By applying the Zero Product Property, which asserts that if the product of two numbers equals zero, then at least one of the quantities must also equal zero, quadratic equations in factored form can be solved.
Any factored quadratic equation, such as (a + b)(a b) = 0, can be solved using the Zero Product Property. If a+b=0, then either an or b must also equal zero, according to the zero product property. We can solve problems like (x+2)(x-5)=0 thanks to this fundamental characteristic.
According to the zero product property, if the sum of two quantities is zero, then either one or both of the quantities must also be zero. This equation can be rewritten as (x + 3) (2 x 1) = 0 to help you solve it.
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You are trying to save $540 for your trip to New York. You started with $54 that you saved up and you earn $9 per hour of babysitting. How many hours will you have to babysit in order to have the money you need?
Answer:
54 Hours
Step-by-step explanation:
first of all 540-54 he started with is 486 and 486/9 is 54 since you get 9 per hour
Answer: 54 Hours of babysitting
Step-by-step explanation: 540-54=486 Then you take 486 and you divide it by 9 to see how many hours you have to work and that would be 54 hours.
How do you graph inverse operations?.
The inverse operations can be graphed by determining the inverse of the function by swapping the x and y variables,
Not all functions have inverses, and in order for a function to have an inverse, it must be a one-to-one function that is, there must not be repeated output for many inputs which indicates that not all functions have inverses. The various steps to graph inverse functions can be noted as -
By switching the x and y variables, first determine the function's inverse, and then solve for y. The inverse function, for instance, will be x = f-1 if the original function is y = f(x) (y).By switching the original function's x and y values, plot the inverse function's points. For instance, if the original function is y = 2x + 1, the inverse function would be x = (y-1)/2, and instead of plotting the point (0,1), you would plot (1,0), (2,-1) and so on (-1,2)Over the line y = x, reflect the original function's graph. You will then be shown the inverse function's graph.Lastly, it is required to correctly identify the axes and the points.Read more about inverse operations on:
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What does ∑ ∑ mean?.
The mathematical symbol ∑∑ is used to represent a double summation. It is a way of expressing the sum of two series of numbers.
Double summation is a way of expressing the sum of two series of numbers, written as ∑∑. The upper sigma symbol represents the outer summation, while the lower sigma symbol represents the inner summation. The two series of numbers that form the double summation can be related or unrelated.
The double summation is written in the following form: ∑∑ aij, where aij is an element from the two series of numbers, i and j are the upper and lower limits of the double summation, respectively.
This type of expression is used to find the sum of a set of numbers that are related to each other in some way, such as the sum of the elements in a matrix or a table, or the sum of two series of numbers that are not related. The double summation is a useful tool for expressing the sum of two series of numbers and is widely used in mathematics and science.
Complete answer:
What does ∑∑ mean?
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What is the range of the function f x − x 3 2 7?.
Answer:
Step-by-step explanation:
nhbjbjhbnjbjnjnjny6778899
Use the vertical line test to determine if the graph represents a function.
The graph that depicts a function is graph when the vertical line test is used (b).
What is meant by vertical line test?By visually counting the number of times the curve crosses vertical lines, the vertical line test is a graphical approach for verifying whether a curve in the plane accurately depicts the graph of a function. the graph of a function can only be intersected by any vertical line in the plane once as a result.
A graph must satisfy the vertical line test in order to be considered a function representation. The vertical line test requires that the line from the x-axis only once crosses an associated y-value.
Graphs (a), (c), and (e) fail the vertical line test, indicating that they do not reflect a function.
So, graph is the name of the graph that represents a function (b)
The complete question is:
Use the vertical- line Test to determine which graph represents a function? I'm thinking it's the first one...
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A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 12400 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of
120-kilogram crates that can be loaded onto the shipping container?
Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is 8000 + 120C <= 27500
What is inequality?An inequality is a relationship that allows us to contrast two or more mathematical expressions.
Knowing that;
Each carton weighs 120 kg.
The container's maximum weight when loaded is 27500 kg.
Weight of the container as it is currently loaded: 8000 kg
Now that we have merged, we have;
Solution
because 8000 grams have already been loaded kilograms
into the container
each crate weighs 120 kilograms.
so 8000 + 120C <= 27500
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How do you find the equation of a function in factored form?.
Using factoring, we do the following actions to make rational expressions simpler:
As much as you can, factor the numerator and denominator. Any factors that appear in both the numerator and the denominator should be eliminated. Your expression gets simplified as a result. How is an expression factorized:
Step 1 is to identify the expression's prime factors.
Step 2: Find the GCF by enclosing the common factors.
Write each term in the expression as a combination of the GCF and the final factor in step 3.
Step 4: Simplify the equation by applying the distributive property.
