It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original.
What is rational expressions?
The ratio of two polynomials is a rational expression. F can be expressed in the form p/q, where p and q are polynomials, if f is a rational expression.
Fractional terms are seen in rational expressions. We include constraints because with some x values, the equation may become undefined. Undefined inquiries are hypothetical or ideal. The seven expressions for undefined words are (∞-∞),∞^∞, N/0, 0⁰, 1^∞, ∞/∞ and 0×∞ respectively. N/0 is the most typical constraint on rational expressions. Any number divided by 0 is therefore undefined. For instance, if you substitute 0 for x in the case of the function f(x) = 6/x2, the outcome is 6/0, which is undefined. If you graphed this function, you would see a break at x=0.
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Anna is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y=3+2. 3xy=3+2. 3x, where yy represents the total cost in dollars and cents, and xx represents the number of miles she travels. What could the number 3 represent in the equation?.
Answer:
The number 3 represents the fixed cost in the equation which is the flat charge.
The Morgan family and the Collins family each used their sprinklers last summer. The Morgan family's sprinkler was used for 35 hours. The Collins family's sprinkler was used for 40 hours. There was a combined total output of 1725 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 45 L per hour?
Answer:
you have to multiply 45^2
2025
What is 1+1
A. 2
B. 3
C. -24,000
D. Some ridiculous number
Answer:
a
Step-by-step explanation:
ik my math
After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?
After a reflection of the figure, the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1). What is the line of reflection?
y = 2x
y = –x
x = 2
y = 2
Line of reflection for the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) will be x = 2..
What is mean by Reflection?
Reflection is the process of taking the time to think deeply about the experiences, events, and choices that shape our lives. Reflection allows us to consider how our views and opinions have changed over time, and to take stock of our successes and failures. Reflection can also help us understand our personal values and beliefs and how we can use them to make more informed decisions in the future. Reflection involves looking inward and assessing our thoughts and feelings, as well as looking outward and considering our interactions with the world around us. Taking time for reflection can help us gain insight into our behaviors and motivations, as well as identify areas of our lives that need improvement. It can also help us stay mindful of our goals and stay on the path to achieving them. Reflection is an important part of personal growth and development, and can be a valuable tool for gaining self-awareness and increasing our emotional intelligence.
Given that;
After a reflection of the figure,
The image vertices are A'(5, 1), B'(3, –1), and C'(7, –1).
And, In the figure;
The vertices are A(-1, 1), B'(1, –1), and C'(-3, –1).
Now, When we take the reflection about the line x = 2.
Then, we get the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) of the vertices A(-1, 1), B'(1, –1), and C'(-3, –1).
Therefore, Line of reflection for the image vertices are A'(5, 1), B'(3, –1), and C'(7, –1) will be x = 2.
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y = 1/4x+1 y =1/4x-1
How many solutions does this system
of equations have?
Answer:
3
Step-by-step explanation:
3 because you have to find x, you have to find x and y and then the overall answer
The given system of equations,
y = 1/4 x + 1
y = 1/4 x - 1
has no solution.
Given a system of equations.
There are two equations in the system.
We have to find the number of solutions for the system if it exists.
Consider the equations,
y = 1/4 x + 1
y = 1/4 x - 1
Since both the equations are in y value, they are equal.
1/4 x + 1 = 1/4 x - 1
1/4 x - 1/4 x = -1 - 1
0 = -2
This is not possible.
This means that the given system has no solution.
Hence the given system of equations has no solution.
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A rectangular box has dimensions 40 cm by 35 cm by 30 cm.
calculate the largest number of cubes of length 10 cm that can be placed inside the box.
The largest number of cubes that can be placed in the rectangular box is 42
How to find the cubes the box can containThe problem is solved by solving for the volume of the rectangular box and dividing by the given size of cube
The formula for the volume of rectangular box is given by
= length * width * height
= 40 * 35 * 30
= 42000 cm³
A cube of length 10 cm has a volume of 1000
= 10 * 10 * 10 = 1000
the largest number of cubes of length 10 cm that can be placed inside the box.
= 42000 / 1000
= 42
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If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
The t-test is appropriate because it can handle small sample sizes and is robust to violations of normality assumptions.
What are Statistical Tests?Mathematical statistical tests are techniques for data analysis and drawing conclusions about a population from a sample. These tests employ mathematical formulae and probability theory to assess if a participant's result is statistically significant, implying that it is unlikely to have happened by chance. Comparing two or more groups, figuring out how variables relate to one another, and assessing the accuracy and validity of data may all be done using statistical tests. They are frequently used to derive inferences from experimental or observational data in disciplines including psychology, economics, and sociology.The outcomes of these tests are used to determine whether to accept or reject a hypothesis and can offer important insights into the underlying patterns and relationships in data.
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Need some help with this!
Answer:
4 liters
Step-by-step explanation:
We need to first figure out what the proportional value is.
(Y ×? = X)
10(Y) × 2.5 = 25 (X)
If the capacity of X is equivalent to 10 liters, then we need to use the same proportional value to get the number of liters for Y.
