Let u=1nx and v=1ny. Write y^3x^5 in terms of u and v

On solving the provided question, we can say that by equation =2.75x = 50feet and 4.5x = 900 feet in actual  

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here, we have

1 in = 20 feet

let it be x 20 feet,

then by equation =2.75x = 50feet and 4.5x = 900 feet in actual  

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You can find the complex roots of a 6th-degree polynomial by using approaches such as the rational root theorem.

The most common approach is to use the Rational Root Theorem, which can be used to determine the possible rational roots of the polynomial - these are the roots that can be expressed as a fraction with an integer numerator and an integer denominator.

Once you have identified these possible rational roots, you can then use the Synthetic Division algorithm to divide the polynomial with each of the rational roots to determine the actual roots of the equation.

Another approach is to use the Sturm’s Theorem, which can be used to determine the number of real and complex roots of the equation.

Finally, you can also use numerical methods, such as the Newton-Raphson method, to calculate the complex roots of the polynomial.

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The domain of the function [tex]f(x) = 7[/tex] is (-∞, ∞). It means that all real numbers are domains for the given function.

The domain of the function is the set of numbers for which the function is defined. It acts as input for the function and gives output known as range.

The range of the function is the set of numbers of possible output values.It is derived from set of inputs known as domain.

The domain of the expression  [tex]f(x)=7[/tex] is all real numbers except where the expression is undefined. In this given case, there is no real number that makes the expression undefined.

Hence, The domain for the given expression is (-∞, ∞).

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One of the options is c=d because matching angles are made and the same corners are congruent when a line joins two parallel lines.

In geometry, parallel lines are coplanar, straight lines that don't intersect anywhere. Parallel planes are those in the same three-dimensional space that never cross one another. Curves do not touch or intersect when they are parallel to one another and keep a predetermined minimum distance between them. Lines in a plane are considered to be parallel if their spacing is constant. Objects cannot cross parallel lines. Perpendicular lines are those that intersect at a precise angle of 90 degrees.

Due to vertical angles, A = d is also a possible answer. The outcome is that b+d=180 since b+c=180 and c=d, and b+d=180 as a result. Therefore, the answer is B, C, E, where a=d, c=d, and b+d=180.

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The way that mutual funds are similar to common stocks is D. Investing in a mutual fund gives the investor a proportionate ownership in that fund.

Mutual funds are investment vehicles that pool together money from many different investors and use that money to buy a diversified portfolio of stocks, bonds, or other securities.

Just like when you buy a single stock, when you invest in a mutual fund, you become a shareholder of the fund and own a proportionate share of the underlying securities in the fund.

The correct option is D

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In a shortcut method, 1500 divided by 50 equals 30.

Before we start to count the division, we should know that the number 500 is called the divisor or the denominator, and the number 1500 is called the dividend or the numerator.

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Answer:

-4

Step-by-step explanation:

Let x = the unknown number

Twice of x would = 2x

Write out the equation

2x + 13 = 5

Solve

2x = -8

x = -4

The time Billy should get up to be right on time for school is 6:52 am.

The formula to calculate the time Billy should get up to be right on time for school is as follows: Time Billy Should Get Up = School Start Time - (Time to Get Dressed + Time to Eat Breakfast + Time to Walk to School). In this case, the formula is: Time Billy Should Get Up = 8:35 am - (32 minutes + 13 minutes + 17 minutes). In order to solve this equation, first we must convert the minutes to hours. 32 minutes is equal to 0.53 hours and 13 minutes is equal to 0.22 hours. 17 minutes is equal to 0.28 hours. Thus, the formula is: Time Billy Should Get Up = 8:35 am - (0.53 hours + 0.22 hours + 0.28 hours). Now, we can solve for the time Billy should get up. 8:35 am minus 0.53 hours is 7:42 am. Then, 7:42 am minus 0.22 hours is 7:20 am. Finally, 7:20 am minus 0.28 hours is 6:52 am. Therefore, the time Billy should get up to be right on time for school is 6:52 am.

