the adult population in millions in 2015 was 197.37 million
The student question is asking about the adult population in millions, given that the Bureau of Labor Statistics announced that 141.13 million were employed, 16.59 million were unemployed, and 39.65 million were not in the labor force in 2015.
To find the adult population, we need to add the number of employed, unemployed, and not in the labor force adults. This can be done as follows:
Adult population = Employed + Unemployed + Not in the labor force
= 141.13 million + 16.59 million + 39.65 million= 197.37 million
Therefore, the adult population in millions in 2015 was 197.37 million (rounded to two decimal places).
for more questions on population
https://brainly.com/question/25896797
#SPJ11
Solve the expression one-half x (48 ÷ 6) – 2 + 5 using PEMDAS.
7
8
9
10
The value of the expression using PEDMAS is 7.
What is PEDMAS?The acronym PEMDAS, which can alternatively stand for "Please Forgive My Dear Aunt Sally," is a mnemonic tool for remembering the order of operations in mathematical and algebraic formulas. Its acronym is:
P - Parenthesis (operations inside parentheses are done first)
E: Exponents (operations involving exponents are done next)
Divide and multiply is abbreviated MD (these operations are done left to right, whichever comes first)
AS stands for addition and subtraction (these operations are done left to right, whichever comes first). No matter how they approach it or how they understand it, PEMDAS helps to ensure that the same statement is assessed in the same way by various people. In mathematics, it is crucial to understand this idea, especially when working with complicated expressions or formulae.
The given expression is 1/2 x (48 ÷ 6) – 2 + 5.
Simplifying the expressions we have:
1/2 x (48 ÷ 6) – 2 + 5
= 1/2 x 8 - 2 + 5
= 4 - 2 + 5
= 7
Hence, the value of the expression using PEDMAS is 7.
Learn more about PEDMAS here:
https://brainly.com/question/24086845
#SPJ1
At her birthday party, Jayla wants to play a game where team members race through an obstacle course with bean bags on their heads. She bought a box of 100 bean bags in assorted colors to use in the game. She randomly selected 14 bean bags from the box and then put them back. Here are the colors she selected:
red, blue, green, blue, yellow, red, green, blue, red, yellow, red, green, blue, red
Based on the data, estimate how many red bean bags are in the box.
If necessary, round your answer to the nearest whole number.
Answer:
Jayla selected 14 bean bags randomly with replacement from a box of 100 bean bags, and 6 of them were red. To estimate how many red bean bags are in the box, we can use proportion:
Let's call "x" the number of red bean bags in the box. Then we can set up a proportion:
(red bean bags in the box) / (total bean bags in the box) = (red bean bags selected) / (total bean bags selected)
x / 100 = 6 / 14
Simplifying the right side, we get:
x / 100 = 3 / 7
Multiplying both sides by 100, we get:
x = 300 / 7
Rounding to the nearest whole number, we get:
x ≈ 43
Therefore, based on the data, we can estimate that there are approximately 43 red bean bags in the box.
Answer + Explanation:
To estimate how many red bean bags are in the box, we can use a sampling method called "balloting." Balloting is a way of estimating the number of items of a specific type in a larger population by taking a random sample and counting how many of that type are in the sample.
In this case, we have a population of 100 bean bags and a sample size of 14. We can calculate the sample proportion of red bean bags by dividing the number of red bean bags in the sample by the total number of bean bags in the sample, which gives:
(4/14) × 100% ≈ 28.6%
This means that, on average, we would expect 28.6% of the 100 bean bags in the box to be red. To estimate the actual number of red bean bags, we can multiply the sample proportion by the total number of bean bags in the box:
28.6% × 100 = 28.6
So the closest estimate for the number of red bean bags in the box is 29.
Note that this is just an estimate, and the actual number of red bean bags in the box may be higher or lower than the estimated value.
Consider the table of values shown to the right.
a. Write a linear function to model the relationship between
y and x.
b. Explain the meaning of the slope of this problem.
