The sum of the reciprocals of two consecutive odd integers is 12/35. Find the two integers.

The solution of the system of linear equations is 6x + 7y = 594x + 5y = 41 is x = 4, y = 5.

A system of linear equations is a set of two or more equations with the same variables. To solve a system of linear equations, we can use different methods like substitution, elimination, or matrices.

To solve the system of linear equations:

6x + 7y = 59

4x + 5y = 41

One method is to use substitution. To use substitution, we can solve one of the equations for one of the variables and then substitute it into the other equation.

Solve the first equation for x:

6x + 7y = 59  

x = (59 - 7y) / 6

Substitute this expression for x into the second equation:

4((59 - 7y) / 6) + 5y = 41

118/3 - 14y/3 + 5y = 41

y/3 = 5/3

Solve the equation for y:

y = 5

Now use the value of y to find x in the first equation

x = (59 - 7(5))/6

= (59 - 35)/6

= 4

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The diagonal length of the fence is 89.44 units.

Square is a polygon which has 4 sides. All four sides of the square are equal length and perpendicular to each other, that means the angle between two adjacent side is 90°.

Given:

The area of the square field is 40,000 squared unit.

We want to but a fence diagonally through the field.

To find the diagonal:

The diagonal of square,

d=a√2, where d is the diagonal and a is the side of the square.

d = √(40000)√2

d = √(80000)

d = 89.44.

Therefore, the length of the fence is 89.44 units.

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Answer:

0.5

Step-by-step explanation:

The square root of x can be rewritten as [tex]x^{0.5}[/tex].

Therefore f(x) can now be written as

f(x)=4[tex]x^{0.5}[/tex], and so the power of the function is 0.5

Answer:

x and y are all real numbers

Step-by-step explanation:

Multiply the second equation by 2: 4x-6y=4

Now, we see:

4x - 6y = 4

4x - 6y = 4

Subtract the equations:

0 = 0

This is always true, so x and y are all real numbers!

The process of plotting the graph for the parent function on the calculator is explained below.

Here we have to define the process of  plotting the graph for the parent function on the calculator .

In order to plot these, we have to know the definition of parent function.

The term parent function is known as the functions may be classified and grouped into families and each of these groups each have one basic equation called a parent function.

And the parent functions have the U-shaped graph called the parabola and they all have a second degree with the highest exponent.

In order to plot the graph on the calculator, then the

First steps is to label the graph and then we have to set the x and y axis limit on the graph.

then the next steps is to input the function on the graph and makes the table for it.

Then label the table values on it.

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By evaluating a cost equation, we will see that Sam needs to pay $4.17

We know that one pound of chocolate costs $6.95, then we have the cost equation:

y = $6.95*x

Where y is the cost and x is the number of pounds of chocolate that you want to buy.

So, if you want to buy 0.6 of a pound, then we have x = 0.6

Then we can evaluate the equation to get:

y = $6.95*0.6

y = $4.17

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By using the substitution method, we will see that the solution of the system is:

x = -4.4

y = 14.4

Here we want to solve the system of equations:

y = -6x - 12

2x + 4y = -4

y substitution, we already can see that y is isolated on the first equation, so we can substitute it on the second equation to get:

2x + 4*(-6x - 12) = -4

2x - 12x - 48 = -4

-10x = -4 + 48

-10x = 44

x = 44/-10

x = -4.4

And the value of y is:

y = -6*-4.4 - 12

y = 14.4

That is the solution for the system.

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The solution of the system of equation is as follows:

x = -2 and y = 0

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

The system of equation can be solved using substitution method as follows:

y = -6x - 12

2x + 4y = -4

substitute the value of y in equation(ii)

Hence,

2x + 4(-6x - 12) = -4

2x - 24x - 48 = -4

-22x - 48 = -4

add 48 to both sides of the equation

-22x - 48 + 48 = -4 + 48

-22x  = 44

divide both sides by -22

x = 44 / -22

x = -2

let's find the value of y

y = - 6x - 12

y = -6(-2) - 12

y = 12 - 12

y = 0

Therefore,

x = -12 and y = 0

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The area of the shaded region is 198 ft2.

