How do you describe the nature of the roots of an equation?

The Factors of the given quadratic equation "3x² -x -4" is (3x - 4)(x + 1)  .

The Factors of a quadratic equations  is defined as the number which when multiplied together gives the original equation .

the equation is given as : 3x² -x -4 ;

writing it as equation ,

we get , 3x² -x -4 = 0 ;

To write the factors we use split the middle term method , we get ;

⇒ 3x² +3x -4x -4 = 0 ;

⇒ 3x(x [tex]+[/tex] 1) -4(x [tex]+[/tex] 1) = 0

⇒ (3x - 4)(x [tex]+[/tex] 1) = 0 ;

Therefore , the factors of the given equation will be (3x - 4)(x + 1) .

The given question is incomplete , the complete question is

What is the factor of the quadratic Equation 3x² -x -4 ?

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The system of inequalities is:

x + y ≤ 8      (1)

5x +8y ≥ 80    (2)

The graphical solution is attached and one possible solution is (-30,30).

What is inequality?

The relation between two unequal expressions is defined as inequality.

Given that, the person makes $15 per hour of lifeguarding and $8 per hour clearing tables.

It is also given that x represents the number of hours of lifeguarding and y represents the number of hours of clearing tables.

The person has at most 8 hours a week, therefore, it follows:

x + y ≤ 8      (1)

The earnings of the person in a week are:

15x + 8y

Since the earnings must be no less than $80, it follows:

15x +8y ≥ 80    (2)

Hence, the system of inequalities is:

x + y ≤ 8      (1)

5x +8y ≥ 80    (2)

The graphical solution is attached and one possible solution is (-30,30).

No, All equilateral triangles need not to be always congruent with one another .

Justification of answer:

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

1. All 3 side of an equilateral triangles have same length .

2. All 3 angles of an equilateral triangles have same measure.

3. Each angles of an equilateral triangles is 60 degree .

4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} * a^2[/tex]

5 . Perimeter of an equilateral triangles = 3*a

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The expression expressed as a single fraction is -2y(yx-2)/3x(yx+5)

You should know that simplification involves making an expression look more simpler than it was

The given expression is  2/(x+5/y)÷3/(y-2/x)

First of all let us express the denominator as a single fraction

x+5/y

⇒(yx +5)/y

In the same way express the expression y-2/x = (yx-2)÷x

By substitution we have

(-2)/yx+5)/(y/3)÷(yx-2/x)

⇒(-2y)/(yx+5) ÷ (3x/ (yx -2)

Simplifying this further to get

(-2y)/(yx +5) * (yx -2)/(3x)

⇒-2y(yx-2)/3x(yx +5)

In conclusion, the expression expressed as a single fraction is -2y(yx-2)/3x(yx+5)

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Correct question:

Which expression is equivalent to the following complex fraction? -2/x+5/y/3/y-2/x

Answer:the answer is

Step-by-step explanation:

just did the test

To easily recognize comparable triangles, you can apply three theorems that are peculiar to triangles.

Two triangles can be compared using one of three theorems: Angle-Angle (AA), Side-Angle-Side (SAS), and Angle-Angle-Side (SS-AS) (SSS).

The symbol representing two triangles with the same angles on all three sides is SSS, which stands for "side, side, side." If two triangles' third sides match those of another triangle, the two triangles are said to be congruent.

The SAS regulation states as much. If the two sides and included angle of one triangle match the two sides and included angle of another triangle, the triangles are congruent. Any angle formed by two specified sides is considered to be an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AA postulate of Euclidean geometry. The AA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

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Children should be able to recite the letters and alphabets typically by the age of three.

An alphabet is a standardized system of fundamental written graphemes that correspond to the phonemes of certain spoken languages. a group of letters or other symbols used to write one or more languages, especially if they are organized in a regular sequence. a set of symbols or signals used to represent letters.

Children should be able to recite the letters typically by the age of three. All kids, nevertheless, are unique. While some toddlers may learn when they are two, others might not begin until they are late in the third year. The majority of the time, repetition is how kids pick up the alphabet.

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Answer:

You could graph the points and recognize that it's a quadratic equation.

If you solve for the equation, it is clear that this table follows the relation:

[tex]f(x)=x^2-1[/tex].

Step-by-step explanation:

The picture attached shows the graph.

Answer:

Answer Below

Step-by-step explanation:

A rhombus is a quadrilateral with 2 diagonals.

Answer:

It's B, and the last one

Step-by-step explanation:

because 20% of omnivores like to exercise as opposed to the 14% of vegetarians.

