Note that the limit of the expression as x approaches infinity is 1/2.
How did we arrive at this conclusion ?start by multiplying both the numerator and denominator by the conjugate expression
√ (x ² - 9x + 1) + x,
this will eliminates the root in the numerator
lim x->∞ [(√(x ² - 9x + 1) - x) * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)
Expanding the numerator
lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)
Simplifying further:
lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)
we can see that the 1/x ² term approaches zero, and the expression simplifies to
lim x->∞ [(1 - 0)] / (√(1 - 0) + 1)
= 1/2
So it is correct to state that the limit of the expression as x approaches infinity is 1/2.
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Please help!!!!!!!!!!!
Solve for X
Find the measure of each angle using the solution to part C
Suppose that the functions f and g are defined as follows.
Find f.g and f+ g. Then, give their domains using interval notation.
Using interval notation, the domain of f.g and f+g is [1/4, ∞).
Given, f(x)= 1/ (5x² + 3) and [tex]g(x) = \sqrt{4x-1}[/tex]
To find f.g, we substitute g(x) into f(x) and simplify:
f.g(x) = f(g(x))
[tex]=f(\sqrt{4x-1})[/tex]
[tex]=\frac{1}{5(\sqrt{4x-1})^2 +3}[/tex]
= 1/(5(4x-1)+3)
= 1 / (20x - 2)
To find f+g, we add the functions f(x) and g(x):
f+g(x) = f(x) + g(x)
= [tex]\frac{1}{5x^2+3}+\sqrt{4x-1}[/tex]
The domain of f.g and f+g is the intersection of the domains of f(x) and g(x).
The domain of f(x) is all real numbers except for the values of x that make the denominator zero, i.e., 5x² + 3 = 0. This equation has no real solutions, so the domain of f(x) is all real numbers.
The domain of g(x) is the set of all real numbers that make the argument of the square root non-negative, i.e., 4x - 1 ≥ 0. Solving this inequality, we get x ≥ 1/4.
Therefore, the domain of f.g and f+g is x ≥ 1/4.
Using interval notation, the domain of f.g and f+g is [1/4, ∞).
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A regular pentagon has an apothem of
3 cm and a side length of 4.4 cm, find
its area.
The area of the polygon is 33cm²
What is area of polygon?A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
The area of a polygon is expressed as;
A = 1/2 × p × a
where p is the perimeter of the polygon and a is the apothem.A pentagon is a 5 sides polygon.
Therefore;
Perimeter = 5 × 4.4
= 22cm
apothem = 3cm
area = 1/2 × 22 × 3
= 11× 3
= 33 cm²
therefore the area of the Pentagon in is 33cm²
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The radius of a circle is 7 inches the radius of circle, B is 3inches greater than the radius of circle A. If the radius of circle C is 4 inches greater than the radius of circle B the radius of circle D is 2 inches less than the radius of circle C, see what is the area of each circle
The area of each circle would be given below:
Circle A= 153.86 in²
Circle B = 314in²
Circle C = 615.44in²
Circle D = 452.16 in²
How to calculate the area of circle?To calculate the area of a circle, the formula that should be used is given below such as follows:
Area of circle = πr²
For circle A;
radius = 7 in
area = 3.14×7×7 = 153.86 in²
For circle B;
radius = 3+7 = 10in
area = 3.14×10×10 = 314in²
For circle C;
radius = 10+4 = 14 in
area = 3.14×14×14
= 615.44in²
For circle D;
radius = 14-2 = 12in
radius = 3.14×12×12
= 452.16 in²
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Let v = 2i - 3j Find ||2v||
For the given vector v = 2i - 3j, the value of the vector magnitude ||2v|| is 2√13.
To find the norm, or magnitude, of a vector, we use the Pythagorean theorem in the following way:
||v|| = √(v₁² + v₂² + ... + vn²)
In this case, we have v = 2i - 3j, so:
||v|| = √((2)² + (-3)²)
= √(4 + 9)
= √13
So the norm of the vector v is √13.
To find ||2v||, we simply double the vector and then find its norm:
2v = 2(2i - 3j)
= 4i - 6j
||2v|| = √((4)² + (-6)²)
= √(16 + 36)
= √52
= 2√13
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Find the volume of the cylinder. Use π = 3.14.
(If answered correctly with an explanation giving brainlyest)
A. 321.54 ft3
B. 10,048 ft3
C. 8,038.4 ft3
D. 100.48 ft3
The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Note: Radius = diameter/2 = 32/2 = 16 ft.
By substituting the parameters, we have:
Volume of cylinder, V = 3.14 × 16² × 10
Volume of cylinder, V = 8,038.4 cubic feet.