Area is a measure of the size of a two-dimensional region. It is a scalar quantity, meaning it is a single numerical value without any direction. Area is expressed in units such as square feet, square meters, hectares, acres, and square miles. Area is usually used to measure the size of a physical space. It can also be used to measure the amount of a certain material, such as soil or water, that is available in a given space.

The area of the shaded region can be determined by using the formula A = l x w. In this case, the length is 18 ft and the width is 11 ft. Multiplying these two measurements together gives us the result of 198 ft2. This is the area of the shaded region. To verify the answer, we can also calculate the area by subtracting the area of the unshaded triangle (19 ft x 12 ft / 2 = 114 ft2) from the area of the rectangle (19 ft x 12 ft = 228 ft2). This gives us the same result of 198 ft2.

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Total number of serving that David can do with the amount of spice currently present 8 servings.

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. :: or "=" are used to indicate proportions.

Comparing two integers that each stand for a component of a whole results in a percentage. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For example, 1/2 of 10 marbles is the same proportion as 1/2 of 50 marbles.

The ratio of rice to spice = 15: 1

The total spice David is having 40 gm

Total number of serving = 10

Amount of rice per serving = 75 gm

Amount of Spice required per serving = 75/15 = 5 gm

Total number of serving that David can do with the amount of spice currently present = 40/5 = 8

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k = 0 or k = 8, however k = 0 is not feasible if it exists. If not, the equation will only have one variable.

The right answer for an infinite solution is k = 8.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A two-variable equation with a line-shaped graph is said to be linear. The set of points in the coordinate plane that make up the graph of the linear equation are all the solutions to the problem.

Given equations exists kx + 4y = k - 4 and 16x + ky = k Thus, we have

[tex]$$\begin{aligned}& a_1=k, b_1=4, c_1=-(k-4) \\& a_2=16, b_2=k, c_2=-k\end{aligned}$$[/tex]

Here condition is [tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$[/tex]

substitute the values in the above equation, we get

[tex]$$\begin{aligned}& \Rightarrow \frac{\mathrm{k}}{16}=\frac{4}{\mathrm{k}}=\frac{(\mathrm{k}-4)}{(\mathrm{k})} \\& \Rightarrow \frac{\mathrm{k}}{16}=\frac{4}{\mathrm{k}} \\& \text { Also } \frac{4}{\mathrm{k}}=\frac{\mathrm{k}-4}{\mathrm{k}} \\& \Rightarrow \mathrm{k}^2=64 \\& \Rightarrow 4 \mathrm{k}=\mathrm{k}^2-4 \mathrm{k} \\& \Rightarrow \mathrm{k}=\pm 8 \\& \Rightarrow \mathrm{k}^2-8 \mathrm{k}=0\end{aligned}$$[/tex]

simplifying the equation, we get

[tex]$$\Rightarrow \mathrm{k}(\mathrm{k}-8)=0$$[/tex]

k = 0 or k = 8 but k = 0 exists not possible other wise equation will be one variable.

k = 8 exists correct value for infinite solution.

The complete question is;

Find the value of k for which the system of linear equation [tex]$\mathrm{kx}+4 \mathrm{y}=\mathrm{k}-4$[/tex] and [tex]$16 \mathrm{x}+\mathrm{ky}=\mathrm{k}$[/tex] has infinite solution.

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The system if there are fewer equations than variables has infinite solutions.

There are two types of system of equations - consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist.

Consistent system means a solution of the equation exists.

Now, a consistent system may have a unique solution or an infinite number of solutions where we need to assign an arbitrary value to a free variable to find its solutions.

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is an obvious solution to this system , its a consistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite number of solutions exist. There is no particular number of solutions.

Also, we see that (-1,1,0) is also a solution other than the zero solution.

