/tex]

where x and y are variables..

On differentiating the equation, we have;

[tex]2yy' + 0 = 5[/tex]

on simplifying, we have

2yy' = 5

Now solve the equation explicitly for y and differentiate to get y' in terms of x.

2yy' = 5

Separate the variables

[tex]y^2 = 5x + c[/tex]

Taking square root on both the side

[tex]y = \sqrt{5x +c}[/tex]

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The solution to the questions are:

From the question, we have the following parameters that can be used in our computation:

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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Answer:

7 yd

It's a 16 by 13 rectangle. Since 6 yd are already showing on the left side, you know 7yd remain to get 13 yd.