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could someone help me on this (have to turn it in by tomorrow)
Among the given options, V [tex]57^\circ[/tex] is the closest estimate for the measure of the other acute angle.
What is the measure of the other acute angle?To find the measure of the other acute angle, we can use the fact that the sum of the angles of a triangle is 180°. Let x be the measure of the other acute angle. Then we have:
[tex]x + 32.9^\circ + 90^\circ = 180^\circ[/tex]
Simplifying the equation, we get:
[tex]x = 180^\circ - 32.9^\circ - 90^\circ[/tex]
[tex]x = 57.1^\circ[/tex]
So the exact measure of the other acute angle is [tex]57.1^\circ.[/tex]
Therefore, Among the given options, V [tex]57.1^\circ.[/tex] is the closest estimate for the measure of the other acute angle.
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Jordan's monthly bank statement showed the following deposits and withdrawals:
$7.72,
−
−$84.26, $70.42,
−
−$50.15, $107.46
If Jordan's balance in the account was $92.66 at the beginning of the month, what was the account balance at the end of the month?
Jordan's account balance at the end of the month would be $143.85.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To determine Jordan's account balance at the end of the month, we need to add up the deposits and withdrawals to the initial balance.
Initial balance: $92.66
Deposits: $7.72 + $70.42 + $107.46 = $185.60 (sum of positive amounts)
Withdrawals: -$84.26 + (-$50.15) = -$134.41 (sum of negative amounts)
To calculate the account balance at the end of the month, we can add the deposits and withdrawals to the initial balance:
Account balance at the end of the month = Initial balance + Deposits - Withdrawals
= $92.66 + $185.60 - $134.41
= $143.85
Hence, Jordan's account balance at the end of the month would be $143.85.
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Answer questions 3 – 5 about the circle.
Answer:
3. radius = 9.4
4. radius = 22.6
5. diameter = 13.3
Step-by-step explanation:
The diameter of a circle = 2 * radius
For problem 3 and 4, you need to multiply the given radius by 2 to get the diameter.
For problem 5, you need to divide the diameter by 2 to get the radius.
Jamar is going to invest $2200 and leave it in an account for 14 years. Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200
Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.
How is the interest rate for continuous compounding determined?Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:
Total P+I (A) = $4,200.00
Principal (P) = $2,200.00
Compound (n) = Compounding Continuously
Time (t in years) = 14 years
R = 4.619% per year
The calculation steps are as follows:
Solving for rate r as a decimal
r = ln(A/P) / t
r = ln(4,200.00/2,200.00) / 14
r = 0.0461877
Then convert r to R as a percentage:
R = r * 100
R = 0.0461877 * 100
R = 4.62%/year
Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.
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Find the value of linear correlation coefficient r (statistics)
Answer:
r=1
Step-by-step explanation:
The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).
An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–5, 8), (3, 8), (–5, –4), and (3, –4). What is the area, in square inches, of the label needed to cover the face of the box?
96 in2
48 in2
40 in2
20 in2
The area, in square inches, of the label needed to cover the face of the box is 96 in².
Option A is correct.
How do we calculate?We must first determine the length and breadth of the rectangle before multiplying them together to determine the area of the rectangular face.
The distance between the x-coordinates of two opposite points determines the length of the rectangle:
length equals 3 - (-5) = 8.
The distance between the y-coordinates of the same two opposite points determines the rectangle's width:
width = 8 + (-4) = 12
In conclusion, the rectangle's size is: 8 × 12 = 96 square inches is the area formula.
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Please hurry due in an hour
In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.5% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.
The accrued value of Staci's investment in the account in the year 2029 is $26933.59
Calculating the accrued value of the accountThe statements in the question can be sumarrized as
Invested amount = $14,500Rate of interest = 3.5% compounded annually.The formula to calculate amount on investment is
Amount = P * (1 + r)ⁿ
Where
P = Principal = 14,500r = Rate = 3.5%n = time = 2029 - 2011 = 18When the values are substituted in the amount equation, we have
Amount = 14500 * (1 + 3.5%)¹⁸
Evaluate
Amount = 26933.59
Hence, the amount after the investment is $26933.59
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A certain drug is used to treat asthma. In a clinical trial of the drug, 30 of 298 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 9% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below.
1-PropZTest
prop<0.09
z=0.643690407
p=0.7401118941
p=0.1006711409
n=298
Question content area bottom
Part 1
a. Is the test two-tailed, left-tailed, or right-tailed?
Right tailed test
Two-tailed test
Left-tailed test
Part 2
b. What is the test statistic?
z=enter your response here
(Round to two decimal places as needed.)
Part 3
c. What is the P-value?