Pls show work
Thank you
Answer: y= 4x+2
Step-by-step explanation: meaning of slope - the amount of bacteria multiplies by 4 as each minute passes
(sorry English isn't my first language)
need help on this asap
A senator wants to know her approval rating among the constituents in her state. She has her staff obtain 1000 responses to a telephone survey of
registered voters in her state
O Simple Random Sample
O Systematic
O Self-Selected
Convenience
O Stratefied
Answer:B
Step-by-step explanation:
How long a line can you make using all the 5/8 inch strips?
The length of the line can be made is 5x/8 inch, where 'x' is the number of strips.
Finding the Length of a Line:Length is a measure of the size of an object or distance between two points, usually measured in units such as meters, centimeters, inches, feet, or miles.
In the given problem to find the length of a line we need to multiply the length of each strip by the number of strips
Here we have
The length of the strip = 5/8
The length of the line will depend on the number of strips
Let there be 'x' number of strips
The length of the line can be made = x × 5/8
=> 5x/8
Therefore,
The length of the line can be made is 5x/8 inch, where 'x' is the number of strips.
Learn more about Length at
https://brainly.com/question/29250779
#SPJ9
A meal costs $5.75. You offer a 10% discount. The sales tax is 4%. How much should you charge the customer? $
Answer:
To calculate the final cost of the meal, we need to first calculate the discount and then add the sales tax. Discount = 10% of $5.75 = $0.575 Price after discount = $5.75 - $0.575 = $5.175 Sales tax = 4% of $5.175 = $0.207 Final cost = Price after discount + Sales tax = $5.175 + $0.207 = $5.382 Therefore, you should charge the customer $5.382.
well, let's hmmm apply the 10% discount first
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5.75}}{\left( \cfrac{10}{100} \right)5.75} ~~ \approx ~~ 0.58~\hfill \stackrel{ 5.75~~ - ~~0.58 }{\approx\text{\LARGE 5.17}}[/tex]
now let's apply the 4% tax to it
[tex]\stackrel{\textit{4\% of 5.17}}{\left( \cfrac{4}{100} \right)5.17} ~~ \approx ~~ 0.21\hspace{5em}\stackrel{ 5.17~~ + ~~0.21 }{\text{\LARGE 5.38}}\qquad \textit{final charge}[/tex]
The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram
The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram contradicts the rule which states that the sum of all angles in any quadrilateral is 360°.
What is a quadrilateral?
The Latin words quadra refers to number four, and latus refers to the sides, on combining gives quadrilateral. Any polygon with four sides, four angles, and four corners is said to be a quadrilateral. It is a closed shape known as a quadrilateral which is formed by joining any four points, any three of these points must not be on a same line.The quadrilateral has interior angles at each of its four corners. The sum of all for interior angles is always 360°.
Given that The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram:
As we know that trapezoid and parallelogram both are quadrilaterals. so both will have interior angles sum equal to 360°
The given statement is false.
To know more about quadrilaterals, visit:
https://brainly.com/question/29934440
#SPJ1
Adele read an article about how tax-payers completed the majority of their tax forms. Here is what the article stated:
Who completed forms Self Family or friend Professional
47
%
47%47, percent 12
%
12%12, percent 41
%
41%41, percent
She wondered if senior citizens in her community followed this distribution, so she surveyed a random sample of 200
200200 senior citizens about how they completed their taxes. Here are her results:
Who completed forms Self Family or friend Professional
Senior citizens 90
9090 21
2121 89
8989
She wants to use these results to carry out a χ
2
χ 2
\chi, squared goodness-of-fit test to determine if senior citizens in her community complete their taxes differently than the article suggests.
What are the values of the test statistic and P-value for Adele's test?
Answer: x^2 = 1.143;
P-value > 0.25
Step-by-step explanation: I got it right on khan academy!!
The P-value for the test is less than 0.05, indicating strong evidence against the null hypothesis. Adele can conclude that senior citizens in her community complete their taxes differently than what was reported in the article.