We can clearly see that the number of unknown variables , x,y,z is 3 and the number of equations is 2.

Thus, The system if there are fewer equations than variables has infinite solutions.

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The domain of the function f(x)+4 is all real numbers, denoted as x.

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The  simplification of the radical expression gives  √(10×√(5))

A radical expression is an algebraic expression that contains a square root, cube root, or higher-order root. It is written with the radical symbol (√) before the number or expression being rooted.

√(5√(20)) can be simplified as follows:

√(5√(20)) = √(5√(4×5))

                 = √(5×√(4) × √(5))

                 = √(5 × 2 × √(5))

                 = √(10×√(5))

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The answer is 7 points per plane.

Points in math are a way of representing a position in space. Points are usually labeled using two numbers, usually called coordinates, which indicate the point's position on a two-dimensional plane. Each point can be described using an ordered pair of numbers, usually written as (x, y). Points are often used to graph equations, plot data, and describe lines and shapes.

This is because the first player scored 10 points per tank and 8 points per plane, while the second player scored 8 points per tank and 9 points per plane. Therefore, the difference in points per plane is 1 point (9 - 8 = 1). Since the difference in total points between the two players is 3 points (43 - 40 = 3), the difference in points per plane must also be 3 points (3/3 = 1). Therefore, each plane is worth 7 points (1 x 7 = 7).

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The net income or loss is transferred from the income statement to the trial balance.

Income statement is referred to as the statements of the money one or an organization has earned in a month or more broadly in an year.

It is used in corporate sectors and also in the field of accounting.

Trial balance can be considered as the balance where all the records are maintained for further tally of the balance sheet. When we are preparing financial accounts, the trial balance is used to identify and repair problems in those  accounting records. Generally , the trial balance is prepared at the end of an accounting period, such as a month or a year.

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Answer:

The domain would be All Real Numbers. And the range is y>0.

Step-by-step explanation:

You would just look at the graph and see that line goes infinitely so the domain(x) would be all real numbers. For range you just look at the y axis and figure out that all numbers are greater than 0.

If you need the answers in a different format, feel free to tell me.

a. i. The change in the number of years since 2000 is not proportional to the change in the Burger Company's profit. This is because the profit is increasing by a fixed amount of $3,500 per year, not a proportionate amount based on the number of years.

ii. The number of years since 2000 is also not proportional to the Burger Company's profit. This is because the profit is not directly related to the number of years, but rather is increasing by a fixed amount of $3,500 per year.

b. i. The change in the number of miles driven is proportional to the change in the total cost of the rental car because the total cost is directly related to the number of miles driven, with a cost of $0.05 per mile.

ii. The number of miles driven is proportional to the total cost of the rental car because the total cost increases in direct proportion to the number of miles driven, with a cost of $0.05 per mile.

c. i. The change in the number cups of flour is proportional to the change in the number of cups of sugar because for every 3 cups of flour, there is 1 cup of sugar.

ii. The number of cups of flour is proportional to the number of cups of sugar because for every 3 cups of flour, there is 1 cup of sugar.

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The standard form of a line equation is y = mx + b.   Since you need a line that is parallel to y = 5x - 2, the first thing to do is use the same slope (m), which is 5 in this case

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The missing parts of each quadrilateral and their types are:

i. x = 85^o

 Type of quadrilateral; Trapezoid

ii. x = 57^o

  Type of quadrilateral; Trapezoid

A quadrilateral is a given plane shape or figure on a 2 dimensional plane which is bounded by four straight sides. It has a series of types which are; square, rhombus, rectangle, trapezium etc. Each type of quadrilateral has individual differentiating properties.

In the given question, we have;

1. The sum of the internal angles of a quadrilateral is 360^o. So that:

109^o + 96^o + 70^o + x^o = 360^o

275 + x = 360

x = 360 - 275

  = 85

x = 85^o

The missing part is 85^o. And the type of quadrilateral is a trapezoid.