P-value=enter your response here
(Round to four decimal places as needed.)
Part 4
d. What is the null hypothesis, and what do you conclude about it?
Identify the null hypothesis.
A.Upper H 0 : p greater than 0.09
H0: p>0.09
B.Upper H 0 : p less than 0.09
H0: p<0.09
C.Upper H 0 : p not equals 0.09
H0: p≠0.09
D.Upper H 0 : p equals 0.09
H0: p=0.09
Part 5
Decide whether to reject the null hypothesis. Choose the correct answer below.
A.
Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
B.
Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.
C.
Reject the null hypothesis because the P-value is less than or equal to the significance level, α.
D.
Reject the null hypothesis because the P-value is greater than the significance level, α.
Part 6
e. What is the final conclusion?
A.
There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
B.
There is sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.
C.
There is sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
D.
There is not sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.
For the drug used to treat asthma in a clinical trial:
a) A, right-tailedb) 0.64c) 0.7401d) A, p > 0.09A, Fail to reject the null hypothesise) DHow to determine hypothesis?Part 1:
The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.
Part 2:
The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).
Part 3:
The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).
Part 4:
The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
Part 5:
We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.
Part 6:
The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
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James takes a 150000 mortgage for 20 years and makes a monthly payment of 915.00. What percent of the total loan does he pay back in interest?
James pays back approximately 82.33% of the total loan in interest over the 20-year period.
To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.
Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately 0.35% (4.25% annual rate divided by 12 months). The monthly payment of $915.00 is comprised of both principal and interest.
In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.
To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months (20 years x 12 months/year = 240 months) and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.
To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:
$123,500 ÷ $150,000 x 100 ≈ 82.33%
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Helppppppp pleaseeeee
Plsss help meeee quick
Answer:
B
Step-by-step explanation:
Lateral surface contains B,C and D (because A and E are bases)
A (lateral surface area) = 70 + 70 + 56 = 196 cm^2
a rectangle has a length of 5.25cm and area of 44.625cm2. what does the length of the rectangle have to be?
Answer:5.25cm
Step-by-step explanation:
1)look back at your question
2)look after the 6th word
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The solution of the inequality, log₂ 2m > log₂ (m + 5) is {m | m > 5 / 2}.
How to solve logarithm inequality?An inequality is an expression that have <, >, ≤ and ≥ . Therefore, let's solve the logarithmic inequality for the variable m.
Hence,
log₂ 2m > log₂ (m + 5)
Therefore, let's divide both sides by log₂.
Hence,
2m > m + 5
subtract m from both sides of the inequality
2m > m + 5
2m - m > m - m + 5
2m > 5
divide both sides by 2
2m / 2 > 5 / 2
Therefore,
m > 5 / 2
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a couple decides to keep having children until they have a girl, at which point they will stop having children. they also agree to having a maximum of 3 children. the table shows the probability distribution of X=the number of children such a couple would have.
From the discrete distribution given, the standard deviation is of 0.83 children.
How to solveThe distribution is:
P(X=1) =0.5
P(X=2) =0.25
P(X=3) =0.25
The mean is 1.75.
The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.
Hence:
The standard deviation is 0.83 children.
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diegos family spend 130$ total on a night ouy. they purchases 5 tickets to the fair and a family dinner for 55$ how much did each ticket to the fair cost
If Diego's family spent a total of $130, on a night out, then the each ticket for the fair cost's $15.
In order to find the "total-cost" of the tickets, we subtract the cost of the family dinner from the total amount spent;
⇒ Total cost of tickets = Total amount spent - Cost of family dinner,
⇒ Total cost of tickets = $130 - $55,
⇒ Total cost of tickets = $75.
Next, we divide the total cost of the tickets by the number of tickets purchased to find the cost of each ticket:
So, Cost per ticket = (Total cost of tickets)/(Number of tickets),
⇒ Cost per ticket = $75/5,
⇒ Cost per ticket = $15,
Therefore, each ticket to the fair cost $15.
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A radioactive isotope has a half-life of 1,920 years. Let f(t)
be the amount of isotope, in milligrams, that is present after t years. If the sample originally contained 21 milligrams, write an equation modeling this situation.
F(t)=
The equation that models the given situation is: f(t) = 21e^(-0.000361)t
How to solve an exponential decay function?We can model this situation with an exponential decay function.
f(t) = Pe^(rt)
Where:
f(t) = amount of isotope
P = starting amount
r = growth rate
t = time
Let's assume that there is 1 mg of our isotope. Thus,in 1920 years, we will have 1/2 mg. Thus:
(1/2) = (1)e^(1920r)
Take the natural log of both sides to bring the exponent down and to cancel out the e
ln(1/2) = ln(e^(r(1920))
ln(1/2) = r(1920)
ln(1/2)/1920 = r
r = -0000361
Thus, we have:
f(t) = Pe^(-0.000361)t
Plug in 21 for P to get:
f(t) = 21e^(-0.000361)t
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In a large school, it was found that 79% of students are taking a math class, 70% of student are taking an English class, and 67% of students are taking both.
Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.
b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.
What is the probability?Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.
Probability is represented as a fractional value using decimals, fractions, or percentages.
The percentage of students taking a math class =79%
The percentage of students taking an English class = 70%
The percentage of students taking both classes = 67%
Let the event that a student is taking a math class = m
Let the event that a student is taking an English class = e
The probability of m is p(m) = 0.79
The probability of e is p(e) = 0.70
The probability of m and e is p(m and e) = 0.67
The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)
The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)
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find the length of the segment and round to the nearest tenth if necessary
Answer:
14
Step-by-step explanation:
line from center to chord bisect chord
so x = 14
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 24x2 − 6xy − 2. The friends have already collected the following number of cans:
Jessa: 9x2
Tyree: 6x2 − 4
Ben: 4xy + 3
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Therefore , the solution of the given problem of expressions comes out to be the buddies need to gather to reach their objective is
9x² - 10xy - 1.
What does an expression exactly mean?It is preferred to employ shifting numbers, which may also prove to be increasing, diminishing, or blocking, rather than random estimations. Only by exchanging tools, information, or answers to problems could they assist one another. The statement of truth equation may comprise the arguments, elements, or quantitative remarks for strategies like increased disagreement, production, and blending.
Here,
Part A:
=> Jasmine: 9x²
=> 6x² - 4 for Tyree
=> Ben: 4xy + 3
These three phrases added together represent the total amount of canned food collected:
=> 9x² + (6x² - 4) + (4xy + 3)
=> 15x² + 4xy - 1
As a result, the expression for how many cans of food the three buddies have so far amassed is 15x² + 4xy - 1.
Part B's collection objective is 24x² - 6xy - 2.
Collection total: 15x² + 4xy - 1
The distinction between these two phrases shows the quantity of cans the buddies still need to gather:
=> (24x² - 6xy - 2) - (15x² + 4xy - 1)
=> 9x² - 10xy - 1
As a result, the phrase for how many more cans the buddies need to gather to reach their objective is 9x² - 10xy - 1.
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Molly's scout troop sold 148 boxes of cookies last month and 165 boxes this month. Find the percent of increase, rounded to the nearest tenth of a percent.
The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.
How is the percentage increase determined?The percentage increase can be determined by finding the difference or the amount of increase in sales.
This difference is divided by the previous month's sales and multiplied by 100.
The total number of boxes of cookies Molly's Scout Troop sold last month = 148
The total number sold this month = 165
The increase = 17 (165 - 148)
Percentage increase = 11.5% (17 ÷ 148 x 100)
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The Ferris Wheel can carry 4 passengers in each of its 15 cars in one ride. How many passengers can it carry on a total of 35 rides?
The Ferris Wheel can carry 2100 passengers on a total of 35 rides.
According to the question,
Number of cars in the Ferry Wheel = 15
Number of passengers in each car = 4
∴ Number of passengers in 15 cars = 15×4 = 60
So, the number of passengers on the Ferry Wheel = 60
Now,
The number of passengers the Ferry Wheel carries in one ride = 60
∴ The number of passengers in 35 rides = 60×35 = 2100.
Hence the Ferris Wheel can carry 2100 passengers on a total of 35 rides.
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Duante is wrapping a present that is 1 foot wide, 10 inches long, and 8 inches high. What is the minimum amount of
wrapping paper he will need?
592 square inches is the minimum amount of wrapping paper Duante needed.
Duante will need a minimum of 592 square inches of wrapping paper.
Lets convert the dimensions to the same units.
Since there are 12 inches in a foot, the dimensions are:
Width = 1 foot = 12 inches
Length = 10 inches
Height = 8 inches
The rectangular box is known as a cube
The surface area of a b=cuboid is given by SA = 2lw + 2lh + 2wh
where l is length, w is width and and h is the height of the cuboid
Substituting the given values, we get:
SA = 2(10)(12) + 2(10)(8) + 2(12)(8)
= 240 + 160 + 192
= 592
Therefore, Duante will need a minimum of 592 square inches of wrapping paper.
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Simplify with steps. (Write each expression without using the absolute value symbol)
|x+3| if x>5
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
|(x + 3) | if x > 5
This can be written as,
= |x + 3|
Now,
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Thus,
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
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