Why is it that algebra is important

The solution for the inequality is x∈(-∞,4)U(1,+∞)

What is inequality?

Inequality is a statement that compares two values and states that one value is greater than, less than, or not equal to the other value.

To solve the inequality (x-4)(x-1)>0, we can first factor it:

(x-4)(x-1)>0

We can then use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

So we get:

x-4=0 or x-1=0

x = 4 or x = 1

Now we will test the sign of inequality for x-4 and x-1.

x<4 or x>1

Hence, the solution for the inequality is x∈(-∞,4)U(1,+∞)

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Answer:

The expert answer is incorrect. Here's the correct answer.

Step-by-step explanation:

A plan with sufficient specifics to carry out a task or goal is called an action plan.

An action plan is a document used in project management that outlines the activities to take in order to accomplish the project's goals and objectives. Therefore, an action plan specifies the resources you'll need to achieve those goals, creates a timeframe for the tasks or action items, and establishes the team members you'll need to complete it all.

An action plan is a detailed checklist of the steps and materials required to finish a project or reach a goal. It can be viewed as a visual countdown to project completion or a list of tasks necessary to produce desired results.

A plan with sufficient specifics to accomplish a task or goal is called an action plan.

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Answer:

∠ G = 59°

Step-by-step explanation:

angles 1 and G are a linear pair and sum to 180° , that is

∠ 1 + ∠ G = 180°

121° + ∠ G = 180° ( subtract 121° from both sides )

∠ G = 59°

y=580(1.17)ˣ is the exponential equation used to model the quail population.

The mathematical expression f(x)=exp or ex denotes the exponential function. The term, unless specifically stated otherwise, generally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. A mathematical function with the following form is an exponential function: Where x is a variable and an is a constant known as the function's base, the formula is f (x) = an x. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

Here,

Aο=580

r%=17%

r=0.17

y=Aο(1+r)ˣ

y=580(1+0.17)ˣ

y=580(1.17)ˣ

The exponential model to model the quail population is y=580(1.17)ˣ.

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Answer:

The scale of the map is 1 cm: 0.5 km, which means that 1 cm on the map represents 0.5 km in real life.

If Birch Avenue is 3.2 cm long on the map, we can use this scale to find the actual length of the street. To do this, we can multiply the length of the street on the map (3.2 cm) by the scale factor (0.5 km/cm).

3.2 cm * 0.5 km/cm = 1.6 km

So, the actual length of the Birch Avenue is 1.6 km.

Answer:

x = 110°, z = 32°

Step-by-step explanation:

x + 70 = 180 (Exterior angles)

x = 110

4z - 58 + 110 = 180 ( Linear pair)

4z = 128

z = 32

Pls mark as brainliest if possible and cheers!

Answer:yo mom

Step-by-step explanation:

Angela has 15 cans

Brian has 8 cans

Carlos has 12 cans

Danielle has 0 cans

This question uses the comparison theory.

Step 1: Carlos has 12 cans.

Step 2: Brian has 4 fewer than Carlos, so Brian has 8 cans.

Step 3: Angela has 3x many than Brian, so Angela has 24 cans.

Step 4: Everyone has more than Danielle, so Danielle has 0 cans.

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The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.

the vertex of a quadratic function is. [tex]f(x)=a(x-h)^2+k, where (h,k)[/tex] is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.

Steps to plot graph of quadratic function.

a[tex]x^2[/tex] is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.

[tex]a(x+\frac{b}{2a} )^2[/tex] This is a horizontal shift of magnitude |[tex]\frac{b}{2a}[/tex]| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).

This transformation is a vertical shift of magnitude |[tex]\frac{D}{4a}[/tex]| units. The direction of the shift will be decided by the sign of [tex]\frac{D}{4a}[/tex]. The final vertex of the parabola will be at ([tex]\frac{-b}{2a} ,\frac{-D}{4a}[/tex]).

So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

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The weight of the flour pack used by the chef to make chicken nuggets is 0.04 pounds.

Quantity of flour used to make chicken nuggets by the chef = 0.28 pounds

If the chef used 1/7th of the pack of flour;

Quantity of flour used by the chef = 1/7 of 0.28 pounds

= 1/7 × 0.28

= 0.04 pounds

Therefore, the chef used 0.04 poundsof the flour pack

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D.0.125

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Step by Step Exlaination:

A spinner is divided into 8 parts.

Numbered as 9 to 16.

S={9,10,11,12,13,14,15,16}

n(S)=8.

A:probability of getting reater than 15.

A={16}

m(A)=1

p(A)=m(A)/n(S).

