//5. Use substitution to solve the system of equations
3x - y = 4
2x - 3y = 9
Solution: (
)

The two functions used to form the rational function are the ratio of two rational polynomial expression p and q.

A function is called a rational function if it can be expressed in terms of the ratio of p and q.

f( x ) = p( x ) / q( x )

They generally are made up of more than one part.

Each function has a domain and a co - domain , they generally tells us about the limits of the function. We can use the rational function to calculate the domain.

Rational function asymptotes are of 3 types which are known as ,

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9 more than a number in mathematical expression is written as n+9.

Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.

The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 10x-2 > 50].

Let the number be n,

More than signifies addition. Therefore, the expression would be n+9.

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Answer:

800 and 600

Step-by-step explanation:

1 train = 8 minutes

100 trains =8×100

= 800 minutes

1 car= 6 minutes

100 cars = 6×100

= 600 minutes

Answer:

1400 minutes / 23 hrs

Step-by-step explanation:

As per the concept of linear equation, the college student took 13 courses of 3 credit hours.

An equation in math is defined as a mathematical statement with an 'equal to' symbol between two expressions that have equal values

Here we have given that college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses

And we need to find number of students in each category.

While we looking into the given question, we have given the values like the following,

Here the total credits = 59

And the total courses = 18

Then let us consider the number of 3 credit hour courses is referred as x and the number of 4 credit hour courses referred as y

Then based on the given statement, we have written the equation as

=> x + y = 18 ----------------------------(1)

=> 3x+4y=59   --------------------------(2)

Here we have to eliminate y to find the number of 3 credit hour courses, by multiplying Equation 1 by 4

Then we get,

=> 4x + 4y = 72

Then we have to subtract Equation 2 from Equation 3

Then we get,

=> x = 13

Therefore, the resulting value is 13.

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Answer:

[tex]x=13\cos 25^{\circ}[/tex]

Step-by-step explanation:

[tex]\cos 25^{\circ}=\frac{x}{13} \\ \\ x=13 \cos 25^{\circ}[/tex]

Answer:

The height (AE) is 20 cm

Step-by-step explanation:

Volume = 1/3(area of the base) height

600 = 1/3(18 x 5)h

600 = 30h  Divide both sides by 30

[tex]\frac{600}{30}[/tex] = [tex]\frac{30h}{30}[/tex]

20 = h

Step-by-step explanation:

I cannot read what equation you wrote.

but it does not matter.

a quadratic equation has always 2 solutions.

as a cubic equation has always 3 solutions.

and so on.

sometimes they can be identical like for 0 = x² (with 0 as solution 2 times).

and sometimes they can be imaginary like in -1 = x².

but there always are 2 solutions for a quadratic equation.

for example with normal numbers :

1 = x²

the solutions are sqrt(1) = ±1 = +1 and -1.

A function is positive if the output values are greater than the input values and negative if the output values are less than the input values.

To determine if a function is positive or negative, you must first look at the output values of the function. If the output values are greater than the input values, then the function is positive. This means that the output values increase as the input values increase. Conversely, if the output values are less than the input values, then the function is negative. This means that the output values decrease as the input values increase. For example, if a function has an input value of 3 and an output value of 5, then the function is positive because the output is greater than the input. On the other hand, if the same function had an output value of 1, then the function would be negative because the output is less than the input. In summary, a function is positive if the output values are greater than the input values and negative if the output values are less than the input values.

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The number of CDs that Ingrid owns will be 28.

What is the equation's answer?

A direct consequence is the distribution of weights to the significant variables that result in the calculation's optimal.

Nearly twice as many CD promotions are in Brandon's possession than they are in Ingrid's. Brandon says he has 56 CDs.

Let 'x' represent Ingrid's CD collection. Then Brandon will have twice as many CDs.

The equation is then presented as,

Then the equation is given as,

2x = 56

Simplify the equation, then we have

2x = 56

x = 56 / 2

x = 28

The number of CDs that Ingrid owns will be 28.