Y=12(x-6)(x+2) is an illustration of a quadratic function in factored form. This shape can be examined to determine the vertex as well as the graph's x-intercepts.
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the slope-intercept form is used to write a linear equation.
Attendance i decreaing at a rate of 0. 5% per year. If there are 1200 people attending now how many will be attending in 4 year?
So, in 4 years, there will be 1176 people attending.
To find out how many people will be attending in 4 years, you need to determine the total decrease in attendance over that time period. The attendance is decreasing at a rate of 0.5% per year, so over 4 years, the decrease in attendance will be 4 years x 0.5% = 2%
To find out how many people will be attending in 4 years, you can then subtract the 2% decrease from the current attendance of 1200 people:
1200 x (1 - 0.02) = 1176 people
So, in 4 years, there will be 1176 people attending.
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You must ascertain the overall drop in attendance over that time span in order to calculate the number of attendees in 4 years. If enrollment drops by 0.5% annually, it will drop by 2% over the course of four years (4 years x 0.5%).
Then, from the present attendance of 1200 people, subtract the 2% decline to determine how many attendees there will be in 4 years:
1200 times (1-0.02) ≈ 1176 individuals
Therefore, there will be 1176 attendees in 4 years.
Write y = 2x + 5 in standard form
The equation y = 2x + 5 is already in standard form.
Standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B cannot be both zero. In this case, A=2, B=1 and C=5, which meets the standard form equation, y = 2x + 5 is already in standard form.
Answer: y = 2x + 5 in standard form is 2x - y = -5
Step-by-step explanation: I hope this helps!
Rewrite f(x)= x as a piecewise function
The piecewise function will be written as y= -x { x < 0 } and y = x { x > 0 }.
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
Given that the function is f(x)= x. The piecewise function of the given function will vary from x being less than zero and x being greater than zero. The function can be written as y= -x { x < 0 } and y = x { x > 0 }.
The graph of the piecewise function of the given function is attached with the answer below.
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Mateo is making bookmarks with different colored ribbon.The amount of color he has is shown in the table.Each bookmark will be 1/6 yard long.How many more orange bookmarks can he make than aqua bookmarks.
color length(yd)
Aqua 3/4
orange 9/10
yellow 15/16
use reciprocals pls
The orange bookmarks that Mateo can make than aqua bookmarks is 1.
How to calculate the number of bookmark?Based on the information given, let x = number of aqua bookmarks
(1/6) × x = 3/4
x = (3/4) × (6/1)
x = 18/4
x = 4.5
Rounding down shows that we can make 4 aqua bookmarks.
y = number of orange bookmarks
(1/6)y = 9/10
y = (9/10)*(6/1)
y = 54/10
y = 5.4
This rounds down to 5 orange bookmarks.
Therefore, Mateo can make 5-4 = 1 extra orange bookmark compared to aqua.
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Mateo is making bookmarks with different colored ribbon. The
amount of each color he has is shown in the table. Each bookmark
will be yard long. How many more orange bookmarks can he make
than aqua bookmarks?
Table:
Color: Length (yd):
———————————-
Aqua. 3/4
Orange. 9/10
Yellow. 15/16
explicit formula 9,15,21,27
Answer:
n_(n-1)+6
Step-by-step explanation:
n_(n-1)+6
im pretty sure?
What is a solution set called?.
The solution sets are called algebraic sets.
An algebraic set is the locus of zeros of a collection of polynomials, and it is the set of solutions.
A solution set is a set of values that satisfy a given set of equations or inequalities.
The set containing all the solutions of an equation is called the solution set for that equation. If an equation has no solutions, we write ∅ for the solution set. ∅ means the null set.
A linear system with a unique solution has a solution set with one element. Solution sets are a challenge to describe only when they contain many elements.
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What is the solution to the system of equations y equals 1. 5 x 4 and y equals negative x?.
The solution to the system of equations is y equals 1. 5 x 4 and y equals negative x is-= (1.6,-1.6)
In this case option A is correct
The coordinates of the ordered pair (s) that satisfy all of the equations in the system are the solution set to a system of equations. To put it another way, those x and y values will make the equations true. As a result, when a system of equations is graphed, the intersection points of the graphs are the system's solution.
y = 1.5x – 4...........(1)y = –x...........(2)-----------------------Since equation 2's y is -x, we can substitute this into equation 1 as follows: y = 1.5x - 4 -x=1.5x-4 -2.5x=-4 x=1.6Now, when x=1.6, equation 2's result for "y" is -1.6. (1.6,-1.6)To know more about solutions here
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What is the solution to the system of equations y equals 1. 5 x 4 and y equals negative x?.