      = 1/8.

      =0.125

p(A)=0.125

Probability of getting greater than 15 is 0.125

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In the given geometric sequences, it is found that:

A. As the quotient between consecutive terms is the same, the data is a geometric sequence.

B. The recursive formula is:

f(n) = f(n-1)* 2 ^n-1, f(1) = 2

C. She will need a time of 1024 units to complete the 10th station.

When two consecutive words in a sequence have the same difference, the sequence is said to be arithmetic. The sequence is geometric if the quotient between related terms is the same.  

For item a:

When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.

For Item b:

The recursive formula for a geometric sequence with a common ratio  and the first term  is given by:

f(n) = f(n-1)* q ^n-1, f(1) = a

for our case

f(n) = f(n-1)* 2 ^n-1, f(1) = 2

For Item c:

The explicit formula for a geometric sequence with a common ratio  and the first term  is given by:

an  = a1 q^n-1

Hence, in this question:

an = 2(2)^n-1 = 2^n

For the 10th station:

a10 = 2 = 1024

Therefore, She will need a time of 1024 units to complete the 10th station.

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The inequality that is true is option D. Negative 1 greater-than three-fourths

An inequality is a statement in which two expressions or values are not equal to each other, but have a certain relationship, such as 3 + 4 > 7 or x + y < z. Inequalities can be represented by different symbols, such as <, >, ≤, ≥, ≠ which denotes "less than", "greater than", "less than or equal to", "greater than or equal to", and "not equal to" respectively

An equality, on the other hand, is a statement in which two expressions or values are equal to each other, such as 3 + 4 = 7 or x + y = z. It is represented by the symbol "=".

Therefore, the correct answer is as given above

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Answer:

29

Step-by-step explanation:

The total number of apps can be determined by multiplying the number of rows of apps by the number of apps in each row:

6*8 = 48

If she deleted 19 apps, then:

48-19 = 29 apps

Therefore if she deleted 19 apps she'd have 29 remaining.

Evaluating The function

f(x) = 8x - 3 ;

f(0) =  -3

f(4) =  29

f(-4) = -35

f(2) =  13

f(-3) = -27

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The collection of values that might result in a function's outputs is known as the co-domain.

The function

f(x) = 8x - 3

Evaluating

f(0) = 8 *0 - 3  = -3

f(4) = 8*4 -3 = 29

f(-4) = 8*(-4) -3 = -35

f(2) = 8*2 - 3 = 13

f(-3) = 8(-3) -3 = -27

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An interval on the graph above that is increasing include the following: B. -2 < x < 2.

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

On the other hand (conversely), if the output value (range) is decreasing when the input value (domain) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph above, we can reasonably infer and logically deduce that it is increasing over the interval -2 < x < 2.

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Team A won the competition by a narrow margin of 13 points.

Points in math are locations in the coordinate plane that can be described by an ordered pair of numbers. Points are often used to graph equations, draw diagrams, and find the solution to problems. Points can also be used to measure distances, angles, and other geometric objects. Points are an essential part of geometry, algebra, and other math topics.

Team A scored 13 goals and incurred 5 penalties, giving them a total of 8 points. On the other hand, team B scored 18 goals and incurred 12 penalties, giving them a total of 6 points. Therefore, team A won by a difference of 8-6=2 points.

It is important to note that any competition should be based upon fair play and sportsmanship. Foul play should not be allowed and all teams should be equally and fairly judged. Furthermore, proper rules and regulations should be implemented to ensure a fair and level playing field. The competition between teams A and B was a good example of how a competition should be conducted in a fair manner.

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Answer:

a d e

Step-by-step explanation:

Answer:

coefficient of xy^2 is : 864 and that of y^3 is 1728

Step-by-step explanation:

Using binomial theorem,

1st term is 1 (ax)^3 = 8x^3 from which a = 2

2nd term is 3(ax)^2(by) = -144x^2y from which b = -12

3rd term is 3(ax)(by)^2 = 3(2x)(-12y)^2 = 864

4th term is 1(by)^3 = 1(-12y)^3 = -1728y^3

The domain of the graph is D)(-∞,5].

What is domain of the function?

Domain is the set that contains all possible input values for the function. In a graph, it is given by the values of x.The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=[tex]x^2[/tex] and g(x)=1/x are all real integers with the exception of x=0.

In given graph we can observe horizontal extent of the graph is -∝ to 5. Then the domain of the graph is (-∞,5].

Thus the domain of the graph is D)(-∞,5].

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The areas in ascending order are: 0.004 m² (or 40 cm²), 3.7 cm², 41 cm², and 420 mm² (or 0.42 cm²).