2. The sum of the internal angles of a quadrilateral is 360^o. So that:

94^o + 87^o + x^o + 122^o = 360^o

303 + x = 360

x = 360 - 303

  = 57

x = 57^o

The missing part is 57^o. And the type of quadrilateral is a trapezoid.

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If you deposit  $7500 in savings account with interest rate of 5.12% and interest is compounded monthly, then the approximate balance of this savings account be after 3 years is  $8742.5    .

the amount deposited in the savings account (p) = $7500 ;

the interest rate (r) = 5.12%  = 0.0512  ;

number of times interest is compounded (n) = 12 ;

time (t) = 3 years ;

the amount after  "t" years can be calculated by the formula , given as :

⇒ Amount = [tex]p\times (1+\frac{r}{n})^{nt}[/tex] ;

substituting the values ,

we get ;

⇒ Amount = [tex]7500\times (1+\frac{0.0512}{12})^{12\times 3}[/tex] ;

⇒ Amount = [tex]7500\times (1.00426)^{36}[/tex] ;

⇒ Amount = 8742.32584 ;

Amount ≈ $8742.5

Therefore , the approximate balance of this savings account be after 3 years is  $8742.5   .

The given question is incomplete , the complete question is

Suppose you deposit $7500 in a savings account that has an interest rate of 5.12%  .  If the interest is compounded monthly, what will the approximate balance of this savings account be after 3 years ?

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The slope of a line perpendicular to 3x + 2y = 6 and passes through the (2,3) is 2/3.

The slope-intercept version of the line's equation is what we need. In other words, we want y=mx+b in the form of ax+by=c. M is the slope and b is the y-intercept in the slope-intercept form.

The slope of the line parallel to the provided line is equal to the reciprocal of the supplied slope in the negative direction. Therefore, the slope is m=-1/m. The original equation is solved to produce the following result in general form:

Equation of line intercept form is

y=mx+c

3x+2y=6

2y=6-3x

y = [tex]\frac{6-3x}{2}[/tex]

y = [tex]\frac{3-3x}{2}[/tex]

y = -[tex]\frac{3x}{2}[/tex] + 3

the slope of the line is m = -3/2

Slope of line which is perpendicular to the given line = 2/3

The new line passes by (2,3)

Equation of new line is y = 2/3x + 3.

So, the slope of a line perpendicular to 3x + 2y = 6 and passes through the (2,3) is 2/3.

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The complete question is:

What is the slope of a Line perpendicular to 3x + 2y = 6 and passes through the (2,3)?

The value of K is 3.

Value is the worth of something, whether it be tangible or intangible. It is often measured in terms of money, but it can also take the form of respect, honor, or admiration. Value can also refer to the worth of something in terms of its usefulness, importance, or desirability. Ultimately, value is based on personal opinion, so it is subjective.

The graph of g(x) = (1/3)^x – h + k is obtained by translating f(x) = (1/3)^x horizontally by h units and vertically by k units. The vertical translation of 3 units will shift the graph of f(x) up by 3 units on the y-axis, which leads to a value of 3 for K.

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Answer:

-2

Step-by-step explanation:

1/3 x -6= -6/3 or -2

Multiply 1/3 by -6 and that gives you -6/3 or -2

The total interest that Gina will Earn on her deposit through the end of the fifth year is, $32.4.

The simple interest formula is I = Prt, where P is the principal (original amount of deposit), r is the interest rate, and t is the time in years.

In Gina's case, the principal is $150, the interest rate is 4%, and the time is 5 years.