10 ÷ 2.5 = 4
Trough Y can contain 4 liters
Hello factor the polynomial completely with steps please
The factor form of the cubic equation y = x³ + 3 · x² + x + 3 is y = (x² + 1) · (x + 3).
How to factor a cubic equation
In this problem we find a cubic equation, that is, a polynomial of the form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are the real coefficients of the polynomial. Herein we must use algebra properties to find the factor form of the expression:
y = a · Π (x - rₙ) for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficient.m - Grade of the polynomial.First, write the entire equation:
y = x³ + 3 · x² + x + 3
Second, use distributive property of real mumbers:
y = x² · (x + 3) + 1 · (x + 3)
Third, use distributive property of real numbers once again:
y = (x² + 1) · (x + 3)
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Which one doesn't belong?
1. 5 + 7 = 7 + 5
2. 5 * 7 = 7 * 5
3. 2 = 7 - 5
4. 5 - 7 = 7 - 5
Write a post sharing which equation you think doesn't belong and why.
Answer:
3 does not belong because its not long enough
What are the domain and range of the function f(x)= x^2-3x-28/x+4?
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = (x² - 3x - 28) / (x + 4)
Simplify the function, then we have
f(x) = (x² - 7x + 4x - 28) / (x + 4)
f(x) = [x(x - 7) + 4(x - 7)] / (x + 4)
f(x) = [(x + 4)(x - 7)] / (x + 4)
f(x) = x - 7
The Domain of the function is all real numbers except 4. And the range of the function is all real numbers except 11.
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
The diagram is given below.
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Mr. Reynolds is a car salesman. He makes a salary of $55,000 a year. He
also earns a commission of of his total sales for the year. This year, Mr.
Reynolds has a sales total of $295,200. Write and evaluate a function to find
Mr. Reynolds's total earnings for the year.
Answer:you speak French pls
Step-by-step explanation:
:::
Write the following expression using an exponent. (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
For the given expression the exponent would be [tex](2y-9)^5$[/tex].
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = [tex](2y-9)^5$[/tex]
Hence, for the given expression the exponent would be [tex](2y-9)^5$[/tex].
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For the given expression the exponent would be (2y-9)⁵.
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = (2y-9)⁵
Hence, for the given expression the exponent would be (2y-9)⁵.
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An item on sale costs 45% of the original price. The original price was $39.
Use the ALEKS calculator to find the sale price.
$0
X
S
The sales price of the item is $17.55
How to determine the sales priceFrom the question, we have the following parameters that can be used in our computation:
Sales price = 45% of the original price
The original price = $39
The above parameters mean that
Sales price = 45% * original price
Substitute the known values in the above equation, so, we have the following representation
Sales price = 45% * $39
Evaluate
Sales price = $17.55
Hence, the sales price is $17.55
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2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
The zeros of the polynomial function should be between
(2.5, 1.1) & (3.0 -0.8) and (4.0, -0.3) & (4.5, 0.7)How to know the zeros of the polynomial functionThe zeros of a polynomial function is the point where the polynomial crosses the x axis
At this point, the y axis has a value of zero. This point can be seen on the graph easily as the graph will show the x intercept,
For the table, examining the values of the y coordinate to see where the signs change will help to know where the zero will lie.
The table shows that the y values changed sign at 1.1 to -0.8 and -0.3 to 0.7 and hence the zeros will lie between (2.5, 1.1) & (3.0 -0.8) and (4.0, -0.3) & (4.5, 0.7)
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Find the measure of each angle indicated.
Answer:
answer is 124 degree ....
How might you use a perpendicular bisector or an angle bisector in your everyday life?
And why would an orthocenter be the most difficult part of a triangle for someone to identify and use?
You use a perpendicular bisector or an angle bisector in your everyday life and orthocenter be the most difficult part of a triangle.
Everyday life example :
On a clock, the second hand in the middle of the hour hand and minute hand, is working as the angle bisector.
For a perpendicular bisectors, take two ends of a compass needle, with the long end on the North, the short end is pointing South, and the lines of East and West are on the left and right.
Orthocenter :
The orthocenter is the point of intersection of the three altitudes of a triangle. It is the hardest part of the triangle to find because :
It can lie inside a triangle or outside the triangle as it depends on the type of type of the triangle whether it is acute or obtuse. So, in order to identify it we must first know the type of the triangle.
And secondly, the formula for finding orthocenter is quite complicated so it is the hardest part of the triangle to identify and use.
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In 1995, the standard bus fare in a city was $0.25. In 2022, the standard bus fare was $3.25. Find the percent
increase. (Round to the nearest tenth of a percent.)
Answer: 1200 percent increase
Step-by-step explanation:
Increase = New Number - Original Number
divide the increase by the original number and times 100
3.25-0.25=3
3/0.25=12*100
1200 percent
Evan saved $30 on a new TV. If the percent of discount was 20%, how much money did the
TV originally cost?