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JKL triangles could not be similar to triangle abc if triangle a b c with right angle b. Side a b is 12 cm. Side b c is 5 cm. Side a c is 13 cm.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

This is because the lengths of each side JKL is a factor to ABC

respectively .

AB=12,JK=36

AC=13,JL=39

BC=5,KL=25

JKL triangles could not be similar to triangle abc if triangle a b c with right angle b. Side a b is 12 cm. Side b c is 5 cm. Side a c is 13 cm.

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Triangles that cannot be similar to triangle ABC are those that do not meet the necessary conditions for similarity, which are:

Corresponding angles are congruent

Corresponding side lengths are in proportion

Given the information provided, triangle ABC is a right triangle with a right angle at vertex B, and side lengths of 12 cm, 5 cm, and 13 cm.

A triangle with a right angle is already a special case of triangle, as the Pythagorean theorem must apply. Therefore any triangle that does not obey this theorem can not be similar.

So, any triangle that doesn't obey pythagorean theorem, not having the same angles or ratios of side lengths can't be similar to ABC triangle.

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The range of values for the correlation coefficient is - 1 to 1, inclusive is the correct answer.

Value is an important concept in economics, philosophy, and psychology. In economics, value is the amount of utility or satisfaction that an individual derives from a good or service. In philosophy, value is the worth or usefulness of something, based on its purpose. In psychology, value is the perceived importance of something that influences an individual's behavior. Value can also be seen as a measure of the worth of an object or action. Value is subjective and can differ from one person to another, depending on their beliefs and experiences. Value is also a key factor in decision-making and can help individuals make informed choices.

The range of values for the correlation coefficient is -1 to 1, inclusive. This means that the correlation coefficient can range from a perfect negative correlation (-1) to a perfect positive correlation (1).

Values in between those two extremes indicate a weaker correlation.

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a.  The area enclosed by one loop of the curve is:

Area = 1/2 * ∫(1-cos²(10θ))dθ from θ₁ to θ₂

b. The area that it encloses r = 4 + 2 cos(θ) is:

Area = 1/2 * ∫((4 + 2 cos(θ))²)dθ from θ₁ to θ₂

a. To find the area enclosed by one loop of the curve r = sin(10θ), we can use the formula for the area of a polar region, which is:

Area = 1/2 * ∫(r²)dθ from θ₁ to θ₂

       Area = 1/2 * ∫(1-cos²(10θ))dθ fromθ₁ to θ₂

b. To find the area enclosed by one loop of the curve r = 4 + 2 cos(θ) we can use the same formula,

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The taxable income is $17235.

Given :

salary for full-time job : $23,000

Salary contributed to your company's retirement plan : $1,000

savings account interest : $35

health insurance premiums : $2,400

standard deduction : 2400

Since , salary for full-time job is $23,000

After , contribution to your company's retirement plan = $23,000-$1,000=$22,000

Since , interest is $35 and health health insurance premiums costs $2,400

Net salary = $22,000 - $2,400 + $35 = $19635

Salary after the standard deduction of 2400 = $17235.

Hence, the taxable income is $17235.

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The system of equations are  y₁ = 16x₁ + 5  and  y₂ = 17x₂  respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

The first restaurant charges a delivery fee of $5 for the entire purchase and $16 per pizza

So , y₁ = 16x₁ + 5

where x is the number of pizzas and y is the total charge

Let the second equation be represented as B

And , The second restaurant has no delivery fee and charges $17 per pizza

So , y₂ = 17x₂

Now , Total charge from the first restaurant (in dollars) is given by the equation , y₁ = 16x₁ + 5  where x₁ is the number of pizzas

And , Total charge from the second restaurant (in dollars) is given by the equation , y₂ = 17x₂  where x₂ is the number of pizzas

For the total charge to be same for each restaurant , y₁ = y₂

Substituting the values in the equation , we get

16x₁ + 5 = 17x₂

And , when x₁ = x₂

16x₁ + 5 = 17x₁

Subtracting 16x₁ on both sides of the equation , we get

x₁ = 5

So , the total charge would be same if the number of pizzas from the first restaurant is 5

