Hey I need help understanding how to solve application problems involving rational equations

Answer:

1. Given

2. Vertical Angles Theorem (1st Occurrence)

3. Vertical Angles Theorem (1st Occurrence)

4. Transitive Property of Congruence

5. Converse of the Alternate Interior Angles Theorem

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Transitive Property of Congruence

If one pair of angles is congruent to a third angle, then the first angle is congruent to the third angle.

Converse of the Alternate Interior Angles Theorem

If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

[tex]\begin{array}{l|l}\vphantom{\dfrac12} \sf Statements & \sf Reasons \\\cline{1-2}\\1. \; \angle 2 \cong \angle 7 & 1.\; \sf Given\\\\2. \; \angle 2 \cong \angle 3 & 2.\; \sf Vertical\;Angles\;Theorem\;(1st\;Occurrence)\\\\3. \; \angle 6 \cong \angle 7 & 3.\;\sf Vertical\;Angles\;Theorem\;(2nd\;Occurrence)\\\\4. \; \angle 3 \cong \angle 6 & 4.\;\sf Transitive\;Property\;of\;Congruence\\\\5. \; a \parallel b & 5.\;\sf Converse\;of\;the\;Alternate\;Interior\;Angles\;Theorem\\\\ \end{array}[/tex]

From inspection of the given diagram, we can see that angles 2 and 3 are vertical angles, similarly angles 6 and 7 are vertical angles.  Therefore, the Vertical Angles Theorem applies.

According to the Transitive Property of Congruence,  if ∠2 ≅ ∠7 and ∠2 ≅ ∠3 and ∠6 ≅ ∠7 then ∠3 ≅ ∠6.

The two lines a and b are intersected by transversal [tex]\ell[/tex] so that the alternative interior angles 3 and 6 area congruent, then the lines a and b are parallel.  This is the Converse of the Alternate Interior Angles Theorem.

Answer:

The number 11.661903 rounded to the nearest hundredth is 11.66.

Step-by-step explanation:

We have the following number:

And we need to round this number to the nearest hundredth.

To determine that, we can proceed as follows:

1. Round a number to the nearest hundred is equivalent to rounding the number to two decimal places.

2. Now, we can see that the number in the third decimal position or thousandth place is 1:

3. If this number were 5 or greater than 5, we would need to round up that number to the next following number, that is, 7. However, this is not the case.

4. Therefore, if we have to round that number to the nearest hundredth, then the number is 11.66.

Hence, in summary, the number 11.661903 rounded to the nearest hundredth is 11.66.

(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)

Stay positive and Take care,

A fellow mate,

Cheers !

The value of the expression 3(4.1x - 3.9y) - 5 is 12.3x - 11.7y - 5.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, it should be noted that the expression is illustrated as:

3(4.1x - 3.9y) - 5

Open the parentheses

12.3x - 11.7y - 5

Therefore, the value of the expression is 12.3x - 11.7y - 5.

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a) The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2

b) The value of g'(x) = 2 The value of g''(x) =1

c) g has neither a relative maximum nor a relative minimum at x= 1

d) the graph of g has a point of inflection at each of x=-2 ,  x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

There are several types of functions in maths. Some important types are:

Injective function or One-to-one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

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Answer: hope it helps

Step-by-step explanation:

2 1/2 + x = 5 1/3

(2 + 1/2) + x = (5 + 1/3)

6x = 17

x = 17/

6

= 2.83333333

x = 17/

6

≈ 2.833333

[tex] \huge \underline{ \boxed{ \tt Solution: }}[/tex]

[tex] \tt \pink{\large\dagger} \: \: \: \: \: \: 2\dfrac{1}{2} + x = 5\dfrac{1}{3} \\ \tt : \implies \dfrac{5}{2} + x = \dfrac{16}{3} \\ \tt : \implies x = \dfrac{16}{3} - \dfrac{5}{2} \\ \tt : \implies x = \dfrac{16 \times 2}{3 \times 2} - \dfrac{5 \times 3}{2 \times 3} \\ \tt : \implies x = \dfrac{32}{6} - \dfrac{15}{6} \\ \tt : \implies x = \dfrac{32 - 15}{6} \\ \tt : \implies x = \dfrac{17}{6} [/tex]

[tex] \tt \pink{ \star \: Hence \: the \: answer \: is \: \dfrac{17}{6}.}[/tex]

Answer: it's still $100 because the beginning of the year hasn't started yet so you need to wait for the year to end so the 1 percent can be added

Step-by-step explanation:

The required range of the given function is -4  < y < 6.

Range, it is the set of values that come out to an outcome for certain mathematical operations.