Also about 16% of everybody LIKES to exercise, meaning more than 80% DON'T like to exercise

The two functions are inverse to each other if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Functions

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

inverse functions

the inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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The discriminant is 60 and the equation has two real roots with parabola intersecting x - axis at two points.

We are given that the equation is [tex]-3x^{2} +6x +2 = 0[/tex]

The formula for discriminant is given by

D = [tex]{b^{2} -4ac}[/tex] where the equation is of the form [tex]ax^{2} + bx + c = 0[/tex]

Therefore,

a = -3

b = 6

c = 2

Putting these values in formula of discriminant, we get

D = [tex]{6^{2} - 4(-3)(2) }[/tex]

D = 36 +24

D = 60

For the quadratic equation [tex]ax^{2} + bx + c = 0[/tex] , the expression D = [tex]b^{2} - 4ac[/tex] is called the discriminant.

The value of the discriminant shows how many roots does the quadratic equation has:

Now, since D = 60 > 0, we can say that the equation has two real roots and therefore, the parabola is intersecting the x-axis at two places.

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Answer:

52,81,8,926 anything that is not a decimal, fraction,or negative number

Step-by-step explanation:

The solution of the given system of equations 8x+3y=5 and 3x-2y=5 is x = 1 and y = -1

In this question we have been given a system of equations.

8x+3y=5                 ..........(1)

and 3x-2y=5           ..........(2)

We need to find the solution of the given system of equations.

As right hane side of both equations is equal, we equate LHS of both equations.

so, we get,

8x + 3y = 3x - 2y

⇒ 8x - 3x = - 2y - 3y

⇒ 5x = - 5y

⇒ x = - y                      .............(3)

By substituting x = - y in equation (1), we get,

8 ( - y ) + 3y = 5

⇒ - 8y + 3y = 5

⇒ - 5y = 5

⇒ y = - 1

Substitute above value of y in equation (3)

⇒ x = - (- 1)

⇒ x = 1

Therefore, x = 1 and y = -1 is solution of given equations.

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y = MX + b is the required linear graph formula.

Linear equations with two variables have straight-line graphs.

There are numerous ways to express linear equations: Y = mx+ b is the slope-intercept form.

The slope is m and the y-intercept is the point in an equation of the type y = MX + b, such as y = 2x 3. (0, b).

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0,

b).

Plot the y-intercept next.

3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.

Therefore, y = MX + b is the required linear graph formula.

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Answer: No, it is a horizontal line across -4 y

Step-by-step explanation:

The range is { -5, -3, 7 }

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). A function's range is the set of possible values that it can accept. The values that the function outputs when we enter an x value are in this set.

domain = x

range = y

when the domain is -1

y = 2(-1) - 3

y = -2 - 3

y = -5

range is -5

When the domain is 0

y = 2(0) - 3

y = 0 - 3

y = -3

range is -3

when the domain is 5

y = 2(5) - 3

y = 10 - 3

y = 7

range is 7

The range is { -5, -3, 7 }

The complete question is : What is the range of the function y=2x-3 when the domain is {-1,0,5}

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Answer:

{x element R : x!=-sqrt(5) and x!=0 and x!=sqrt(5)}

(assuming a function from reals to reals)

So b:)

Step-by-step explanation:

Add all of the numbers together and then divide that by how many numbers there are.

Mean mode formula  - Mean = {Sum of Observation} ÷ {Total numbers of Observations}

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

              A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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As per the concept of dot plot the team never scored exactly 2 goals in a single game.

In math the term dot plot which is also known as a strip plot or dot chart is referred as a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.

Here we have given that goals scored per game a dot plot going from 0 to 5. 0 has 3 dots, 1 has 2 dots, 2 has 0 dots, 3 has 5 dots, 4 has 3 dots, 5 has 8 dots.

And we need to find a true statement about the dot plot.

As we know that these types of charts are used to graphically depict certain data trends or groupings.

Here we know that the team never scored exactly 2 goals in a single game, based on this we can says the team never scored exactly 2 goals in a single game and the dot plot shows 0 dots in number 2.

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[tex]y = 5(3) {}^{x} [/tex]

The power of 2 is called a square due to the definition of the area of a square.

What are a square and Power?

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

The base number is the factor that is multiplied by itself, and the exponent is the number of times the same base number has been multiplied. Power is defined as a base number raised to the exponent.

The power of two is called a square.

The square function's name derives from the fact that a square with sides of length [tex]l[/tex] equals [tex]l^2[/tex] has a significant role to play in the definition of area.

The area is inversely proportional to size: the area of a form that is [tex]n[/tex] times larger is [tex]n^2[/tex] times larger.

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The equation 6p = 2(52p) getting no solution.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.