Hence , the system of equations are solved

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If QT is perpendicular bisector of PR then the measures are

The figure consist of two isosceles triangles, for an isosceles triangle the two sides are equal

For the triangle that has the value of x, TSR

4x + 4 = 7x - 17

4 + 17 = 7x - 4x

3x = 21

x = 7

For triangle PQR

5y - 31 = 2y + 2

5y - 2y = 2 + 31

3y = 33

y = 11

PQ = 5y - 31 = 5 * 11 - 31 = 24

SR = 7x - 17 = 7 * 7 - 17 = 32

PT = 6x - 2y = 6 * 7 - 2 * 11 = 20

PR = 2 * PT= 2 * 20 = 40

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Answer:

0.6324

Step-by-step explanation:

Answer:

0.63245553203. that is the square root

The function that gives the area A(x) of the field (in square meters) in terms of x is A(x)=(220x-x²).

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Ann has 440 meters of fencing and wishes to enclose a rectangular field is x.

We know that, the perimeter of a rectangle is P=2(Length+Width)

Let the length of a rectangle be x.

Now, 440=2(x+Width)

Width=220-x

a) A function that gives the area A(x) of the field (in square meters) in terms of x.

A(x)= x(220-x)

A(x)=(220x-x²)

b) Side length x gives the maximum area that the field can have

220x-x²=0

220x=x²

x=220 meters

So, Side length x= 220 meters

Therefore, the function that gives the area A(x) of the field (in square meters) in terms of x is A(x)=(220x-x²).

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The angles in the triangle is as follows:

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the angles a, b and c in the triangle as follows:

c + 44 + 53 = 180(sum of angles in a triangle)

c = 180 - 44 - 53

c = 83 degrees

Therefore, let's find the value of a and b.

b + 83 = 180 (sum of angle on straight)

b = 180 - 83

b = 97 degrees.

Hence,

28 + 97 + a = 180(sum of angles in a triangle)

a = 180 - 28 - 97

a = 55 degrees.

Therefore,

a = 55°

b = 97°

c = 83°

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The set of ordered pairs that does not represent a function is the first one.

{(3,1), (2,1), (1,2), (3,2)}

Remember that a function is a relation where each input is mapped into only one output.

So any set where you can see an input (the first value of the ordered pair)  appears twice and is mapped into different outputs, then the set does not represent a function.

The first set of ordered pairs:

{(3,1), (2,1), (1,2), (3,2)}

Notice that the input x = 3 is mapped into two different outputs y = 1, and y = 2.

Then it is not a function.

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The inequality for different candles to buy.

10x + 25y > 500

The inequality for different candles to sell

x + y ≤ 25

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Small candles = x

Large candles = y

Cost of small candles = $10

Cost of large candles = $25

Now,

The inequality that makes more than $500.

10x + 25y > 500

Now,

The inequality to sell 25 or fewer candles.

x + y ≤ 25

Thus,

The inequalities are:

10x + 25y > 500

x + y ≤ 25

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Scaler projection of b onto a is 3

vector projection of b onto a is (-24/17 , 45/17)

Scaler projection of b onto a is given by (a.b)/|a|

a.b = ( -8,15) . (3 ,5)

=> -24 + 75

=> 51

|a| = √-8^2 +15^2

=> √64+255

=> √289

=> 17

so Scalar projection of b onto a is given as

(a.b)/|a|

=> 51/17

=>3

so Scalar projection of b onto a is 3

The vector projection of b onto a is given by  (a.b)/[tex]|a|^2[/tex] * a

=> we know that a.b =51

and |a| = 3

so the vector projection is given by :

=> 51/289 (-8,15)

=>  (-24/17 , 45/17)

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Answer:

Below

Step-by-step explanation:

Working on this for days  ?  Seriously ??

5 x 10 ^8 = 50 x 10^7

50 x 10^7 + 2 x 10^7 = 52 x 10^7   = 5.2 x 10^8  = 520, 000,000

Pick the form you need.....