Here,
A graph of a function is shown,
From the graph, it has been determined that,
The function is defined for domain -11 < x < -3.
As every value on the y- axis for the respective domain represents the element of range so,
The respective domain range of the function on the graph is -4  < y < 6.

Thus, the required range of the given function is -4  < y < 6.

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The value of a is 71°, and the value of b is 109°.

A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.

When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;

From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.

That is 180 - 71 = 109°

Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.

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The percent change in your salary is = 6%

Initial earning per hour =  $12.50

New earning per hour after the raise =  $13.25

The formula that we will be using to solve this question is -

= %change = [final value - initial value] ÷ [initial value] × 100

First, find the difference between the initial value and the final value

=  $13.25 - $12.50

=  $0.75

Divide the difference by the initial ( $12.50) value

=  $0.75 ÷ $12.50

=  0.06

Convert the quotient into a percentage

= 0.06 x 100

= 6%

Therefore, the percentage change in your salary is = 6%

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For the job paying $12.50 per hour, the percent change in your salary after the raise is 6%.

Given data:

Hourly increase:

= Hourly salary after the raise - Hourly salary before the raise

= $13.25 - $12.50

= $0.75

The percent increase is:

= (Hourly increase / Hourly salary before the raise) * 100

= ($0.75 / $12.50) * 100

≈ 6%.

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Answer: A

Step-by-step explanation:

A y-intercept is a point where a function (i.e a line) intercepts the y-axis.

Every point on the y-axis has a x value of 0.

The ordered pair will look like this (0,y)

In answer a, you have an x value of 0 with a corresponding y value of 3.

This point is (0,3).

You could also graph the points and look for where the function crosses the y-axis.

The upper bounds on the probability that Adam sent at least five emails during the time interval is [0, 1].

in math upper bound refers a number that is greater than or equal to any number in a set

Here we have given that, Adam logs in to an email server at time zero. He then spends his time exclusively on writing emails. His friend Brianna also logs in to the server at time 1 (which means 1 hour later) and starts typing emails independently of Adam.

And we need to find the upper bounds on the probability that Adam sent at least five emails during the time interval.

While we looking into the given question, we have identified that Adam Poisson process with a rate λ A/hour and Brianna Poisson process with a rate λ B/hour.

Here let us consider that Y1 and Y2 be the times at which Adam's first and second emails were sent.

Here we know that the Brianna logs in to the server, you are told that Adam has sent exactly one email so far.

So, here the upper limit while logging is 1. So, the lower limit is 0.

Because these is the real life scenario so the negative value is not applicable.

Therefore, the resulting interval is [0, 1].

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8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.

An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.

Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.

8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.

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The exact value of the tan(75°), found using trigonometric identities for the tangent of the sum of two angles, indicates that the exact value of tan(75°) is (1+√3/3)/(1 - √3/3))

Trigonometric identities are equalities of expressions that includes trigonometric functions which are valid for all values of the argument, or the domain of the function.

The exact value of tan(75°) can be found from the formula for the tangent of the sum of two angles as follows;

tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)•tan(B))

tan(75°) = tan(45° + 30°)

tan(45° + 30°) = (tan(45°) + tan(30°))/(1 - tan(45°)•tan(30°))

tan(30°) = √3/3

tan(45°) = 1

tan(45° + 30°) = (1 + √3/3)/(1 - √3/3)

tan(75°) = (1 + √3/3)/(1 - √3/3)

The correct option is therefore option B

[tex]tan(75 ^{ \circ } ) = \dfrac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } [/tex]

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let's take from the basic of one dolla!!!  how long for a buck to turn into two bucks at 4.5%?

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years \end{cases} \\\\\\ 2=1e^{0.045\cdot t} \implies \log_e(2)=\log_e(e^{0.045t})\implies \log_e(2)=0.045t \\\\\\ \ln(2)=0.045t\implies \cfrac{\ln(2)}{0.045}=t\implies 15.4\approx t\qquad \textit{about 15 years and 146 days}[/tex]

After using the quadratic equation the answer is [tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]

What is quadratic equation ?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

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

[tex]\frac{2\left(x-3\right)}{x-2}+\frac{2\left(3-x\right)}{x-1}+\frac{2-x}{1-x}[/tex]

[tex]\frac{2(3-x)}{x-1} + \frac{2-x}{1-x}[/tex]

[tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]

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The number line which describes the the measure of third side of the triangle must be greater than 10 cm is the second figure.

Number line is a straight horizontal line on which numbers are written in a certain intervals.

We can use number line for basic mathematical operations like addition, subtraction, division and multiplication.

Here the situation described is that measure of the third side of the triangle must be greater than 10 cm.

The inequality sign is '> 10'.

