The two found rational expressions with the difference that completes the equation is (x + 2)/(x² - 36) and 1/(x² + 6x).
Explain the term rational expressions?The ratio of 2 polynomials is a rational expression. F can be expressed in the form p/q, where q and p are polynomials, if f is a rational expression.Consider the two rational expressions.
(x + 2)/(x² - 36) ...eq 1
and 1/(x² + 6x) ....eq 2
Subtract the second from the first.
= [(x + 2)/(x² - 36)] - [1/(x² + 6)]
Factorise the denominator of the first equation-
= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]
Taking the LCM
= [x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]
Further simplifying,
= [x² + x + 6]/[x(x-6)(x + 6)]
Thus, the two found rational expressions with the difference that completes the equation is (x + 2)/(x² - 36) and 1/(x² + 6x).
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The complete question is-
Drag each expression to the correct location in the equation. Not all expressions will be used.
Determine the two rational expressions whose difference completes this equation.
x² + x + 6
x(x-6)(x + 6)
how many square feet of cement would be needed for a 7-foot wide continual sidewalk around the outside edge of a 60 foot by 90 foot corner lot?
Using mathematical operations, we know that 1,099ft² of cement would be needed.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, square feet of cement needed:
A: 60' x 7' = 420SF.
90' x 7' = 630SF on side B.
Keep in mind that the corner is 49 SF (7'x7') in size.
The three components are added together as follows:
1,099 square feet = 420SF + 630SF + 49SF.
Therefore, using mathematical operations, we know that 1,099ft² of cement would be needed.
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How do you decide which variable to isolate in order to
use the substitution method to solve a system of linear
equations?
Intro
Answer:
Step-by-step explanation:
it depends on the vaiable you choose to cancel out first. For example, if I had two equations:
-12x+9y=7
9x-12y=6
if you wanted first eliminate the x values, then you distribute a certain number to either equation that will cause the x values to cancel (one being negative, and the other being positive)
b. if we want to get a 80% confidence interval with a small margin of error, say only 8%. how many people do you need to sample?
The number of people needed will be approx 65.
Margin of error = Critical value x Standard deviation for the population.
Margin of error = Critical value x Standard error of the sample.
Given, Margin of error (m) = 0.08
z (at 80% confidence level)=1.282
Sample size(n) = (z/m)^2 p (1-p)
In order to find the sample size, we must know the value of proportion.
The value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.
p = 0.5
∴ Sample size = (z/m)^2 p (1-p)
= (1.282/0.08)^2 × 0.5 × (1-0.5)
= 65
Inferential statistics is a statistical method that deduces from a small but representative sample the characteristics of a bigger population. In other words, it allows the researcher to make assumptions about a wider group, using a smaller portion of that group as a guideline.
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Simplify the expression 4(x+7) using combining like terms or distributive property.
Answer:
4x+28
4 multiplied by x is just 4x and 4x7 is 28
please help precalculus. Given the following piecewise function:
The values of the functions defined in the piecewise function are f(0) = 5 and f(-4) = 11
How to evaluate the piecewise function?From the question, we have the following piecewise function that can be used in our computation:
f(x) = | x + 5 x < -2
x² + 2x + 3 x ≥ -2
Evaluating the function f(0)
In this function, we have the x value to be
x = 0
This x value is at the domain x < -2
So, we make use of
f(x) = x + 5
Substitute 0 for x in f(x) = x + 5
f(0) = 0 + 5
Evaluate
f(0) = 5
Evaluating the function f(-4)
In this function, we have the x value to be
x = -4
This x value is at the domain x ≥ -2
So, we make use of
f(x) = x² + 2x + 3
Substitute -4 for x in f(x) = x² + 2x + 3
f(-4) = (-4)² + 2(-4) + 3
Evaluate
f(-4) = 11
Hence, the value of f(-4) is 11
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a recent survey reported that small businesses spend 24 hours a week marketing their business. a local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week. assuming that the population standard deviation is 6.1 hours, is there sufficient evidence to support the chamber of commerce’s claim at the 0.02 level of significance?
chamber of commerce’s claim at the 0.02 level of significance, z = -1.75
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
a recent survey reported that small businesses spend 24 hours a week marketing their business.
these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week.
assuming that the population standard deviation is 6.1 hours.
Given n = 93, u =24, x' = 23, α=5.5
z = x'- u / α(/√n) = (23-24/5.5/√5) = -1.75
Hence, chamber of commerce’s claim at the 0.02 level of significance, z = -1.75
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at the homecoming game, cheerleaders will throw 100 bundled t-shirts into the crowd. the t-shirt sizes consist of 20 small, 30 medium, and the remainder either large or extra large. suppose you catch a t-shirt. what is the probability that you will catch a t-shirt that is not a size medium?
The probability that you will catch a t-shirt that is not of medium size would be 0.7
What is the probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Small=S=20, M=medium=30,
L = Either large or extra large=50
P(T-shirt that is not a medium)= 1 - P(T-shirt is medium)
= 1 - 30/100
= 1 - 0.3
= 0.7
Hence, the probability that you will catch a t-shirt that is not of medium size would be 0.7
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Lucas, Mason, Logan, and Jayden have 5 grapefruits. They want to share them equally. How much grapefruit will each person get?
47 page 28 math monde svp
Answer:
Step-by-step explanation:
Can you explain more please?
Geometry.....Solve for each variable. Show your work and explain in paragraph form how you solved each problem.
Base Angles Theorem
Converse to Base Angles Theorem
Corollary
Converse to the corollary
Sum of Interior Angles
Exterior angles
The value of x is 35 and the value of y is 82.
What is an isosceles riangle?In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Given that the three angles of the triangle are 40, 2x and y-12. The value of x and y will be calculated as,
2x = y-12
2x + y-12 + 40 = 180
2x + y =180-40+12
2x + y = 152
2x - y = -12
___________
4x = 140
x = 35
y = 2x + 12
y = 2 x 35 + 12
y = 82
Therefore, the value of x is 35 and the value of y is 82.
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for a period of time, an island's population grows exponentially. if the population doubles every 17 years and the current population is 1,725, what will the population be 10 years from now?
After 10 years the population growth will be 3054, if the population doubles after every 17 years.
What is Exponential function?A mathematical function with the form f (x) = ae^x is an exponential function. "x" is a variable, and "a" is a constant that serves as the function's base and must be greater than 0. The transcendental number e, or roughly 2.71828, is the base for exponential functions that is most frequently used.
Growth rate = 100% in 17 years
In 1 year = 5.88% growth
Initial population = P₀ = 1725
Time = 17 years
So, after 10 years population
P= P₀ ( 1 + [tex]\frac{r}{100}[/tex])^t
= 1725 ( 1 + 5.88/100 )^10
=≈ 1725 * 1.77
=≈ 3054
Hence, the population growth after 10 years at the rate of 5.88 % would be 3054.
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-4-5(x+8) please hurry!! WITH EXPLINATION!
Answer:
- 5x - 44
Step-by-step explanation:
-4 - 5(x + 8)
Distribute the -5 to the terms in parenthesis:
-4 - 5x - 40
combine numbers:
- 5x - 44
A DJ added 20 more songs to his MP3 player, making the total more than 61. How many songs were originally on the player?
The number of songs that were originally on the player is 41.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, a DJ added 20 more songs to his MP3 player, making the total more than 61. The number of songs will be the subtraction of the value.
This will be:
= 61 - 20
= 41
The original songs are 41.
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-7x + 4y = 24
4x - 4y = 0
solve by substitution - please add explanation and work
Answer:
(-8, -8)
Step-by-step explanation:
You need to solve one of the equation for x or y. I am going to solve the bottom equation for x
4x -4y = 0 Add 4y to both sides
4x = 4y Divide both sides by 4
x = y Substitute y in for x in the first equation
-7x + 4y = 24
-7y + 4y = 24 Combine like terms
-3y = 24 Divide both sides by -3
y = -8
Since x = y
x = -8
Check:
-7y + 4y = 24
-7(-8) + 4(-8) = 24
56 - 32 = 24
4x - 4y = 0
4(-8) - 4(-8) = 0
-32 + 32 = 0
0 = 0
I want to know how to do this problem
Answer:
Step-by-step explanation: k = 25
If a box of crackers is $3 for 2 boxes of crackers then how much Is it per box?
Mark and some friends went to the movies. They bought tickets to the movies for $9 each and spent $22 at the concession stands. If they spent a total of $67, how many friends went to the movies with Mark?
Answer:
5 people total including Mark. So, 4 friends.
Step-by-step explanation:
$67 total - $22 concession stands
$45 spent on tickets
45/$9per ticket
5 tickets were purch
Solve the inequality, show all of your work:
-4x + 5 > 37
Answer:
x < -8
Step-by-step explanation:
1. Subtract 5 from both sides
-4x + 5 > 37
-4x + 5 - 5 > 37 - 5
2. Simplify
Subtract the numbers:
-4x + 5 - 5 > 37 - 5
-4x > 37 - 5
Subtract the numbers:
-4x > 37 - 5
-4x > 32
3. Divide both sides by the same factor, and flip the relation because the factor is negative
-4x > 32
[tex]\frac{-4x}{-4}[/tex] < [tex]\frac{32}{-4}[/tex]
4. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{-4x}{-4}[/tex] < [tex]\frac{32}{-4}[/tex]
x < [tex]\frac{32}{-4}[/tex]
Divide the numbers:
x < [tex]\frac{32}{-4}[/tex]
x < -8
Solution:
x < -8
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
x < - 8
Step-by-step explanation:
-4x + 5 > 37
-4x > 37 - 5
-4x > 32 ( now I have to divide by -4 )
-4x > 32 / -4
x < - 8
x has to be smaller than -8 for example ( -9 or - 10 )
demonstration: -4 * (-9) + 5 > 37
36 + 5 > 37
41 > 37
whats the answer for shrinking -12(5/6x-5)+2x
Answer: 12x-60
Step-by-step explanation:
-12 x 5/6 = 10
-12 x 5 = -60
10x-60+2x
12x-60
The greatest common factor of 48 and z, some unknown positive integer, is 12. There are two possible values for z between 10 and 30. What is the difference between these two values?.
The greatest common factor being 12, the difference between the two values is 12.
What is GCD?
The greatest common divisor (GCD) from mathematics is the largest positive integer that splits each of two or more non-zero integers.
The symbol gcd stands for the greatest common divisor of the two integers x and y.
For instance, gcd(8,12)=4 is the GCD of the numbers 8 and 12.
According to the given question:
The greatest common factor of 48 and z, some unknown positive integer, is 12. There are two possible values for z between 10 and 30.
Now there are only two numbers between 10 and 30 which has a factor of 12.
The numbers are 12 and 24.
Hence the difference between these two numbers is 24 - 12 = 12
Therefore the required value is 12.
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A statistic summarizing the strength of association between two metric variables is called the ________.
A) product moment correlation
B) covariance correlation
C) inverse correlation
D) bivariate correlation
E) F-statistic
A statistic summarizing the strength of association between two metric variables is called the product moment correlation.
The Pearson product-moment correlation coefficient also known as Pearson’s correlation is a measure of the linear relationship between two variables/measures/questions, in other words, the Pearson product-moment correlation coefficient is a measure of the direction and strength of association that exists between two metric variables measured on at least an interval scale.
A product-moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient illustrates how far away all these data points are from the best fit line. Product-moment correlation quantifies the strength as well as the direction of correlation.
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given the length of a human's femur, x, and the length of a human's humerus, y, would you expect a positive correlation, a negative correlation, or no correlation?
The length of a human's femur, x, and the length of a human's humerus, Y would ,positive correlation.
A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.
A scale from + 1 to -1 is used to calculate the correlation coefficient. Either + 1 or -1 represents a variable's complete connection with another. The correlation is positive when one variable rises as the other rises; it is negative when one variable falls as the other rises.
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2/9-2/15 in fraction form?
Answer:
4/45
Step-by-step explanation:
A plant is already 55 centimeters tall, and it will grow one centimeter every month. The plant's height, (in centimeters), after months is given by the following.H=55+m What is the plant's height after 34 months? PLEASE HELP
The plant's height after 34 months will be 89cm if the plant is already 55 centimeters tall.