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If the function f(x) = 5 + 3x and g(x) = 5 - 9x. The value of f(g(2))  is -34

The given functions are

f(x) = 5 + 3x and g(x) = 5 − 9x.

a. We plug-in 2 in the function g(x) and then the obtained image in the function

f(x)g(2) = 5 − 9 × 2

           = 5 - 18

           = -13

f(g(2)) = f(-13)

        = 5 + 3 × (−13)

        = 5 - 39

        = -34

b. We find the composite function by replacing x in f(x)  by  

g(x) f(g(x)) = 5 + 3g(x)

                = 5 + 3 × (5−9x)

                = 5 + 15 − 27x

f(g(x)) = 20 − 27x

f(g(2)) = 20 − 27 × 2

         = 20 − 54

         = -34

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Using the provided values for the points and the slope, With the formula of slope we can calculate the value of a = 14/5 =2.8 and the ratio as

1:1.49 .

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

point (1,a) divided line joined by  (-1,4) and (4,1).

Since, The slope between these points are same as they all line in a single line, we can ,

[tex]\frac{a-4}{1+1} = \frac{1-a}{4-1}[/tex]

3a-12=2-2a

5a=14

a=14/5 =2.8.

distance between (-1,4) and (1,2.8),

[tex]d1 = \sqrt{(1--1)^2 +(2.8-4)^2}\\=\sqrt{5.44}\\=2.33[/tex]

distance between (1,2.8) and (4,1),

[tex]d2= \sqrt{(4-1)^2 + (1-2.8)^2}\\=\sqrt{12.24}\\=3.49\\\\[/tex]

ratio = d1/d2

= 1: 1.49

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Answer:

5

Step-by-step explanation:

For this case, we have the following equation:

4/5x = 8

We must find a number that when multiplied on both sides of the equation, as a result:

x = 10x

So, if we multiply 8 * 5 = 40

Now, the left side must also be multiplied by 5 to not alter the equation:

(4/5)x*5=4x

x∗5=4x

Finally we have 4x=40

Clearing "x":

\begin{gathered}x = 40/4

x=10

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Answer:

7,0

Step-by-step explanation:

If there were two equation, one on top of the other, there would be infinitely many solutions. but here no solution

If there were two lines that intersected at one point, there would be one solution.

y=0 and y=-5 don't have any solutions. When you ask if a pair of equations have a solution, that means there is an intersection of the equations. The 2 equations will meet somewhere, and that is the solution. To find the solution, you set the equations equal to each other.

0≠-5

It is obvious that 0 and -5 are not equal to each other. Therefore, there is no solution. Also, y=0 and y=-5 are horizontal lines that are parallel to each other. They will never meet, which means there will be no intersection. No intersection means no solutions

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Answer: x=-4

Step-by-step explanation:

You can find this algebraically by either solving for the y-value of the vertex or by adding the two zeros and dividing by two.

In this case: (-5.581, 0) and (-2.419)

-5.581 + -2.419

= -8

-8/2 = -4

An example of perpendicular equations are:

f(x)=2x+4

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

A straight line passing through a point is called a perpendicular line. It forms a 90-degree angle with a specific place where the line passes. The need for determining the perpendicular line is coordinates and a line equation.

Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Rewrite f(x)= as y in step one, Swap X and Y in step one, then solve for y in step three.

Hence, Rewrite f(x)= as y in step one, Swap X and Y in step one, then solve for y in step three.

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Therefore, In the binary number 0 comes out to be false and 1 comes out to be true.

Binary code, the foundation of everything binary utilised in computing systems, provides a numbering system in which there are only two potential values for each digit: 0 or 1.

Here,

In this case, binary logic has two states: false and true. "binary" – It's critical that there be two of them.

If you want to, you can refer to them as 0 and 1, yes and no, or off and on if you're an electrical engineer. They function as intended.

Therefore, In the binary number 0 comes out to be false and 1 comes out to be true.

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Equation y = -3x is perpendicular to Y =- 3x - 4.