To find the interest earned in the first year, we can plug the values into the formula:

     I = 150(0.04)(1) = $6

To find the interest earned in the second year, we calculate the interest on the original deposit plus the interest earned in the first year:

     I = (150 + 6)(0.04)(1) = $6.24

To find the interest earned in the third year, we calculate the interest on the original deposit plus the interest earned in the first and second years:

     I = (150 + 6 + 6.24)(0.04)(1) = $6.48

To find the interest earned in the fourth year, we calculate the interest on the original deposit plus the interest earned in the first, second and third years:

    I = (150 + 6 + 6.24 + 6.48)(0.04)(1) = $6.72

To find the interest earned in the fifth year, we calculate the interest on the original deposit plus the interest earned in the first, second, third and fourth years:

    I = (150 + 6 + 6.24 + 6.48 + 6.72)(0.04)(1) = $6.96

To find the total interest earned through the end of the fifth year, we add up the interest earned in each year:

   6 + 6.24 + 6.48 + 6.72 + 6.96 = $32.4

Therefore, Gina will earn a total of $32.4 in interest on her deposit through the end of the fifth year.

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The function f(7) value is 11.33.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(3) = 6

f(6) = 10

The linear function can be defined as,

f(x) = mx + c

Now,

m = (f(6) - f(3)) / (6 - 3)

m = (10 - 6)/3

m = 4/3

Now,

f(3) = 6

x = 3

So,

f(x) = mx + c

f(3) = 4/3 x 3 + c

6 = 4 + c

c = 6 - 4

c = 2

Now,

f(x) = (4/3)x + 2

For x = 7.

f(7) = 4/3 x 7 + 2

f(7) = 28/3 + 2

f(7) = 11.33

Thus,

The value of f(7) is 11.33.

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The pounds of hamburger Sofia will need to make hamburger patties for dinner is 6/5 of a pound

The quantity of hamburgers in each hamburger patties number of made by Sofia = 2/5 of a pound

The number of hamburger patties Sofia wants to make for dinner = 3

Number of pounds of hamburger will Sofia need for dinner = Quantity of hamburger in each hamburger patties made by Sofia × The number of hamburger patties Sofia wants to make for dinner

= 2/5 × 3

= (2 × 3) / (5 × 1)

= 6/5 of a pound

Hence, Sofia needs 6/5 of a pound of hamburger to make 3 hamburger patties for dinner.

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Therefore , the solution of the given problem of domain comes out to be  

(-∞,6 ) U (6,∞) and (+∞,-6 ) U (-6,-∞) .

The variety of potential arguments that a function can take is referred to as its domain. These numbers represent the cross of an f-like functional (x). A function's domain is the set of possible values that it can be applied to. This set includes the value the method returns following the insertion of the x value. Y = f is the equation for a functions with y and x serving as predictor variables (x). A variable is said to belong to the domain of a function when one specific value of y may be generated from one single value of x.

Here,

Given:

=> y / y-6 + 15/y+6

So,

the domain for first expression is :

=> y-6 = 0

=> y =6

Domain:

=> (-∞,6 ) U (6,∞)

the domain for second expression is :

=> y + 6 = 0

=> y = -6

Domain :

=> (+∞,-6 ) U (-6,-∞)

Therefore , the solution of the given problem of domain comes out to be  

(-∞,6 ) U (6,∞) and (+∞,-6 ) U (-6,-∞) .

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Answer:

20%

Step-by-step explanation:

There are several strategies for resolving systems of linear equations, including:

(1) Graphing Techniques

(2) The Substitution Method

(3) Using a linear combination

(4) The Matrix Approach

(1) Graphing Techniques: This is helpful if you only require a general answer or are confident that the intersection occurs at integer locations. Simply plot the two lines to determine their intersection.

(2) The Substitution Method: One linear equation for y must first be solved in terms of x. Then, in the other linear equation, replace y with that expression. You'll receive a formula in x. If you can solve this, you'll know the intersection's x-coordinate. Then, to determine the equivalent y-coordinate, insert x into either equation.

(3) Using a linear combination: In order for the x-terms or the y-terms to cancel out, add (or subtract) a multiple of one equation to (or from) the other equation. To obtain the other coordinate, first solve for x (or y, depending on which is remaining) and then substitute.

(4) The Matrix Approach: Actually, this is only a simplified notation of the Linear Combination method.

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