Answer:
$150
Step-by-step explanation:
we can make a ratio
20/100=30/x
cross multiple
20x=30(100)
20x=3,000
/20 /20
x=150 hopes this helps
help asappppp i dont understand graphs
The function that is represented by the graph is defined as follows:
A. f(x) = (x - 1)(x + 2)(x + 4).
How to obtain the function represented by the graph?The function represented by the graph is obtained using the Factor Theorem, as we can identify the roots of the function from the graph.
The Factor Theorem states that the function can be declared according to it's linear factors, as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which:
a is the leading coefficient of the polynomial.[tex]x_1, x_2, \cdots, x_n[/tex] are the roots of the polynomial.From the graph given in this problem, the roots of the polynomial are listed as follows:
-4, -2 and 1.
Hence the function can be defined as follows:
f(x) = (x - 1)(x + 2)(x + 4).
Considering a leading coefficient of 1, option A is correct.
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seasonality causes comparability problems in ratio analysis. a common solution is to use an average account balance as opposed to an ending account balance. t or f
The given statement is true.
Seasonal inventory or revenue fluctuations that are not based on sales can artificially inflate or deflate the value of the company's assets.
What is Seasonal inventory ?
Products with a seasonal inventory are those that sell more frequently at particular times of the year. Weather, events, and holidays can affect how much demand there is for these products.
Holiday merchandise was probably your first thought when thinking about seasonal inventory. Labor Day weekend, Halloween, and Christmas are a few examples of holiday inventory. Every one of them sells particular goods that people only purchase around the holidays.
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Which relation is not a function?
Answer: C, the table.
Step-by-step explanation:
In a function, there can only be one output (y) per input (x), but you can have multiple inputs (x) per one output (y).
Using this logic, we see that the answer is;
C
How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen? PLSSSS EXPLAIN!!!!
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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Solve each system by elimination: 2x+y=5 3x-2y=4
Answer: 2x+y +5 we know that because if u get 2x+y we do 2xxy and get 2xy
Step-by-step explanation:
Choose the system of inequalities that best matches the graph below.
y
5
4
3
KE
-6-5-4-3-2-1 01 23 4 5 6
-1
IN
03
3
S
X
The inequalities that represent the line in the graph will be y < x - 3 and y = -(2/3)x. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the blue line has a slope of 1 and the y-intercept is at (0, -3), then the inequality is calculated as,
y < x - 3
The red line is passing through the origin and (3, -2), then the equation is given as,
y - 0 = [(-2 - 0) / (3 - 0)](x - 0)
y = -(2/3)x
The disparities that address the line in the chart will be y < x - 3 and y = - (2/3)x. Then the right choice is B.
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not allowed
a) Find the mode shown below.
15, 8, 21, 2, 12, 22, 19, 8, 19, 8
Answer:8
Step-by-step explanation: Mode is the value or values in the data set that occurs most frequently.
Suppose a sightseeing tour company charges $7.50 for each hour you rent a motorized scooter, plus a non-refundable fee of $45. Write an equation that represents the total cost, y, of renting the scooter in relation to the number of hours, x.
An equation that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45
What is meant by an equation?3x - 5 = 16 is an illustration of an equation. By solving for x, we discover that the variable's value is 7, or x = 7. By deleting parenthesis and merging related terms, you can simplify either side of an equation and obtain the solution. Together with the variables for which the equation must be solved, the values of the variables that must satisfy the equality to compose the answer are referred to as the unknowns. Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
Given,
You must pay a non-refundable $45, plus $7.50 per hour, to rent a motorized scooter from a sightseeing tour company.
The equation is y=7.50x+45
Therefore, a formula that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45.
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help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer:
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
What is the image point of (0,1) after translation right 5 and up 5 units?
Answer: (5,6)
Step-by-step explanation: 5 units right is adding 5 to your X. 5 units up is adding 5 to your Y.
For left and down, you'd subtract 5. For instance, "What is the image point of (8,9) after a translation of 5 units left, and 5 units down. The answer would be (3,4)
a rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. what is the length, in units, of the longer diagonal?
The length of the longer diagonal of the given rhombus with side length 51units and shorter diagonal 48 units is equal to 90units.
As given in the question,
Side length of the given rhombus 's' = 51 units
Length of the shorter diagonal of given rhombus 'a' = 48 units
Let us consider length of the longer diagonal of the given rhombus be 'b'
As per the property of the rhombus:
Diagonals of the rhombus bisects each other at right angle
Triangle formed by side length bisecting diagonals is right angled triangle.
Using Pythagoras theorem we have,
(Side length)² = (a/2)² + (b/2)²
Substitute the values
⇒ (51)² = (48/2)² + (b/2)²
⇒2601 = 576 + (b/2)²
⇒(b/2)² = 2601 -576
⇒(b/2)² = 2025
⇒b/2 = √2025
⇒ b/2 =45
⇒ b = 90units
Therefore, the length of the longer diagonal of the given rhombus is equal to 90units.
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