(1.6,-1.6)(1.5,-1.6)(1.6,-1.5)0+12 Coins Earned
Will the quotient of the division problem shown below be positive or negative?
(-8) ÷ (-4)
Answer: Positive
Hope this helps :)
Step-by-step explanation:
When multiplying or dividing with two negative numbers, the product/quotient will always be positive.
-8/-4 = 2
Answer: Positive
Step-by-step explanation:
Example for multiplication:
Imagine 4 friends that owe you $8 each.
Each friend that pays you back represents their payback as -$8.
-$8 * 4 friends = -$32 that they owe you.
The moment they give it back, you now have +$32. The Debt was taken away.
Example for Division:
Imagine splitting 8 dollars in debt with 4 friends, each friend then has $2 in debt. Each payback means you have +$2.
Another visual way to think of this is with Number Lines.
On a number line, when you multiply by a larger absolute value the numbers get bigger and go farther away from 0. So, taking a negative and multiplying it by a positive makes it MORE negative, as opposed to multiplying it by negative and then it reflects the number line,
What is the inverse of 7 *?.
The inverse of 7 is 1/7.
A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1.
The reciprocal of a and 1/a.
For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1.
Multiplicative inverse:
The multiplicative inverse of a number can either be expressed as a fraction or as a number raised to the power of a negative one. A number multiplied by its multiplicative inverse is one.
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a total of 516 tickets were sold for the school play. they were either adult tickets or student tickets. there were 66 more student tickets sold than adult tickets. How many adult tickets were sold
In the word problem the number of the adult ticket is 225.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here total number of tickets = 516.
Which is contains adult and students tickets. Then let us take x is number of adult ticket and y is number of student tickets then,
=> x + y = 516 ------> 1
Now there were 66 more student tickets sold than adult tickets then
=> y = x+66 -----> 2
Now put 2 into 1 then
=> x+66+x = 516
=> 2x = 516-66 = 450
=> x = 225.
Now put x = 225 into then
=> y = 225+66 = 291.
Hence the number of adult tickets is 291.
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Does 6 8 15 form a triangle?.
No, it is not possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(6cm + 8cm) =15cm
14cm = 15cm
LHS<RHS
A triangle is not possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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What angle has 120 degrees?.
An obtuse angle has 120 degrees in them.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Any angle more than 90 degrees is called obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
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PLEASE HELP ASAP
which expression can be used to find the sum of the polynomials?
The correct expression to solve te sum of polynomials is [(-3x)+(-8x)]+4x+[9+5] (D).
To solve any polynomials problems, it is important for us to take a close look on the orders of each number. For the sum and substraction operation, we need to categorize each number based on its orders.
From the case, we have a problem as:
(9 - 3x²) + (-8x² + 4x + 5)
We can categorize each order:
Order 2 = (-3x²) and (-8x²)
Order 1 = 4x
Order 0 = 9 and 5
Hence, we can solve the problem as:
(9 - 3x²) + (-8x² + 4x + 5)
= [(-3x²) + (-8x²)] + 4x + (9 + 5)
= -11x² + 4x + 14
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What are the possible ways in which two consecutive odd numbers are added to sum of 2023?
Possible way in which two consecutive odd numbers are added to sum of 2023 is by evaluation using the formula (2n - 1) + (2n + 1) = 2023, so that we have 1010.5 + 1012.5 = 2023
What are consecutive odd numbersConsecutive odd numbers are a sequence of numbers that are separated by a difference of 2 and are all odd numbers. For example the first four odd numbers are: 1, 3, 5, and 7. Odd numbers can be generated using the formula 2n -1.
We shall represent the first odd number with (2n - 1) so that the two consecutive odd numbers will be expressed as:
(2n - 1) + (2n + 1) = 2023
2n + 2n = 2023
4n = 2023
n = 2023/4 {divide through by 4}
n = 505.75
Therefore the two consecutive odd numbers added to sum of 2023 are derived as:
2(505.75) - 1 = 1010.5 and 2(505.75) + 1 = 1012.5
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Answer: Well, let’s consider a number, [math]n[/math], it could be even or odd, it doesn’t ...
Step-by-step explanation:
Why are complex fractions called complex?.
Complex fractions are called complex because they contain one or more fractions within the numerator and/or denominator of the fraction. These fractions within the fraction make the fraction more complex or difficult to simplify than a regular fraction, which only has a single numerator and denominator.
The term "complex" in mathematics often refers to something that is composed of multiple parts or layers, and that requires more steps or understanding to work with or solve.
In this case, the presence of one or more fractions within the fraction makes it more complex than a regular fraction, hence the name "complex fraction."
Another reason for the term complex is that the fractions in the numerator and denominator may have different or even the same variables, making it difficult to cancel them or simplify the expression.