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. In every case, perpendicular lines cross or intersect. Any two perpendicular lines will always have an angle of 90 degrees.

Given

y = -3x - 4

Using slope intercept form.

y = mx + b

The reciprocal of the slope of the perpendicular line is negative.

By doing this, you alter the slope's sign to the opposite, in this case to 3. The slope of the perpendicular line is then equal to 1/3 by finding the reciprocal by flipping the denominator and numerator.

Equation y = -3x is perpendicular to Y =- 3x - 4.

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I don't see the picture. Can you send it in the message.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle. AAS congruence may be demonstrated with a few simple methods.

When two triangles in geometry are the same size and shape, they are said to be congruent. The Angle-Angle-Side (AAS) congruence theorem is one of several approaches to demonstrate that two triangles are congruent.

According to the AAS congruence theorem, triangles are congruent if two angles and the side that connects them in one triangle are congruent with two angles and the side that connects them in another triangle. This is how this theorem is expressed:

If ∠A = ∠E, ∠B = ∠F, and AB = EF, then ∆ABC ≅ ∆DEF

In other terms, triangles ABC and DEF are congruent if two angles and the side between them in triangle ABC are equivalent to two angles and the side between them in triangle DEF.

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The range is the set of all "y" values in an ordered pair, while the domain is really the set of all "x" values.

Keep in mind which ordered pairs are represented by the following symbols: (x, y).

A collection of ordered pairs isn't a function if an x value has had more than one y value associated with it, as as in the relation (4, 1), (4, 2), where the x value of 4 has y values of 1 and 2.

Thus,  If there is only one y-value for every x-value, then the relation is called a function.

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Function application is the process of applying a function to a domain-specific argument in order to get the relevant value from the function's range.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Apply is a function in mathematics and computer science that applies arguments to a function.An example of a rule is a function, which produces one output for a single input.

Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x. I submitted written applications to a number of businesses. For this position, a high school graduation is required. Teenage dropouts are not required to apply. Apply a second coat of paint to the wall once the first one has dried and been thinly applied.

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Saha uses 3 teaspoons of hot chocolate mix for every 8 ounces of milk. for 48 ounces of milk, he needs 18 teaspoons of hot chocolate.

The problem can be solved using unitary method or using ratio.

- Unitary method

Using this method, first, compute how many teaspoons of chocolate needed for 1 ounce of milk.

8 ounces of milk need 3 teaspoons of hot chocolate. Hence,

1 ounce of milk need 3/8 teaspoons of hot chocolate

48 ounce of milk need 3/8 x 48 = 18 teaspoons of hot chocolate

- Using ratio

Let p = number of teaspoons of hot chocolate needed for 48 ounces of milk. Then,

3 : 8 = p : 48

8p = 3 x 48

p = 3 x 48/8 = 3 x 6 = 18 teaspoons

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The mean of given data is 5.

To find: Mean of the given data

Given data: 5

Mean: Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here sum of observation is 5

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data

Total number of observation is 1

The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset

Now substitute the values in above formula

=[tex]\frac{5}{1}[/tex]=5

Therefore, the mean is 5.

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Yes, the given Relation is a Function.

Relation: It belongs to the Cartesian product's subgroup. Or just a lot of points (ordered pairs). In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets.

To Analyze a relationship between two values to see if it can be classified as a function:

1)Choose the input values.

2)Determine the results.

3)Consider the connection to be a function if each input value results in just one output value. Do not classify the relationship as a function if any input value results in two or more outputs.

In the given table all ordered pairs have unique x values so the given relation is a function.

Yes, the given Relation is a Function.

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A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer, so it is not considered a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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Answer: y=2/5x +5

Step-by-step explanation: slope is 2/5 y intercept is 5

Answer:

(a) 2

Step-by-step explanation:

We can assume this is a 3-4-5 triangle from the two given sides, 5 and 3(2--1) so then we know the y difference of the y coordinate should be + or - 4 from -2 giving us two solutions of 2 and -6 since this is a multiple choice and a is 2 he answer is 2