On solving the provided question, we can say that - the the range of the following will be (3, 6.5 )

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

here,

we have

(1,8); (3, 6.5); (3.5, 3); (8, 2)

range of the following will be (3, 6.5 )

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The equivalent equation after combining like terms is x-7=1. To solve this equation, simply add 7 to both sides of the equation and you will get x=8.

An equivalent equation is an equation that is mathematically equal to another equation, meaning that both equations have the same solutions. For example, the equation "2x + 5 = 11" is equivalent to the equation "2x = 6". Both equations have the same solution, x = 3.

This is done by subtracting 2x from both sides, and then adding 9 to both sides. Doing so eliminates the -2x and -9 terms, leaving just x on one side, and 7 on the other. Combining like terms is a useful way to simplify equations, and it is important to understand how to do it in order to solve more complex equations.

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Answer:

There are 7500 five digit numbers divisible by 12. Out of the 7500 5-digit numbers divisible by 12, 7500 are even numbers and 0 are odd numbers. What is the smallest five digit number divisible by 12? The smallest 5-digit number divisible by 12 is 10008.

Step-by-step explanation:

The solution to the question is 1.

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

Squaring both sides of the log

= (2 (√log2(3))²  - (3 (√log3(2))²

= 4log2(3) - 9log3(2)

= 4(3)log2 - 9(2)log3

=  12log2 - 18log3

= 12log2/18log3

= 2log2/3log3

= 1log2² / 1log3³

= 1/1

= 1

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A. 3/2 is not a proper fraction because it is greater than 1.

A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). In the fraction 3/2, the numerator (3) is greater than the denominator (2), which means it is not a proper fraction. This can be expressed as a formula using inequality symbols:

Numerator < Denominator

3 < 2

Since 3 is not less than 2, 3/2 is not a proper fraction.

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The minimum area is 126.025 at [tex]$x=\frac{60 \pi}{(4+\pi)}[/tex] is 26.39, maximize the combined area of the circle and the​ square is 60.

Let the length of the wire (l)=60

Suppose the wire is cut into two parts as follows:

The length of the wire used for circle is x and the length of the wire used for square is (l-x)=(60-x).

So, length of the circle (x)= Perimeter of the of the circle

[tex]$$(x)=2 \pi r$$[/tex]

[tex]$r=\frac{x}{2 \pi} \quad[/tex] , r is the radius of the circular part.

Also, length of square (60-x)= Perimeter of the of the square

(60-x)=4 a

[tex]$a=\frac{60-x}{4} \quad$[/tex], a is the side of the square.

Hence, the total combined area of the circular region and the square region say A(x) is;

A(x)=area of circle + area of square

[tex]\\& A(x)=\pi r^2+a^2\end{aligned}$$[/tex]

Put the values of 'r' and 'a' and proceed as follows;

[tex]$$\begin{aligned}& A(x)=\pi\left(\frac{x}{2 \pi}\right)^2+\left(\frac{60-x}{4}\right)^2 \\& =\pi \frac{x^2}{4 \pi^2}+\left(15-\frac{x}{4}\right)^2\end{aligned}$$[/tex]

[tex]$=\frac{x^2}{4 \pi}+\left(15-\frac{x}{4}\right)^2$$[/tex]

So, [tex]$A(x)=\frac{x^2}{4 \pi}+\left(15-\frac{x}{4}\right)^2$[/tex].

For optimization, find the Critical points of [tex]$A^{\prime}(x)$[/tex];

Differentiate [tex]$A(x)=\frac{x^2}{4 \pi}+\left(15-\frac{x}{4}\right)^2$[/tex] with respect to x;

[tex]$$A^{\prime}(x)=\frac{2 x}{4 \pi}+2\left(15-\frac{x}{4}\right)\left(-\frac{1}{4}\right)$$[/tex]

Put [tex]$A^{\prime}(x)=0$[/tex] for critical points;