To carry out a χ2 goodness-of-fit test, Adele needs to compare the observed frequencies of how senior citizens completed their taxes with the expected frequencies based on the distribution reported in the article. The test statistic for this type of test is calculated as the sum of the squared differences between the observed and expected frequencies divided by the expected frequencies. In this case, the test statistic is 15.67. The degrees of freedom for the test are equal to the number of categories minus one, which in this case is 3 - 1 = 2. Using a significance level of 0.05, the critical value for the test is 5.99. Since the test statistic of 15.67 is greater than the critical value of 5.99, we reject the null hypothesis that the senior citizens in the community complete their taxes according to the distribution reported in the article.
Find out more about the null hypothesis.
brainly.com/question/18330330
#SPJ4
a bag contains ten black marbles, twenty white marbles, and five grey marbles. you pick one without looking. what is the probability that the marble will be either white or black? show your work.
The probability that the marble drawn from the bag will be either white or black is 2/3 or approximately 0.667.
To calculate this probability, we first need to find the total number of marbles in the bag, which is 10 + 20 + 5 = 35. Then, we need to find the total number of marbles that are either white or black, which is 10 + 20 = 30.
Finally, we divide the number of white or black marbles by the total number of marbles to get the probability:
30/35 = 2/3 ≈ 0.667
Therefore, the probability is approximately 0.667 or 2/3. This means that there is a higher chance of drawing a white or black marble than a grey marble, as there are more white and black marbles in the bag than grey marbles.
To know more about probability, refer here:
https://brainly.com/question/29964401#
#SPJ11
Sp
4
A square has an area of 100 sq meters. What is the perimeter of the square?
The area of a square is given by the formula A = s^2, where s is the length of a side of the square. If the area of the square is 100 sq meters, then:
s^2 = 100
Taking the square root of both sides, we get:
s = 10
Therefore, the length of a side of the square is 10 meters. Since all four sides of a square are equal, the perimeter of the square is:
4s = 4(10) = 40 meters
the acceptance scheme for purchasing lots containing a large number of batteries is to test no more than 75 randomly selected batteries and to reject a lot if a single battery fails. suppose the probability of a failure is 0.001. (a) what is the probability that a lot is accepted? (b) what is the probability that a lot is rejected on the 20th test? (c) what is the probability that it is rejected in 10 or fewer trials?
If the probability of failure is 0.001, then the probability that
(a) lot is accepted is 0.9277,
(b) lot is rejected on 20th test is 0.000981,
(c) lot is rejected in 10 or fewer trials is 0.01.
Let the random-variable "X" represent number of batteries to test to get the first-battery which fails; in other words, to get first success.
Since, the trials are independent, X has a geometric distribution
Part (a) :
Let X = the number of trials,
So, the probability that the lot is accepted is :
⇒ P(X=75) = (0.999)⁷⁵×(0.001)⁰ = 0.9277,
Part (b) :
let Y = the numbers of trials before the first failure (geometric distribution and
So, the probability that lot is rejected on 20th-test is :
⇒ P(Y=20) = (0.001)⁰×(0.999)¹⁹ = 0.000981,
Part (c) :
The probability that it is rejected in 10 or fewer trials is :
⇒ 1- P(no Failures)
⇒ 1 – (0.001)⁰(0.999)¹⁰ = 0.01.
Learn more about Probability here
https://brainly.com/question/14897010
#SPJ4
3. Put the following integers in the descending order: -1, 10, -12, 0, -100, 100, 105
PLEASE ANSWER FAST!!!!!!!!!!!!!
B. The line of symmetry should have been 4 instead of –4.
We are given the quadratic:
, with a=1, b=-8, c=15.
and the quadratic equation is [tex]x^2[/tex]-[tex]8[/tex][tex]x[/tex]+[tex]15[/tex]=0
We know that the x-coordinate of the vertex, which is the point where the line of symmetry passes through is
.
Thus, the x-coordinate of the vertex is .
Thus, the line of symmetry is x=4.
A line of symmetry is a line that divides a shape into two equal parts that are mirror images of each other. It is also called a mirror line or axis of symmetry.
Learn more about line of symmetry here:
https://brainly.com/question/30963765
#SPJ1
Please help asap
A summer camp took a survey of how much time their campers spend reading daily. Sixty campers said that they spend between 1 and 2 hours reading daily.
What is the total number of campers that were surveyed?
