The statement is equivalent to numerical value 81.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the statement as -
"base 3 and exponent 4"
We can write mathematically as -
{x} = 3⁴
{x} = 3 x 3 x 3 x 3
{x} = 81
Therefore, the statement is equivalent to numerical value 81.
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Sloan is going to make a berry salad for a party.
Her salad will include only blueberries, raspberries, and strawberries. She wants the ratio of blueberries to strawberries to be 2:5, and the ratio of blueberries to all berries to be 4:23. How many of each type of berry can she put in the salad?
The number of each type of berry that she can put in her salad would include the following:
Blueberry = 4
Blueberry = 4Strawberry = 10
Blueberry = 4Strawberry = 10Raspberry = 13
How to calculate the quantity of berries in the salad?The salad that was prepared by Sloan contains the following berries:
Ratio of Blueberry to strawberries = 2:5
The ratio of blueberry and others = 4:23
Therefore,
Since every 2 blueberry = 5 strawberry, 4 blueberry = 10 strawberry.
The quantity of raspberry = 23-10 = 13
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Please help me by finding the degree measure of angle x
Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is the Pythagorean theorem?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.
Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.
Here, in this triangle by Pythagorean theorem
[tex]A^2 = B ^2 + c^2[/tex]
AC = [tex]\sqrt{14^2- 9^2}[/tex]
AC = [tex]\sqrt{196- 81}[/tex]
Ac = [tex]\sqrt{115}[/tex]
Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.
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What is the value of
3/10^3
Answer:
c
Step-by-step explanation:
9/10
a hospital director is told that 55% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is less than the expected percentage. a sample of 230 patients found that 115 were insured. determine the p-value of the test statistic. round your answer to four decimal places.
The p-value of the test statistic is 0.0401, which is less than the commonly used significance level of 0.05.
In statistical analysis, hypothesis testing is an essential method used to make inferences about population parameters using sample data. In this case, a hospital director wants to test a claim that the percentage of insured patients is less than the expected percentage.
The alternative hypothesis is that the percentage of insured patients is less than the expected percentage. To test this hypothesis, the director will use a one-tailed z-test for proportions. The test statistic is calculated as:
z = (p - P) / √(P(1-P) / n)
where p is the sample proportion, P is the expected proportion under the null hypothesis, and n is the sample size.
In this case, the sample proportion is 115/230 = 0.5, and the expected proportion is not specified. However, since the null hypothesis is that the percentage of insured patients is equal to the expected percentage, we can use the observed percentage of 55% as a reasonable estimate of the expected percentage. Thus, P = 0.55.
Plugging in these values, we get:
z = (0.5 - 0.55) / √(0.55 * 0.45 / 230) = -1.74
p-value = -1.74/0.069 = 0.0401
Trough this one we have identified that the test statistic's p-value is 0.0401, indicating that it is below the widely accepted significance level of 0.05.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.
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PLEASE HELP 50POINTS!!!!!
Can you always use synthetic division for dividing polynomials?
Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.
Dividing Polynomials:We use the division of polynomials to find the quotients of two polynomials. Two polynomials can be divided by simply multiplying and dividing by the largest power in each term.
The two different ways to divide polynomials are 1. Long division method and 2. The synthetic division method. The synthetic division method is the quickest way to divide polynomials between these two approaches.
Advantages of performing a Synthetic Division:
Only if the divisor is a linear factor can we use the synthetic division approach. In contrast to the long division method, which uses division and subtraction, the synthetic division approach uses multiplication and addition. There are just a few calculations needed. There is no need for variables to do the calculation.This method is less prone to errors than the polynomial long division method.
Therefore,
We can say
Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.
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Can anyone help me out please I really need it…
Answer:
x= 39.549°
Step-by-step explanation:
please review answer.
Find the distance of a chord of Length 16cm From the centre of a Circle of radius 12.Cm.
The distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The the distance can be observed to be of the side of a right triangle with the hypotenuse as the radius of the circle and the base side half of the chord, if x is used to represent the distance of the chord from the centre of the circle.
so by Pythagoras rule we can write:
12² = x² + 8²
144 = x² + 64
x² = 144 - 64 {collect like terms}
x² = 80
x = √80 {take square root of both sides}
x = 8.9443
Therefore, the distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.