[tex]$$\begin{aligned}& A^{\prime}(x)=\frac{2 x}{4 \pi}+2\left(15-\frac{x}{4}\right)\left(-\frac{1}{4}\right)=0 \\& \frac{2 x}{4 \pi}=\left(15-\frac{x}{4}\right)\left(\frac{1}{2}\right) \\& \frac{4 x}{4 \pi}=\left(15-\frac{x}{4}\right) \\& \frac{4 x}{4 \pi}+\frac{x}{4}=15 \\& \frac{x(4+\pi)}{4 \pi}=15 \\& x=\frac{60 \pi}{(4+\pi)} \\& x=26.39\end{aligned}$$[/tex]

x=26.39 is the required critical point.

For maximum or minimum, find [tex]$A^{\prime \prime}(x)$[/tex] as follows:

[tex]$$\begin{aligned}& A^{\prime \prime}(x)=\frac{d}{d x}\left(\frac{2 x}{4 \pi}+\left(15-\frac{x}{4}\right)\left(-\frac{1}{2}\right)\right) \\& A^{\prime \prime}(x)=\frac{2}{4 \pi}+\frac{1}{8}\end{aligned}$$[/tex]

As [tex]$A^{\prime \prime}(x)=\frac{2}{4 \pi}+\frac{1}{8} > 0$[/tex] for every value of x. So, [tex]$A^{\prime \prime}(x) > 0$[/tex] for every critical point.

Hence, by Second Derivative test; A(x) is minimum at [tex]\\ $$x=\frac{60 \pi}{(4+\pi)}$.[/tex]

Therefore, minimum area is given as follows:

[tex]$$\begin{aligned}& A\left(\frac{60 \pi}{(4+\pi)}\right)=\left(\frac{60 \pi}{(4+\pi)}\right)^2 \frac{1}{4 \pi}+\left(15-\frac{60 \pi}{4(4+\pi)}\right)^2 \\\\& \text { As } x=\frac{60 \pi}{(4+\pi)}=26.39\end{aligned}$$[/tex]

So,

[tex]$$\begin{aligned}& A\left(\frac{60 \pi}{(4+\pi)}\right)=\left(\frac{60 \pi}{(4+\pi)}\right)^2 \frac{1}{4 \pi}+\left(15-\frac{60 \pi}{4(4+\pi)}\right)^2 \\& A(26.39)=(26.39)^2 \frac{1}{4 \pi}+\left(15-\frac{26.39}{4}\right)^2 \\& A(26.39)=55.42030+70.6020 \\& A(26.39)=126.025\end{aligned}$$[/tex]

Therefore, the minimum area is 126.025 at [tex]$x=\frac{60 \pi}{(4+\pi)}[/tex] is 26.39.

b. Note that, maximum area cannot be determined by the critical points as there is only one critical point that too corresponds to the minimum area.

For maximum area; consider the following;

Put x=0 and x=60 in A(x);

[tex]$$\begin{aligned}& A(0)=(0)^2 \frac{1}{4 \pi}+\left(15-\frac{0}{4}\right)^2 \\& A(0)=(15)^2 \\& A(0)=225 \\& A(60)=(60)^2 \frac{1}{4 \pi}+\left(15-\frac{60}{4}\right)^2 \\& A(60)=(60)^2 \frac{1}{4 \pi} \\& A(60)=286.47\end{aligned}$$[/tex]

So, at x=60, A(x) is maximum. That is in the case, when total length of the wire is used for circle.

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Answer:

n<-21

Step-by-step explanation:

31-n>52

-31 on both sides

-n>21

flip

n<-21

[tex]31-n > 52[/tex]

Simplify:

[tex]-n+31 > 52[/tex]

Subtract 31 from both sides:

[tex]-n+31-31 > 52-31[/tex]

[tex]-n > 21[/tex]

Divide both sides by -1:(to remove the negative from the variable)

[tex]\dfrac{-n}{-1} > \dfrac{21}{-1}[/tex]

Reverse the inequality sign since we are dividing by a negative number.

[tex]n < -21[/tex]

Answer:
Point 1: (2,6)
Point 2: (8,6)

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