find the domain of
4x^2/x^3

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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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:

The correct answer is: 204.6

Step-by-step explanation:

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

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 solution set of the inequalities given in the task content is described as; (-infinity, -17) U [ -9, infinity).

It follows from the task content that the solution set containing values of w which render the pair of inequalities true be determined.

On this note, since the inequalities given are;

-14 > w + 3 or 3w ≥ -27

By solving the inequalities individually; we have;

-14 > w + 3

Subtract 3 from both sides of the equation so that we have;

-14 - 3 > w; Therefore, -17 > w.

Also, 3w ≥ -27

Therefore; w ≥ -9.

On this note, it follows that; w < -17 or w ≥ -9.

Consequently, the solution set of the inequalities can be represented using interval notation as;

(-infinity, -17) U [ -9, infinity)

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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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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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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.

EAnswer:her son is eight

Step-by-step explanation:

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: 24,000 ft.

Step-by-step explanation:

1in.(8)= 8 in.

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

The range of the function is:  (- ∞,3) or - ∞ < x < 3

Range (statistics), is the difference between the highest and the lowest values in a set. Interval (mathematics), also called range, is a set of real numbers that includes all numbers between any two numbers in the set.

Given that

U (x) =  -2x² +  3

V(x) = 1/x

(u-v)(x)  can be represented as

U(x) – v(x)

So, we have:

-2x²+ 3 - 1/x

= (-2x³ + 3x -1)/ x

Therefore, the range of the function is (- ∞,3) or -∞ < x < 3

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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]

Answer:

x = -4.5

Step-by-step explanation:

[tex]20 = 2 - 4x[/tex]

[tex]18 = - 4x[/tex]

[tex] - 4.5 = x[/tex]

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 see the graph in the below attachment. The graph of inequality is      x > -6 .

Given,

In the question:

The inequality is given as:

-4(x + 3) ≤ -2x

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Now, According to the question:

Solution set of inequality -4(x + 3) ≤ -2x

-4(x + 3) ≤ -2x

Apply the Distributive property :

-4x - 12 < -2x

Rearrange the variables:

-4x + 2x < 12

Combine like terms:

-2x  < 12

Divide both sides:

x > -12/2

Cross out the common factor:

x > -6

Hence, To see the graph in the below attachment. The graph of inequality is x > -6 .

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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:

y - 2 = 3(x + 1)

Step-by-step explanation:

The slope is 3 and the point is (-1,2)

From the plot pointed, you go up three unit and 1 unit to the right to get back on the line.  This is 3/1 or 3.

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])  

Replace m =3

Replace [tex]y_{1}[/tex] = 2

Replace [tex]x_{1}[/tex] = -1

y - 2 = 3(x - -1)

y - 2 = 3(x +1)

There is exactly one solution. The ordered pair for the given set of solutions is (-4,-3). Option A is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is

x/4 -y/2 =1/2

x+4y=-16

[tex]\begin{bmatrix}\frac{x}{4}-\frac{y}{2}=\frac{1}{2}\\ x+4y=-16\end{bmatrix} \\\\ \begin{bmatrix}2\left(y+1\right)+4y=-16\end{bmatrix} \\\\ \begin{bmatrix}6y+2=-16\end{bmatrix} \\\\ y = -3[/tex]

Substitute the value of y in equation (2)

[tex]x=2\left(-3+1\right) \\\\ x=-4 \\\\ x=-4,\:y=-3[/tex]

Thus, there is exactly one solution. The ordered pair for the given set of solutions is (-4,-3). Option A is correct.

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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:

[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.

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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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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The constant of proportionality k, of the given equation y = (2/7)x  is 2/7.

Proportionality :

Proportion is a mathematical comparison between two numbers.

here

y=2/7x

y [tex]\ \propto[/tex] 2

shows that y is  directly proportional  to 2.

y [tex]\ \propto[/tex] 1/ 7x

shows that y is inversely proportional  to 7x.

The constant of proportionality is given as:

y = kx or  y = k/x

where k is the proportionality constant

The constant of proportionality k, of the given equation y = (2/7)x  is 2/7.

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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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Answer:

This is what I got, hope it helps!

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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