Since the inequality sign does not contain the equal to (≥) sign, the point 10 does not belong to this set.

So we will mark an open circle at the point 10 and draw a line afterwards.

Hence the second number line describes the situation that the third side of the triangle must be greater than 10 cm.

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Answer:

Step-by-step explanation:

the ability to hold, receive, store, or accommodate. : a measure of content : the measured ability to contain : volume. a beaker with a capacity of one liter.

Answer:

Capacity is the maximum amount that something can contain; Volume, or the amount that something can produce.

Capacity is a noun

Hope this helps

Answer: C.5/12

Step-by-step explanation:

Answer:

c.7.4

Step-by-step explanation:

<BDE=90°

Now,in RT.angled triangle BDE,

BD=√(BE)²-(DE)²

or, BD=√64-9

or,BD=√55

:.BD=7.41

Answer:

8.44 minutes

Step-by-step explanation:

The tank initially contained 105 liters so the amount of water needed is 181 - 105 = 76 litters

if the rate is 9 L/min then the number of minutes is

76/9 = 8.44 minutes

Answer:

1,258,925,411.79cm

Step-by-step explanation:

earth quake is measured with the Richter Scale,

R (Magnitue) = log (I / I°)

where I° is the base intensity to the Richter Scale and will be taken as 1

9.1 = log I

10^9.1 = I

thus,

intensity I = 1,258,925,411.79 cm

Answer:

x > –1/2

or x > –0.5

Step-by-step explanation:

2x + 8 > – 4x + 5

2x + 4x > 5 – 8

6x > –3

x > –3/6

x > –1/2

or x > –0.5

When 2x-4 = 6, the value of 3x + 2 is 17.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

When 2x - 4 = 6, the value of x will be:

2x - 4 = 6

2x = 6 + 4

2x = 10

Divide

x = 5

Therefore, 3x + 2 will be:

3x + 2 = 3(5) + 2

= 15 + 2

= 17

The value is 17.

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Answer:

A potential energy function is given by U(x) = (3.6)x + (1.2)x3. What is the force function F(x) that is associated with this potential energy function

Step-by-step explanation:

Answer:

y=7

Step-by-step explanation:

y is always the same and it is 7

At 300 miles the rental costs for Company A and Company B are the same.

An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.

Given :

Vehicle A: 150 + 0.5m = Cost A

Cost B = 60 + 0.8m for truck B.

Given that a one-day scenario was required by the challenge, the two equations are as follows:

Price B =60+0.8m Price A =150+0.5m

By combining the two equations, we get

150 + 0.5m = 60 + 0.8m.

150-60=0.8m-0.5m

90=0.3m

m=90/0.3

m=300 miles

Consequently, there are 300 miles in a day.

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From the given matrices, the values w,x,x and z are 5,-8,4 and -3 respectively.

Matrices is the rectangular arrangement of numbers and letters in rows and columns  

An equation is defined as a mathematical expression showing the equality of two sides of the statement

The given matrices are;

[tex]2\left[\begin{array}{ccc}w&2&\\5&z&\/\end{array}\right] -3\left[\begin{array}{ccc}2&x&\\-2&-6&\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]

Opening the brackets in the matrices

[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] -\left[\begin{array}{ccc}6&3x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]

Adding the Left hand side

[tex]\left[\begin{array}{ccc}2w-6&4-3x\\16&2x+18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y12&6\\\end{array}\right][/tex]

Equate Left hand side with Right hand side to form linear equations

2w-6=16

2w=10

w=5

4-3x=28

-3x=28-4

-3x=24

x=-8

16=4x

4=x

2z+18=12

2x=12-18

2x=-6

x=-3

These are how the various values are gotten

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The quotient will be = 2m^2 + 6m - 9m

The remainder will be = 0

Long division algorithm is below:

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Answer:

1.33333 , it just keeps going

Step-by-step explanation:

divide 4/3 you can use a long division or a calculator.

Hope this helps!!

The following given table with input and output is a function.

A relation between a domain and range is called a function when each value in the domain only has one value in the range. This notion is violated by relations that are not functions. They have at least one domain value that corresponds to two or more range values.

Into, onto, bijective and surjective are the types of function.

As every input has only one output so the given table is function.

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The following given table with input and output is a function.

What is function?

A function is a self-contained block of code that performs a specific task. It is a logical grouping of instructions and operations that can be used multiple times throughout a program. Functions help to keep code organized and modular, making it easier to debug and maintain. They also allow for code reuse, which can result in faster development times and greater efficiency. Furthermore, functions can be used to pass data between different parts of a program, making it easier to share information and reduce the need for redundant code.

Write names of type of functions.
Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.

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