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Write the exponential function that describes the situation.
The initial amount of the function is 11 and then it decreases by a factor of 8/9 with each unit increase in x
The function that describes the situation is y=
Answer: The form for an exponential equation is f(t)=P0(1+r)t/h where P0 is the initial value, t is the time variable, r is the rate and h is the number needed to ensure the units of t match up with the rate. Plug in the initial value for P and the rate for r. You will have f(t)=1,000(1.03)t/h.
Step-by-step explanation:.....
Diane obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 9.65%. Her loan is for $17,100 for 76 days. Assume
1
365
De not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
each day is
of a year Answer each part below.
(a) And the interest that will be owed after 76 days.
$
(b) Assuming Diane doesn't make any payments, find the amount owed after 76 days.
?
I need help fast
a) The simple interest that will be owed the bank by Diane after 76 days is $343.59.
b) The final amount that Diane will repay the bank after 76 days is $17,443.59.
What is the simple interest?The simple interest is an interest system that does not compound interest.
Compounding interest means that interest is added to the principal before subsequent interests are computed.
But under the simple interest system, interest is based on the principal from one period to the next.
The loan amount = $17,100
Simple interest rate = 9.65%
Loan period = 76 days
Total interest = $17,100 x 9.65% x 76/365 = $343.59
Final amount = $17,443.59 ($17,100 + $343.59)
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In a geometric sequence, the first term, a_1, is equal to 3, and the third term, a_{3}, is equal to 192 Which number represents the common ratio of the geometric sequence?
Answer:
r = 8
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₁ = 3 and a₃ = 192 , then
a₁ = 3 → (1)
a₁r² = 192 → (2)
divide (2) by (1) on both sides
[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then
r² = 64 ( take square root of both sides )
r = [tex]\sqrt{64}[/tex] = 8
오
NK=(12
If the quadrilateral below is a rhombus, find the missing
measures. MK = 24, JL = 20, and m/MJL = 50°. Round to 1
decimal place.
NL=10
ML=(68
JM=(68
m&KNL=(
), m&KJL=(
m_MLK=
), m/JKM=(
The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°
What is the perimeter of Rhombus?A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.
When the two diagonals of a rhombus are known,
The perimeter = 2√p² + q²
where 'p' and 'q' are the diagonals.
Given data ,
Let the rhombus be represented as JKLM
where MK and JL are the diagonals and N is the midpoint of intersection
The measure of MK = 24
The measure of JL = 20
The measure of NK = 12
The measure of ∠MJL = 50°
Now , the diagonals of a rhombus bisect each other , so
NK = MK/2 = 12
And , NL = JL / 2 = 10
Now , to calculate the measure of ML ,
In triangle MNL, ∠N = 90°
MN = NK = 12 , NL = 10
Using Pythagorean theorem of triangles , we get
ML² = MN² + NL²
ML² = 12² + 10²
ML² = 244
ML = √244
On simplifying the equation , we get
ML = 2√61 = 15.62
The measure of ML = measure of JM = 15.62 ( all sides are equal )
The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )
∠KJL = ∠MJL (diagonals bisect angles)
The measure of ∠KJL = 50°
∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°
∠MJK = ∠MLK (opposite angles are equal)
The measure of ∠MLK = 100°
∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)
50 + 90 + ∠JKM = 180
The measure of ∠JKM = 40°
∠JKL = 2 x ∠JKM (diagonal bisect angle)
The measure of ∠JKL = 2 x 40
The measure of ∠JKL = 80°
∠JKL = ∠JML (opposite angles are equal)
The measure of ∠JML = 80°
Hence , the measures of rhombus is solved
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City officials conclude they should budget "s" million dollars for a new library
building if the population increases by "p" thousand people in a ten-year census. The formula:
s = 2 + 1/3(p + 1)^2/5
expresses the relationship between population and
library budget for the city. How much can the population increase without the city
going over budget if they have $5 million for a new library building?
In linear equation, 242 can the population increase without the city going over budget if they have $5 million for a new library building .
Which equation is linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Substitute the value of s into formula for P -
P = ( 3(5-2)) 5/2 - 1
= (3(3))5/2 - 1
P = 95/2 - 1
P = 243 - 1
= 242
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question number 15 is the one i am struggling on someone please help a girl out
The value of x is given as follows:
[tex]x = 2.5\sqrt{2}{/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For a right triangle with an angle of 45º, we have that:
The side lengths are equal.The hypotenuse is of [tex]s\sqrt{2}[/tex]This is because the angle of 45º has an equal value of the sine and of the cosine.
Hence the side length of the top triangle is given as follows:
s = 5.
For the bottom triangle, the side length is of x, while the hypotenuse is of 5, hence:
x² + x² = 5²
2x² = 25
[tex]x = \sqrt{\frac{25}{2}}[/tex]
[tex]x = \frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]x = 2.5\sqrt{2}{/tex]
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there are three coins in a box. one is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 80% of the time. (a) when one of these coins were selected at random and flipped, what is the probability that it shows heads? (1 po
The probability of the selected coin showing heads is 0.77, or 77%.
Probability is the measure of the likelihood of an event occurring. In this scenario, we have three coins in a box, each with different properties.
To calculate the probability of an event occurring, we need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are three possible coins we could select, each with a different probability of showing heads.
Now, we need to determine the total number of possible outcomes, which is simply the number of coins we have, which is three.
Next, we need to determine the number of favorable outcomes. For Coin 1, the probability of showing heads is 1 (since it has two heads). For Coin 2, the probability of showing heads is 0.5 (since it is a fair coin with equal probability of heads and tails). For Coin 3, the probability of showing heads is 0.8.
To calculate the probability of showing heads when we randomly select one of these coins, we need to weigh the probabilities of each coin being selected with their corresponding probabilities of showing heads.
Let's say that the probability of selecting each coin is equal (since we have no information to suggest otherwise). Then, the probability of selecting Coin 1 is 1/3, the probability of selecting Coin 2 is 1/3, and the probability of selecting Coin 3 is 1/3.
To calculate the overall probability of showing heads, we can use the following formula:
P(heads) = (P(Coin 1) * P(heads on Coin 1)) + (P(Coin 2) * P(heads on Coin 2)) + (P(Coin 3) * P(heads on Coin 3))
= (1/3 * 1) + (1/3 * 0.5) + (1/3 * 0.8)
= 0.77
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the perimeter of a square with side length $x$ units is equal to the circumference of a circle with radius 2 units. what is the value of $x$? express your answer as a decimal to the nearest hundredth.
The value of $×$ is 3.14 units
What is perimeter ?Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.
The perimeter of a square is expressed as 4l
The circumference of a circle = 2πr
This means that;
4l = 2πr
4l = 2× 3.142 × 2
4l = 12.57
divide both sides by 4
l = 12.57/4
l = 3.14 units(nearest hundredth)
therefore the value of the side length is 3.14 units
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help meeeeeeeeee!!!!!
-
a
a
a
a
a
a
a
a
What is the arc length of GH? G 10 mm 60° H Express your answer as a simplified fraction in terms of T.
Answer:
[tex]\huge\boxed{\sf S=\frac{20}{6} \pi \ mm}[/tex]
Step-by-step explanation:
Given data:Radius = r = 10 mm
Degree = θ = 60°
Required:Arc length = S = ?
Formula:[tex]\displaystyle S=\frac{\theta}{360} \times 2 \pi r[/tex]
Solution:Insert the values in formula.
[tex]\displaystyle S = \frac{60}{360} \times 2 \pi (10)\\\\S=\frac{1}{6} \times 20 \pi\\\\S=\frac{20}{6} \pi \ mm\\\\\rule[225]{225}{2}[/tex]
Mackenzie's company reimburses her $0. 75 per mile that she drives for business. If she goes on a business trip and drives a total of 982 miles, how much will her reimbursement be?
Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.
Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.
Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.
Reimbursement = miles driven x rate per mile
Filling the value in above equation.
So,
Reimbursement = 982 miles x $0.75/mile
Reimbursement = $736.50
Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.
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suppose you are asked to guess a number between 1 and 15 (inclusive), and after each guess you are told whether it is higher or lower. what is the minimum number of guesses required to guarantee that you know the number?
3 is the minimum number of guesses required to guarantee that you know the number.
If we use a binary search approach, we can guess the number in a minimum number of steps.
First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.
Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.
We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.
Therefore, we can guarantee that we know the number in three guesses using this binary search approach.
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Write a letter to the editor of a newspaper, making the public aware of rising air and noise pollution in your area. (rdmcoyvtvs meat for fuñ)mention the bad air quality index that appears in the newspaper daily and write about the bad effects of air and noise pollution and suggest some measures to curb it.
Follow=Follow
like
don't forget to make brainalist and keep smiling
Answer: Dear Editor,
I am writing to bring to your attention the serious issue of rising air and noise pollution in our area. The daily air quality index that appears in the newspaper highlights the extent of the problem, and I believe it is important for the public to be aware of its effects.
Air pollution has been linked to a number of health problems, including respiratory issues, heart disease, and even cancer. The presence of harmful pollutants in the air we breathe is cause for concern and demands immediate attention. Similarly, noise pollution can lead to hearing loss, sleep disturbance, and increased stress levels.
It is imperative that we take action to curb the effects of air and noise pollution. There are several measures that can be taken, both by individuals and by the government. On an individual level, we can reduce our carbon footprint by using public transportation, carpooling, or biking instead of driving alone. We can also plant trees and install air purifiers in our homes.
The government, on the other hand, can take steps to regulate industrial emissions, enforce stricter penalties for violators, and promote the use of clean energy sources. Additionally, they can create green spaces and establish noise-free zones in residential areas.
In conclusion, the rise in air and noise pollution is a pressing issue that affects the health and well-being of everyone in our community. I urge the public to take this matter seriously and support efforts to reduce its impact. Together, we can work towards a cleaner and healthier future.
Sincerely,
[Your Name]
Step-by-step explanation:
Carson is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Carson will earn $20 every time one of his songs is played
in a commercial and he will earn $120 every time one of his songs is played in a
movie. Carson's songs were played on 5 more commercials than movies, and his total
earnings on the royalties from all commercials and movies was $38o. Determine the
number of commercials and the number of movies on which Carson's songs were
played.
Carson's songs were played on commercials and
movies.
Answer:
20×5=100
380-100=280
280÷120=2 and 40 remain
40÷20=2
5+2=7commercials 2 moviesthe base of the rectangle is 7 more than its height x. if the perimeter of the rectangle is greater than 30in find the height
The height of the rectangle must be greater than 4 inches if the perimeter of the rectangle is greater than 30 inches.
In geometry, a rectangle is a quadrilateral with four right angles, and opposite sides are equal in length. The perimeter of a rectangle is the total distance around it.
Let's assume that the height of the rectangle is x inches. According to the problem, the base is 7 more than its height, which means the base is (x + 7) inches.
Now, we can calculate the perimeter of the rectangle using the formula:
Perimeter = 2(length + width)
In a rectangle, the length and width are the same as the base and height, respectively. So, in our case, the perimeter of the rectangle will be:
Perimeter = 2(x + (x + 7)) = 4x + 14
As we are given that the perimeter of the rectangle is greater than 30 inches, we can write the inequality:
4x + 14 > 30
Solving for x, we get:
4x > 16
x > 4
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Suppose you took a job walking the neighbor's dog because you had borrowed $50.00 from your parents, and you need to pay them back. For this job, you are paid $15 per week to walk the dog for 20 minutes each weekday. Suppose you took a job walking the neighbor's dog because you had borrowed $50.00 from your parents, and you need to pay them back. For this job, you are paid $15 per week to walk the dog for 20 minutes each weekday. Working on the Desmos Graphing Calculator, complete the table showing how many weeks it will take to pay your parents back the money you borrowed. Take a screenshot of your graph when you are finished to submit later in the assignment.