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How many solutions does Y =- 3x 5 have?.
The given equation y = -3x + 5 has infinitely many solutions.
We have linear equation y = -3x + 5
We need to encounter how many solutions can satisfy the given equation.
We know that,
y = -3x + 5 is a linear equation in two variables in the form ax + by + c = 0
For x = 0, y = 0 + 5 = 5. Therefore, (0, 5) is one solution.
For x = 1, y = -3 × 1 + 5 = 2. Therefore, (1, 2) is another solution.
For y = 0, -3x + 5 = 0, x = 5/3. Therefore, (5/3, 0) is another solution.
Clearly, for different values of x, we get different values for y. Thus, any value substituted in the place of x in the given equation will form another solution for the given equation. So, there is no limitation to the number of different solutions obtained by substituting real values for x in the given linear equation. Thus, a linear equation in two variables can have infinitely many solutions.
Thus, y = -3x + 5 has infinitely many solutions.
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Chandler, the owner of a boutique, kept track of which sizes were worn by the store's customers. small 3 medium 32 large 22 What is the experimental probability that the next customer to come into Chandler's boutique wears a size small? Write your answer as a fraction or whole number.
The experimental probability that the next customer to come into Chandler's boutique wears a size small is; 1/19
How to find the experimental probability?Theoretical probability is defined as the term used to describe what we expect to happen based on math theory, while experimental probability refers to what actually happens when the actual situation is tried out as an experiment.
In this question, we are given;
Number of small wears = 3
Number of medium wears = 32
Number of large wears = 22
Thus;
Total number of wears = 3 + 32 + 22
= 57
Probability that next customer wears small size = 3/57 = 1/19
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What is your research plan? Write a short paragraph about how you plan to conduct you research. Where will you gather your notes? What keys words will you use to find information on your topic? Where will you record your notes and bibliographic information?
Research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.
What is Research Plan?A research plan is the main part of a grant application and describes a principal investigator's proposed research.
A research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.
We write a research plan by given steps.
Define the project purpose.
Identify individual objectives.
Select a research method.
Recruit participants and allocate tasks.
Prepare a project summary.
Create a realistic timeline.
Determine how to present your results.
The bibliographic information has Author name, Title of publication., Article title (if using a journal), Date of publication, Place of publication., Publisher, Volume number of a journal, magazine or encyclopedia and
Page number(s)
Hence, research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.
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Please helppppp meeeeee !!!!!!
Answer:
72.5 / 2.5 = 29
29 - 8 = 21
21 / 3 = 7
7
Step-by-step explanation:
What is commutative property of real numbers?.
The commutative property applies only to addition and multiplication of real numbers.
What is commutative property in math?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.
The commutative property of real numbers states that for any real numbers a and b, a + b = b + a and a * b = b * a. In other words, the order in which two real numbers are added or multiplied does not change the result. This property applies to both addition and multiplication of real numbers.
Therefore, the commutative property applies only to addition and multiplication of real numbers.
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george places a mirror on the ground 45ft from the base of building. He walks backward until he can see the top of the building in the middle of the mirror. At that point, George’s eyes are 6th above the ground and he is 7.5ft from the mirror. Use similar triangles to find the height of the building.
The height of the building is given as follows:
36 ft.
How to obtain the height of the building?In this problem, we have two similar triangles, meaning that their side lengths are proportional.
As the triangles are similar, the equation involving proportions for the equivalent side lengths is given as follows:
x/6 = 45/7.5.
Applying the division on the right side of the equality, we have that:
45/7.5 = 6.
Hence:
x/6 = 6.
Applying cross multiplication, the height is given as follows:
x = 6(6) = 36 ft.
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Shenelle has $25 to spend at the movie theater. She wants to see the regular admission showing of a 3D movie and buy
snacks. Define a variable and write an inequality to represent
the amount of money Shenelle can spend on snacks. Then solve the inequality and interpret the solution. Explain your reasoning.
Movie Ticket
Matinee 2D $5.50
Matinee 3D $7.25
Regular Admission 2D $8.50
Regular Admission 3D $10.25
The inequality that represents the amount of money Shenelle can spend on snacks is given as follows:
x + 10.25 ≤ 25.
The solution to the inequality is of:
x ≤ 14.75.
Meaning that she can spend at most $14.75 on the snacks.
How to define the inequality?The total amount that Shenelle has is given as follows:
$25.
Her spendings are given as follows:
$10.25 on the regular admission of the 3D movie.x on snacks.Hence the inequality is given as follows:
x + 10.25 ≤ 25.
The solution is obtained as follows:
x ≤ 25 - 10.25.
x ≤ 14.75.
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