What is an ascending order?

Ascending order is the arrangement of a set of numbers or data in a sequence from smallest to largest. It is a way of organizing data in increasing numerical or alphabetical order. For example, the numbers 1, 2, 3, 4, 5 in ascending order is a sequence where each number is greater than the previous one. Similarly, arranging words in alphabetical order from A to Z is also an example of ascending order.

The areas in ascending order are:

0.004 m² = 40 cm²

3.7 cm²

41 cm²

420 mm² = 0.42 cm²

So, the areas in ascending order are: 0.004 m² (or 40 cm²), 3.7 cm², 41 cm², and 420 mm² (or 0.42 cm²).

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The distance between any two points is represented by the length of the line segment separating them. The two locations are connected by a solitary line.

The length of the line segment connecting any two points represents the distance between them.

There is just one line that connects the two places.

Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.

The length of the line segment is the separation between two points.

Congruent segments are those that are the same length.

By using a ruler to construct a line, we may determine how far apart two points are from one another.

Therefore, the distance between any two points is represented by the length of the line segment separating them. The two locations are connected by a solitary line.

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The side that is opposite to the 60° angle, BC = y × √3 = y√3 will be the medium length.

What is angle ?

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

A 30-60-90 triangle is a special triangle since the length of its sides is always in a consistent relationship with one another.

In the below-given 30-60-90 triangle ABC, ∠ C = 30°,∠ A = 60°, and ∠ B = 90°. We can understand the relationship between each of the sides from the below definitions:

The side that is opposite to the 30° angle, AB = y will always be the smallest since 30° is the smallest angle in this triangle

The side that is opposite to the 60° angle, BC = y × √3 = y√3 will be the medium length because 60° is the mid-sized degree angle in this triangle

On the side that is opposite to the 90° angle, the hypotenuse AC = 2y will be the largest side because 90° is the largest angle.

The side that is opposite to the 60° angle, BC = y × √3 = y√3 will be the medium length.

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The simplest form of the equation, y = 23x + 68, is the same equation of y = 23x + 68, as this is the simplest form.

y = 23x + 68 is a linear equation that it in the slope - intercept form which means that there is no need to simplify it further.

The slope - intercept form is:

y = mx + b

Where:

m = slope of the line

b = y - intercept of the line

The equation shows that the slope is 23 and that the y - intercept is 68. This means therefore , that the equation is as simple as it can be.

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a) 7x

b) 2a + 6b

c) -3b + 7d + 3bd

d) 7ab - 2ac - c

e) 16a + 6

f) 26x - 2

g) 4b + 1

h) -5j - 10

i) 2g + 7

Enrique's statement some numbers have an odd number of factors is correct

Rob's statement was that the factors of a number is always an even number, while Enrique's admitted that odd number can be involved

A factor refers to a number that divides another number without remainder.

The statement can be verified by finding a number that will have both odd and even factors.

Let the number be 40

factors of 40 : 1, 2, 4, 5, 8, 10, 20 and 40.

5 is and odd number and 8 is even number and 5 * 8 = 40

Because of this, it is right to say that  Enrique is correct

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Applying the triangle proportionality theorem, the length of AD that will make DE║AB is: AD = 60.

According to the triangle proportionality theorem, the equation or proportion we can create to find x is expressed as:

(2x - 4) / 5x = 3x / 8x

Cross multiply:

8x(2x - 4) = (3x)(5x)

16x² - 32x = 15x²

x² - 32x = 0

Solve to find x by factoring:

The equation x² - 32x = 0 can be solved by factoring:

x(x - 32) = 0

So either x = 0 or x - 32 = 0, meaning x = 32.

The solutions to the equation are x = 0 and x = 32.

Using x = 32:

AD = 2x - 4 = 2(32) - 4

AD = 60

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The volume of this prism is 3150 cm³.

step1:

given 11cm, 19cm, 14cm, 11cm

To find: volume of given prism

the given prism is combination two prism

Triangular prism

cuboidal prism

volume of cuboidal prism =l*b*h

                                          =(15*14*11) cm^3

                                           =2310cm^3

step2:

volume of triangular prism=1/2*l*b*h

                                           =1/2*15*8*14    

                                            =840cm^3

step3:

volume of given prism=volume of cuboid + volume of triangular prism

                                     =(2310+840)cm^3

                                      =3150cm^3

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There are three ways to solve systems of linear equations in two variables graphing ,substitution method ,elimination method.

What in mathematics is a linear equation?

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.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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Answe

Step-by-step explanation: