Prove that the limit x tends to 1 (2x^4-6x^3+x^2+3)÷(x-1)=-8
Answer:
full answer in below
Step-by-step explanation:
To prove that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is equal to -8, we can use the definition of a limit and the fact that (x-1) is not equal to zero at x=1.
The definition of a limit states that:
If we have a function f(x) and a number L, then the limit of f(x) as x approaches a is L, if and only if, for every ε > 0, there exists a δ > 0 such that for every x:
|f(x) - L| < ε when 0 < |x - a| < δ
So, to prove that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is -8, we need to show that:
|(2x^4-6x^3+x^2+3)÷(x-1) + 8| < ε when 0 < |x - 1| < δ
We know that (x-1) is not equal to zero at x=1, so we can safely divide both sides of the equation by (x-1) and simplify it to:
|2x^4-6x^3+x^2+11| < ε when 0 < |x - 1| < δ
Now, we can choose ε = 0.1 and δ = 0.1, so we have:
|2x^4-6x^3+x^2+11| < 0.1 when 0 < |x - 1| < 0.1
If we plug in x=1, we have:
|2(1)^4-6(1^3)+(1)^2+11| < 0.1
which simplifies to:
|11| < 0.1
and we see that this is true, since |11| = 11 is less than 0.1.
We can also plug in some values around x=1, for example x=0.99 and x=1.01:
|2(0.99)^4-6(0.99)^3+(0.99)^2+11| < 0.1
and
|2(1.01)^4-6(1.01)^3+(1.01)^2+11| < 0.1
In both cases, we can see that the inequality is true, and the absolute value of the expression on the left side is less than 0.1.
Therefore, we have shown that for any ε > 0, there exists a δ > 0 such that for every x:
|(2x^4-6x^3+x^2+3)÷(x-1) + 8| < ε when 0 < |x - 1| < δ
And thus, by the definition of a limit, we have proven that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is -8.
Answer:
is that calculus?
am confuse in your question
can you try take derivative both numerator and denominator with respect to x
by using L - Hospitable rule
Please help me with this question.
The constants A and B for the differential equation are given as follows:
A = 0.B = -64.How to obtain the constants A and B?The solutions to the differential equation are given as follows:
y(t) = e^(8t).y(t) = e^(-8t).This means that the roots of the characteristic equation are given as follows:
r = -8 and r = 8.
Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:
(r + 8)(r - 8) = r² - 64.
Hence the differential equation is given as follows:
y'' - 64y = 0.
Hence the constants are given as follows:
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7. Find the area of the triangle using trigonometry.
The area of the triangle shown is 51.96 unit²
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The area of a triangle can be found given two adjacent sides and an angle between the two sides. It is given as:
Area = (1/2) * product of adjacent sides * sin(angle)
Hence:
Area of triangle shown = (1/2) * 10 * 12 * sin(60) = 51.96
The area is 51.96
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2) In 2000, the population of a town in 20,000 and decreased by 2% each year.
a) Write an equation to model this scenario.
b) What will the population be in 2025?
Answer:
a) General Equation for this scenario is
[tex]\boxed{P_n = P(.98)^n\\\\}[/tex]
where P is the starting population and Pₙ is the population at the end of n years
For this specific case,
[tex]\boxed{P_n = 20000(0.98)^n}[/tex]
b) Population in 2025 will be the population after 25 years:
[tex]P_{25} = 20000(0.98)^{25} = \boxed{12,069}[/tex]
Step-by-step explanation:
In general, if the population at year 0 is P and it decreases by 2% each year then the population after one year will be given by
P - decrease in one year
Decrease in population for 1 year = 2% of P [tex]= 0.02P[/tex]
So P(after 1 year) :
[tex]P - 0.02P\\\\ = P(1-0.02) \\\\= 0.98P[/tex]
After 2 years the population will be population after 1 year (0.98P) - decrease in population for 1 year (0.02 x 0.98P)
So population at end of 2 years would be
[tex]0.98P - 0.98P(0.02)\\\\= 0.98P(1-0.02)\\\\=0.98P(0.98)\\\\= P(0.98)^2[/tex]
In general after n years the population would be
[tex]P(0.98)^n\\\\[/tex]
If the population in year 2000 is 20,000 then population at the end of 25 years is:
[tex]20000(0.98)^{25}[/tex]
[tex]\rm\:{=\:12,069\:\;\:rounded\:down\:to\:the\:nearest\:integer}[/tex]
All of the employees at the acmesoft company are either programmers or salespeople. The programmers are always tell the truth, the salespeople always lie. Threes Acmesoft employees - A, B, and C-were standing together in the hallway. A visitor passed by and asked A. "Are you a programmer or a salesperson?" A mumbled an answer that the visitor could not hear clearly. The visitor then asked B, "what did A say?" B replied. "A said that he is a salesperson."At this point, the third employee, C, said ,"Don't believe B; he is lying! What are B and C?
1/ B and C are both programmers
2/ B is a programmer and C is a salesperson
3/ B is a salesperson and C is a programmer
4/ B and C are both salesperson
Answer:
Step-by-step explanation:
3/ B is a salesperson and C is a programmer.
The correct option is: 2/ B is a programmer, and C is a salesperson
Let's analyze the statements and determine what B and C are:
A mumbled a response that the visitor couldn't hear clearly. We don't have any information from A's response.
B said, "A said that he is a salesperson." Since we know that salespeople always lie, we can infer that B is lying about A's response. Therefore, if A is a programmer (telling the truth), then B must be a salesperson.
C said, "Don't believe B; he is lying!" If we already determined that B is a salesperson (lying about A's response), then C is suggesting that B's statement is false, which means A's response is the opposite of what B said. So if B claimed that A is a salesperson (which was a lie), then A must be a programmer (telling the truth).
Based on the above analysis:
A is a programmer.
B is a salesperson.
C is a programmer.
So, the correct option is: 2/ B is a programmer, and C is a salesperson.
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If QS bisects angle PQR, find m angle PQR
Answer:
94
Step-by-step explanation: PQS = (7x - 6)°
SQR = (4x + 15)° since QS bisect PQR these two expressions must be equal
so
7x - 6 = 4x + 15 transfer like terms to the same side of the equation
7x - 4x = 15 + 6
3x = 21 divide both sides by 3
x = 7
also the sum of these two would give us the measure of PQR
7x + 4x + 15 - 6 = PQR
11x + 9 = PQR replace x with 7
11*7 + 9 = 86 this is the measure of angle PQR and also supplementary to PQT so the measure of PQT = 180 - 86
Consider the National Assessment of Educational Progress (NAEP) scores for an eighth-grade math test, which we assume are approximately Normal, (282, 40) . Give the -score for a student who received a score of 310.
Give your answer to two decimal places.
-score=
The z score for a student who received a score of 310 is 0.75
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The z score shows by how many standard deviation the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that the eighth-grade math test is Normal, (282, 40), hence mran = 282, stand. deviation = 40
For a score of 310:
z = (310 - 282) / 40 = 0.75
The z score is 0.75
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Which choice shows 13 • (7 • 4) correctly rewritten using the associative property and then correctly simplified?
The choice that shows 13 · (7 · 4) correctly rewritten using the associative property and then correctly simplified is presented as follows;
(13 · 7) · 4 = 91 · 4 = 364What is the associative property of multiplication?The associative property of multiplication stated that the multiplication of three numbers produces the same result in any way the numbers are grouped.
Mathematically, the associative property of multiplication can be presented as follows;
(a × b) × c = a × (b × c)
The specified operation involving the multiplication of three numbers are presented as follows;
13 · (7 · 4)
The associative property of multiplication indicates that we get;
13 · (7 · 4) = (13 · 7) · 4
13 × 7 = 91
Therefore, (13 · 7) · 4 = (13 × 7) × 4
(13 × 7) × 4 = 91 × 4 = 364
The option that shows the associative property correctly written and then correctly simplified is therefore;
(13 · 7) · 4 = 91 · 4 = 364The possible options in the question, obtained from a similar online question are;
(13 · 74) = 96213 · 4 · 7 = 52 · 7 = 364(13 · 7) · 4 = 91 · 4 = 36413 · (4 · 7) = 13 · 28 = 364
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What is the surface area? 5 cm 6 cm 5 cm 7 cm 4 cm square centimeters
The surface area of the square pyramid is 224 ft²
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Surface area is the total area occupied by the surface of the object. It is gotten by summing the individual area of each surface.
For the pyramid:
Surface area = 4 * area of triangle + Area of square base
Substituting gives:
Surface area = (8 ft * 8 ft) + 4(1/2 * 8ft * 10 ft) = 224 ft²
The surface area is 224 ft²
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Answer:
Step-by-step explanation:
What is the surface area?
5 cm
6 cm
5 cm
6 cm
4 cm
square centimeters
Please please look at the picture and answer the question thank you
Answer:
[tex]\boxed{-2 < x\le1}[/tex]
Representation on number line is in attached image.
Notice that -2 has an unfilled circle and 1 has a filled circle. Important
Step-by-step explanation:
The given inequality is
[tex]2 < 4x+10\le14[/tex]
Subtract 10 throughout:
[tex]2-10 < 4x+10-10\le14-10\\\[/tex]
[tex]-8 < 4x\le4[/tex]
Divide throughout by 4:
[tex]-2 < x\le1[/tex]
Answer: [tex]\boxed{-2 < x\le1}[/tex]
This is represented on the number line as follows: Notice the use of the
Write a function that models the data.
Ay
40
20
y =
(2,45)
(1, 15)
(0,5)
2
4 x
As a result, slant asymptotes of y = x -4 are found to be the solution to the provided function problem.
What does the word function refer to?Mathematics includes the study of numbers and their variations, equations and associated structures, and the regions and potential uses of geometry. A "function" is the connection between a collection of inputs that individually produce a related output. An output-input relationship known as a function is one in which each input leads to a single, identifiable outcome.
Here,
Because there are no restrictions on the kind of rational function, it is possible to build one from each of the 3 asymptotes.
In addition to the graphs of the linear equation it represents, this is shown in the accompanying graph. The function's asymptotes are these.
The horizontal points include x = -4 and
There are two horizontal asymptotes: y = 0 and
Y = x – 4 are the slant asymptotes.
Additional comments
In our example function, an exponential function is used. That isn't frequently thought of as a polynomial, despite the fact that it may be stated as an infinite degree polynomial. Most authors define a rational function in terms of the fraction of polynomials.
As a result, slant equipotential lines are y = x and are the answer to the given function problem.
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Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1 pls hurry I will give brainlist
The graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).
What is the slope?
One of the most important things to understand about lines is the definition of slope. The slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate the slope by dividing the change in the y-value between two points over the change in the x-value.
To find the slope of the line, you can use the point-slope formula which is (y2-y1)/(x2-x1) = m,
where m is the slope and (x1,y1) and (x2,y2) are points on the line.
So using the given points in the question, we get (0-2)/(3-0) = -2/3 = -0.66 = -3/2.
And the y-intercept is the point where the line crosses the y-axis, which is 2 in this case.
Hence, the graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).
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Complete the table by converting the amount in cents to dollars.
cents 4
70
58
204
S
0.75
3009
The conversion from cents to Dollar we get :
4 cent = 4/100 = $ 0.04
70 cents = 70/100 = $ 0.7
58 cents = 58/100 = $.58
204 cents = 204/100 = $ 2.04 = $2 and 4 cents
.75 cents = .75 / 100 = $ 0.0075
3009 cents = 3009/100 = $ 30.09 = $30 and 9 cents
What is Conversion ?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.
Cents are equivalent to one dollar. Dollars are represented by paper banknotes, which come in denominations of $100, $50, $20, $10, $5, and $1. Coins include cents.
The act of converting one value into another, such as from inches to millimeters or from liters to gallons, is known as conversion. The following measurements: length, weight, capacity, temperature, and speed are all measured in units.
The values in cents
4 cent = 4/100 = $ 0.04
70 cents = 70/100 = $ 0.7
58 cents = 58/100 = $.58
204 cents = 204/100 = $ 2.04 = $2 and 4 cents
.75 cents = .75 / 100 = $ 0.0075
3009 cents = 3009/100 = $ 30.09 = $30 and 9 cents.
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Lucas decides to use 5/8 cups of berries instead,but uses the same amounts of mango and yogurt. If he wants to make three 8 fluid ounce servings of smoothie,how much almond milk should he add
Using the mathematical operations of addition and subtraction, the quantity of almond milk that Lucas should add to his recipe to make three 8-fluid-ounce servings of the smoothie is 1¹/₈ cups.
What are mathematical operations?Mathematical operations include addition, division, subtraction, and multiplication.
In this situation, we can determine the needed quantity of almond milk using multiplication, subtraction, and addition.
The total quantity of smoothie is obtained by multiplying three cups by 8 fluid ounces. The quantity of almond milk is determined by subtracting the sum of other ingredients from the total quantity.
Lucas' usual recipe for two 8 fluid ounces:
Berries 3/8 cups
Mango 1/2 cups
Yogurt = 3/4 cups
Almond Milk = 3/8 cups
Total cups made = 2 cups (16 fluid ounces = 2 x 8)
New recipe for three 8 fluid ounces:
Berries 5/8 cups
Mango 1/2 cups
Yogurt = 3/4 cups
Almond milk = x
1 cup = 8 fluid ounces
Total cups to be made = 3 cups (24 fluid ounces = 3 x 8)
5/8 + 1/2 + 3/4 + x = 24/8
= 15/8 + x = 24/8
x = 9/8 (24/8 - 15/8)
= 1¹/₈ cups
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Question Completion:Lucas makes a smoothie using the recipe (berries 3/8, mango 1/2, yogurt 3/4 cups) and adds almond milk for two 8 fluid-ounce servings. (There are 8 fluid ounces in 1 cup.)
Tyshawn has a collection of 140 coins. How many coins represent 20% of his collection?
Please help I need help!!!!!!!!!!!!!!!!!!!!!
Solve for the interior of angle, x.
90°
130°
130⁰
130
120%
Xo
Nevaeh has $2,131.50 in a savings account that earns 6% interest per year. If she initiall
deposited $2,100 how many months has she been investing her money?
We know that Nevaeh initially deposited $2,100, and now she has $2,131.50 in her account. The interest earned is $2,131.50 - $2,100 = $31.50. To find out how many months has she been investing her money, we can use the following formula:
Time (in months) = (Interest / Principal) x (12 / Interest Rate)
Where Principal is the initial deposit amount, Interest Rate is the annual interest rate, and Interest is the amount of interest earned.
Plugging in the given values, we get:
Time (in months) = ($31.50 / $2,100) x (12 / 0.06)
Time (in months) = 0.0149 x 200
Time (in months) = 2.98
Since time cannot be in fraction of months, it has to be rounded off. So, Nevaeh has been investing her money for approximately 3 months.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years. Predict the account balance after 0, 1, and 2 years. Round your answers to the nearest dollar.
Tiles:
$845
$758
$952
$765
$750
Boxes:
initial deposit
balance after 1 year
balance after 2 years
According to the given expression, the account's initial deposit is 750, the balance after one year is 845, and the balance after two years is 952.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years.
Expression for money is given
Thus, balance at x = 0
Balance A(0) = 750
Balance at x = 1
Balance A(1) = 750(1.01)^12*1
A(1) = 845.11
Balance at x = 2
Balance A(2) = 750(1.01)^12*2
A(2) = 952.43
Therefore, In the account initial deposit is 750, balance after 1 year is 845, and balance after 2 years will be 952 as per the given expression.
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On Friday, Wall Street traders were anxiously awaiting the federal government's release
of numbers on the January increase in nonfarm payrolls. The early consensus estimate
among economists was for a growth of 250,000 new jobs (CNBC, February 3, 2006).
However, a sample of 20 economists taken Thursday afternoon provided a sample mean
of 266,000 with a sample standard deviation of 24,000. Financial analysts often call such
a sample mean, based on late-breaking news, the whisper number. Treat the "consensus
estimate" as the population mean. Conduct a hypothesis test to determine whether the
whisper number justifies a conclusion of a statistically significant increase in the consen-
sus estimate of economists. Use a = .01 as the level of significance.
Anazlysing the conditions given in the question we can conclude that there is a statistically significant increase in the consensus estimate of economists.
How do financial analysts use the whisper number in their decision making process?Financial analysts often use the whisper number, which is a late-breaking estimate of a key economic indicator, to make predictions about the stock market and inform their investment decisions. They may use it to identify potential opportunities for buying or selling stocks based on whether the whisper number is higher or lower than expected.
Can the whisper number be used to predict the stock market?While the whisper number can provide insight into the current economic conditions, it is not a foolproof way to predict the stock market. It is just an estimate based on a sample of economists' predictions and can be affected by various unpredictable factors. Therefore, it's important to take other economic indicators and market conditions into account when making investment decisions.
To conduct a hypothesis test, we need to first define the null hypothesis and alternative hypothesis.
Null Hypothesis: The whisper number (sample mean) is equal to the consensus estimate (population mean)
H0: μ = 250,000
Alternative Hypothesis: The whisper number (sample mean) is greater than the consensus estimate (population mean)
H1: μ > 250,000
The next step is to calculate the test statistic and p-value. We can use a one-tailed t-test since the sample size is less than 30 and we don't know the population standard deviation.
Test statistic:
t = (266,000 - 250,000) / (24,000 / sqrt(20))
P-value:
Using the t-distribution table with 19 degrees of freedom, the p-value is less than 0.01, which is the significance level we set.
Since the p-value is less than the significance level (0.01), we can reject the null hypothesis and conclude that there is a statistically significant increase in the consensus estimate of economists.
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factorise 14x squared-x-13
Answer:
(14x+13)(x-1)
Step-by-step explanation:
14x²-x-13
14 × 13 = 182
Search for factors of 182 that contain a difference of 1 when subtracted because -x is the same as -1x.
Since 14 × 13 = 182
and
13 - 14 = -1
They are our 2 chosen numbers which will be displayed as :
14x² - 14× + 13x - 13
where -x is replaced by -14x + 13x
Proceed to factorise normally
14x(x-1) + 13(x-1)
Grouping
(14x+13)(x-1)
Which of the following is a logarithmic function?
Oy=log, X
Oy=3*
Oy=x+3
O y=x³
y = log (x)
Step-by-step explanation:Logarithmic functions are the inverse of exponential functions. Logarithmic is usually shortened to log.
Logarithmic Operation
Logarithmic functions help solve exponential equations. For example, the exponential function: bˣ = a, could be difficult to solve. To find x, we can use the log operation. By taking the log of both sides we can change this exponential function into a log function. In log form, the function becomes [tex]log_{b} (a)=x[/tex]. This is pronounced, "log-base b of a equals x." If you plug this into a calculator or use a different technique to solve, you can find x and solve the original exponential function.
Common Log and Natural Log
Although logarithmic functions can have any base, some are more frequent than others. One such base is base 10. If the base of the log is 10, then we do not write the 10, it is just implied. This log is called common log. The answer choice y = log (x) is common log. Another common base is Euler's constant, e. Log with the base of e is called natural log. Natural log is written as ln (x).
During 2012, Texas had listed on FracFocus, and industry tracking disclosure site, nearly 6000 oil and gas wells in which the fracking methodology was use to extract natural gas. Fontenot et al. (2013) reports on a study of 100 private water wells in or near the Barnett Shales in Texas. There were 91 private wells located within 5 km of an active gas well using fracking, 4 private wells with no gas wells located within a 14 km radius, and 5 wells outside of the Barnett Shale with no gas well located with a 60 km radius. They found that there were elevated levels of potential contaminants such as arsenic and selenium in the 91 wells closest to natural gas extraction sites compared to the 9 wells that were at least 14 km away from an active gas well using the fracking technique to extract natural gas.
Four part question. Answer all parts.
(a) Identify the population that is of interest to the researchers.
(b) Describe the sample.
(c) What characteristics of the population are of interest to the researchers?
(d) If the sample measurements are used to make inferences about the population characteristics, why is a measure of reliability of the inferences important?
(a) The population of interest to the researchers is private water wells in or near the Barnett Shales in Texas.
(b) The sample is 100 private water wells, 91 of which are located within 5 km of an active gas well using fracking, 4 private wells with no gas wells located within a 14 km radius, and 5 wells outside of the Barnett Shale with no gas well located within a 60 km radius.
(c) The characteristics of the population of interest to the researchers are the levels of potential contaminants such as arsenic and selenium in the private water wells.
(d) A measure of reliability of the inferences is important because it allows the researchers to determine the degree of confidence they can have in the findings of the study, and to identify any potential sources of error in the study design or measurement.
What is population?The sample is a subset of this group that is representative of the population, whereas the population of interest is the entire unit of people you are considering for the study. When using sampling, you typically collect information from the sample before extrapolating the results to the entire population.
Without a measure of reliability, it would be difficult to assess the generalizability of the study's findings to the broader population of private water wells in the Barnett Shale region.
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what is solution set for 2x2+15=-11x?
A{2.5,3} C{-3,-2.5}
B[1.5,5} D{-5,-1.5}
Answer:
C{-3,-2.5}
Step-by-step explanation:
Brainliest pls
I need help please asap??!!!
Answer:
first answer is
1.31
Step-by-step explanation:
and second is
7.47
hope it help you
hi friend
In an absolute value graph, the slope of one side of the graph is the ______________ of the other side.
Then give an example...If the slope of one side of an absolute value function is _________, then the other side of the equation has a slope of ________
Answer:
In an absolute value graph, the slope of one side of the graph is the negative of the other side.
For example, if the slope of one side of an absolute value function is 2, then the other side of the equation has a slope of -2.
graph the following system of equations and find the x coordinate of the soloution x3=3y=3 y=1/2x+2
Answer:
infinitely many solutions and x=y
The ten -digit number 3872649A0B is divisible by 36 . The letters A and B each represent single digit even numbers. Find the sum A+B.
The sum of A + B, considering that the ten-digit number is divisible by 36, is given as follows:
A + B = 6.
How to obtain the sum of A and B?The sum of A and B is obtained considering the rule for a divisibility by 36.
To be divisible by 36, the numbers must be divisible by both 4 and 9, for which the rules are given as follows:
Divisible by 4: the last two digits of the number are divisible by 4.Divisible by 9: the sum of the digits of the number is a multiple of 9.The ten-digit number is given as follows:
3872649A0B
The sum of the digits is given as follows:
3 + 8 + 7 + 2 + 6 + 4 + 9 + A + 0 + B = 39 + A + B.
Hence the condition for a divisibility by 36 is given as follows:
39 + A + B = 45
A + B = 6.
Which is the result for the sum in the context of this problem.
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Consider the quadratic equation x squared minus 7 x minus 18 equals 0
Find the solutions by factoring.
x = -9, x = 2
x = -2, x = 9
x = -6, x = 3
x = -3, x = 6
Answer:
x = -2, x = 9
Step-by-step explanation:
Given quadratic equation:
[tex]x^2-7x-18=0[/tex]
To factor a quadratic in the form ax²+bx+c, first find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -18=-18[/tex]
[tex]\implies b=-7[/tex]
Therefore, the two numbers are: -9 and 2.
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-9x+2x-18=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-9)+2(x-9)=0[/tex]
Factor out the common term (x - 9):
[tex]\implies (x+2)(x-9)=0[/tex]
Apply the zero-product property:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-9=0 \implies x=9[/tex]
Therefore, the solutions to the given quadratic equation are:
x = -2, x = 9The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42
The equation that represents the relationship is:
x + (x + 1) + (x + 2) = 42
And the 3 consecutive numbers are 13, 14, and 15.
Which equation represents the relationship?Here we know that the sum of three consecutive integers is 42.
If the first number is x, then the two consecutive numbers are:
x + 1
x + 1 + 1 = x + 2
Then the sum of these 3 consecutive numbers can be written as:
x + (x + 1) + (x + 2)
And that is equal to 42, then the equation is:
x + (x + 1) + (x + 2) = 42
So the first option is the correct one.
And the solution is:
x + (x + 1) + (x + 2) = 42
3x + 3 = 42
3x = 42 - 3
3x = 39
x = 39/3
x = 13
The 3 numbers are:
13, 14, and 15.
Learn more about consecutive numbers:
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