What is meant by height?Height is defined in mathematics as the vertical distance from the object's top to its base. It is occasionally referred to as 'altitude.' The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry.
Height and elevation all refer to the vertical distance between the top and bottom of something or between a base and anything above it. Height refers to something measured vertically, whether it be high or low.
Given, the relation between the height and the months is:
H(m)=55+m
Now, we have to find the height of the plant after 34 months.
So, we substitute m=34 in the expression to obtain height,
H(m)=55+m
H(34)=55+34
H(34)=89cm
Hence the height will be 89cm
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What is the minimum number of different résumé formats that an individual should have prepared? a. 1 b. 2 c. 3 d. 4 please select the best answer from the choices provided a b c d
(B) 2 separate resume formats should be the absolute minimum number that someone should have created.
What is a résumé?A résumé, also known as a curriculum vitae (CV), is a written statement that a person uses to describe their educational history, professional experience, and accomplishments.
Although there are many uses for resumes, they are most frequently employed to find new jobs.
A standard résumé includes a "summary" of relevant educational background and work history.
So, a condensed format should be used for the first.
One page should be plenty for a good resume.
However, a two-page format might be employed when things are crammed onto one page.
For extra information about yourself, utilize a two-page format.
Typically, we submit the streamlined version before our interview.
In order to give the interviewer access to extra material, we might demonstrate our extended format during the interview.
Therefore, (B) 2 separate resume formats should be the absolute minimum number that someone should have created.
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Correct question:
What is the minimum number of different résumé formats that an individual should have prepared?
a. 1
b. 2
c. 3
d. 4
uuuhhhmmmm i need help with 2 work sheets called dizzy over decimals multiplying decimals and dizzy over decimals dividing decimals so can someone find those and give me written answers worked out
write the reciprocal of 3
This is a random question
The required reciprocal of 3 would be 1/3.
What is the reciprocal?The reciprocal of a number multiplied by a number is 1.
The coefficient of the inverse of the function f(x)=nx is the reciprocal of a number n. A function's inverse is the function with its points flipped.
The reciprocal of a number is the same as its multiplicative inverse.
(The multiplying opposite) It is the number 'turned upside down.
The product of a number and its reciprocal is always 1
So in this case, we can write 3 as: 3/1
The reciprocal is 1/3.
Therefore, the required reciprocal of 3 would be 1/3.
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1/3 Answer:
this is a random answer
Step-by-step explanation:
A park ranger claims that the average number of acres in his State Park is less than 2000 acres.
A random sample of five parks is selected and the number of acres is shown below:
959, 1187, 493, 6249, 541
Assume the variable must be normally distributed, at [tex]\alpha =0.01[/tex] is there enough evidence to support the claim? To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.
Answer:
ypotheses:
H0: μ = 2000
H1: μ < 2000
Claim: The average number of acres in the State Park is less than 2000.
Critical Value (s): -1.645 (z-score)
Acceptance Region: z < -1.645
Rejection Region: z ≥ -1.645
Test Value: z = -3.537
Conclusion: Since -3.537 is less than -1.645, we reject the null hypothesis and accept the alternate view. There is enough evidence to support the claim that the average number of acres in the State Park is less than 2000.
Step-by-step explanation:
.2 times .2 times .2
Your answer is 8.
[tex]2x2x2=8[/tex]
describe how the line best fit and the correlation coefficient can be used to determine the correlation between
Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.
What is line of best fit?
Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.
Two variables are said to be correlated or to have a correlation coefficient when "changes in the value of one variable produce changes in the variable of the other variable."
In order to find the correlation between two variables on a graph, the question asks for the line of best fit and correlation coefficient.
Only when there is a linear correlation between the variables—that is, when the relationship between the variables is linear on a graph—does the correlation coefficient hold true.
Variation in "x" on the graph leads to variation in "y." Variation in "y" on the graph results in variation in "x." The variables "x" and "y" are jointly dependent on the graph.
The correlation coefficient between two variables on the graph is calculated in this manner.
Hence, using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.
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