6p = 2(52p)

First, divide both sides by 2

6/2p = 2(52p)/2

3p= 52p

3= 52

No solution.

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The percent of the decrease in the average monthly revenue is 10%.

We can calculate the percent of the decrease by using the following formula:

The percent of the decrease = (previous revenue - current revenue) / previous revenue  × 100%

Last year, the average monthly revenue at the Cedarburg Times newspaper was $66,490.

This year, the average monthly revenue so far has been $59,841.

The percent of the decrease = (previous revenue - current revenue) / previous revenue  × 100%

previous revenue = $66,490.

current revenue = $59,841

The percent of the decrease = ($66,490 - $59,841) / $66,490 × 100%

The percent of the decrease = 6,649 / $66,490 × 100%

The percent of the decrease = 0.1 × 100%

Apply the multiplication operation, and we get

The percent of the decrease = 10%

Thus, the drop in the average monthly revenue is 10%.

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By examining the function's graph, there are four alternative techniques to decide if a limit is there.

1. if the graph has a hole in the line with a point for that value of x on a different value of y, then the limit DOES exist.

2. The limit still exists if there is a gap in the graph at the value that x is nearing and no other point for a different value of the function.

3. The limit does not exist if the graph exhibits a vertical asymptote, which is a pair of lines that approach the value of the limit and continue upward or downward without constraints.

4. The limit does not exist as x approaches a particular integer if the graph is approaching two different numbers from two different directions. There can't be two distinct numbers.

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Population of ants is 10,000 at the start of April. since then, it triples each month. Now, the calculated values become -

a) Table is complete below.

b) Notice that in every month there is an increase of 3 times population from month to month.

c) There are 8,10,000 ants in 4 months from April.

d) In the month of 6, there are 72,90,000 no. of ants.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population in statistics is the group of people from which a statistical sample is taken for a research.

Month since April                                   Number of Ants

         0                                                         10,000

         1                                                         30,000

         2                                                         90,000

         3                                                        270,000

         4                                                         810,000

Every month, the ant population triples so the multiply the previous population by 3 to find out the new population.

0 months from April = 10,000 × 1 = 10,000 ants

1 month from  April = 10,000 × 3 = 30,000 ants

2 months from April = 30,000 × 3 = 90,000 ants

3 months from April = 90,000 × 3 = 2,70,000 ants

4 months from April = 270,000 × 3 = 8,10,000 ants.

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The process of forecasting future expenses and savings is called financial planning.

Forecasting is the process of predicting future events or outcomes based on past data, trends, and other information. It is an important tool for businesses, allowing them to plan ahead and make informed decisions. Forecasting can help organizations anticipate changes in the market, anticipate customer demand, plan investments, and more. If done properly, it can help organizations achieve their goals and maximize profits.

Financial planning is the process of creating a budget, setting goals, and developing strategies to help manage money and reach financial goals. It includes estimating future income and expenses, assessing current financial resources, and creating a plan for spending, saving, and investing. Financial planning can help you to stay on track towards meeting your financial goals and create a secure financial future.

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Answer:

Step-by-step explanation:

To solve the equation 5(3+6a) = -15+6(5+5a), we need to use the rules of algebra to isolate the variable "a" on one side of the equation and simplify the other side.

First, we can distribute the 5 on the left side of the equation to obtain 53 + 56a = -15+6(5+5a). This gives us 15 + 30a = -15+6(5+5a).

Next, we can distribute the 6 on the right side of the equation to obtain 15 + 30a = -15+65 + 65a. This gives us 15 + 30a = -15+30 + 30a.

Now we can combine like terms on both sides of the equation to obtain 30a = -15 + 30, which simplifies to 30a = 15. Finally, we can divide both sides of the equation by 30 to obtain a = 0.5.

Therefore, the solution to the equation 5(3+6a) = -15+6(5+5a) is a = 0.5

Answer:

x = 26

Step-by-step explanation:

Angles ABC and CBD are supplementary, so they add up to 180.

(2x - 10) + (5x +8) = 180

7x - 2 = 180

7x = 182

x = 182/7 = 26

To find all pairs in an array of integers whose sum is equal to a given number, iterate through the array and for each element, check if there is another element in the array that, when added to the current element, is equal to the given number, and if such an element is found, add the pair (current element, other element) to a list of pairs; repeat this process until all elements in the array have been checked.

A group of objects, pictures, or numbers organized in rows and columns is known as an array. Arrays provide as concrete examples of multiplication concepts.

Arrays are needed in cases where you need  to store and manipulate large amounts of data efficiently.

Some of the benefits of using arrays include:

There are numerous techniques for locating all pairs in an integer array whose total is equal to a specific value. Here is one strategy you may employ:

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