The graplh shows that it will take 3.33 weeks to pay up the money borrowed
How to find the equation to plotted on the graphA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = money borrowed from your parents = $50.00
m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15
x = number of weeks
y = amount remaining
The equation is
y = 15x - 50
From the graph the pay will be completed at x = 3.33 (3.33, 0)
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This next question is a little bit tricky, but keep in mind the Disney World / Bush Gardens example from the lectures.
What is the probability that someone uses a cell phone while driving or had no speeding violation?
Find the probability that someone uses a cell phone while driving, add to that the probability that someone did not receive a speeding violation, then subtract the value in the square where those two overlap.
Round your answer to the hundredths place.
The probability of both events is the sum minus the intersection. The answer should be rounded to two decimal places.
To calculate the probability of someone using a cell phone while driving or had no speeding violation, first calculate the individual probabilities of each event. The probability of someone using a cell phone while driving is P(cell phone) and the probability of someone having no speeding violation is P(no speeding violation). Then, add these two probabilities together, P(cell phone) + P(no speeding violation). This will give you the total probability of both events occurring. Finally, subtract the probability of the intersection, which is the probability of someone using a cell phone while driving and having no speeding violation. This will give you the total probability of someone using a cell phone while driving or having no speeding violation. Round the answer to the hundredths place.
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A dietician recommends 48 grams of protein each day for his patient. At the end of the day, the patient has only eaten 40 grams of protein. What percent of her daily intake has the patient eaten?
Answer:
83%
Step-by-step explanation:
To find the percentage divide 40 by 48
40/48 = 0.83333333333333
Round to 0.83
Multiply by 100
The patient has only eaten 83% of her daily intake.
Given: Sin Ø = 2/3 and Ø is in the second quadrant; evaluate the following expression. Sin2Ø
Please explain!!
HELP POLSSSSSSSSSSSSSSSSSSS
Answer:
The angle is 180°
Step-by-step explanation:
[tex]{}[/tex]
Answer: look at the image for the answer and solution
Step-by-step explanation:
the cost to rent a car from lou's garage is 50 + 0.1m dollars for m miles. The cost of a car ar Jerry's Garage is 25 + 0.05m dollars for the same number of miles
Answer:
To find out which rental car company is cheaper, you need to compare the cost for the same number of miles driven. Let's say you drive a total of "m" miles.
The cost for renting a car from Lou's Garage is 50 + 0.1m dollars.
The cost for renting a car from Jerry's Garage is 25 + 0.05m dollars.
To determine which option is cheaper, you need to compare these two expressions and find out which one is less. To do this, you can subtract the second expression from the first expression:
50 + 0.1m - (25 + 0.05m) = 25 + 0.05m
This equation shows that the cost of renting a car from Lou's Garage is 25 + 0.05m dollars more expensive than renting a car from Jerry's Garage for the same number of miles driven. Therefore, Jerry's Garage is the cheaper option.
[tex]64^{2x+1} =1024[/tex]
Answer:
x = 1/3
Step-by-step explanation:
64^2x+1 = 1024
4^3(2x+1) = 4^5
Since the bases are the same, two expressions are only equal if the exponents are also equal.
3 (2x + 1) = 5
Divided each term by 3
2x + 1 = 5/3
2x = 2/3
x = 1/3
Which renames 5/12and3/8 using a common denominator
Common denominator of 5/12 and 3/8 is 24.
To rename 5/12 and 3/8 using a common denominator, we need to find the least common multiple (LCM) of the denominators 12 and 8, which is 24.
To convert 5/12 to an equivalent fraction with a denominator of 24, we can multiply both the numerator and denominator by 2 to get:
5/12 = (5 x 2)/(12 x 2) = 10/24
To convert 3/8 to an equivalent fraction with a denominator of 24, we can multiply both the numerator and denominator by 3 to get:
3/8 = (3 x 3)/(8 x 3) = 9/24
So, 5/12 and 3/8 can be renamed as 10/24 and 9/24, respectively, using a common denominator of 24.
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