___ campers
The total number of campers surveyed is 150.
What is percentage?The symbol for percentage is "%". Percentages are commonly used in a wide range of contexts, such as in finance, statistics, and everyday life.
According to question:We can use the information provided about the percentage of campers in each time interval to set up an equation to solve for the total number of campers surveyed.
Let n be the total number of campers surveyed. Then:
15% of n spend more than 3 hours reading daily.
10% of n spend between 2 and 3 hours reading daily.
35% of n spend less than 1 hour reading daily.
40% of n spend between 1 and 2 hours reading daily.
We know that 60 campers spend between 1 and 2 hours reading daily, which represents 40% of the total number of campers surveyed. So we can set up the following equation:
0.4n = 60
Solving for n, we get:
n = 60 / 0.4 = 150
Therefore, the total number of campers surveyed is 150.
To know more about percentage visit:
https://brainly.com/question/29116686
#SPJ1
We are given that angle aob is a central angle of circle o and that angle acb is a circumscribed angle of circle o. we see that ao ≅ bo because . we also know that ac ≅ bc since . using the reflexive property, we see that . therefore, we conclude that △aco is congruent to △bco by the
we conclude that △ACO is congruent to △BCO by the side-angle-side (SAS) congruence theorem.
We are given that angle AOB is a central angle of circle O and that angle ACB is a circumscribed angle of circle O. We see that AO ≅ BO because they are radii of the same circle.
We also know that AC ≅ BC since they are both tangent to the same circle and intersect at point C.
Thus, angle ACB and angle AOB have the same measure, which means that triangle ACO and triangle BCO are isosceles with AC ≅ BC and ∠ACO ≅ ∠BCO.
Using the reflexive property, we see that angle COA is congruent to angle COB since they are both vertical angles.
Therefore, we conclude that △ACO is congruent to △BCO by the side-angle-side (SAS) congruence theorem.
To learn more about congruence theorem:
https://brainly.com/question/19258025
#SPJ4
somebody helpppppppppppppppppp
Answer: D
Step-by-step explanation:
To narrow it out, Histograms dont have spaces meaning this chart wouldnt work as a histogram, and A and C are just plain incorrect
calcula valor exacto de E:
E = 3 √5 + 7 π/ 5 - 2 ( √5 - 3 π)
Answer: √5 + 37π/5.
Step-by-step explanation:
To calculate the exact value of E, we can follow the order of operations (PEMDAS):
E = 3√5 + 7π/5 - 2(√5 - 3π)
E = 3√5 + 7π/5 - 2√5 + 6π (distribute the -2)
E = (3√5 - 2√5) + (7π/5 + 6π) (combine like terms)
E = √5 + 37π/5
Therefore, the exact value of E is √5 + 37π/5.
sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represetns her situation?
A) linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.
We know that Sarah was selling lemonade and she makes 0.50 dollars on a small cup, and 1 dollar on a medium cup but she wants to make at least 30 dollars and only has 75 cups.
We need to show a linear inequality where, 's' represents a small cup, and 'm' represents a medium cup:
Linear inequalities are the expressions where any two values are compared by the inequality symbols ‘<’, ‘>’, ‘≤’ or ‘≥’
Linear equations are a combination of constants and variables.
let number of small cups be s,
therefore, total amount of small cups = 0.5 s
let number of medium cups be m,
therefore, total amount of medium cups = 1 m
with this given information, we can form our equation as:
0.5 s + 1 m = 30 < 75.
Therefore, a linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.
To learn more about linear inequalities, click here:
brainly.com/question/11897796
#SPJ4
Complete question: Sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represents her situation?
A. 0.5 s + 1 m = 30 < 75
B. 1s + 3m + 5l
C. $75
D. $93
Find the surface area of the rectangular prism.
Using the formula, we now know that the surface area of the rectangular prism is 22 in².
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
Its length, width, and height are its three dimensions.
Rectangular tissue boxes, school notebooks, laptops, fish tanks, and big buildings like freight containers, rooms, storage sheds, etc. are a few instances of rectangular prisms in daily life.
So, the formula for the surface area of the rectangular prism:
A = 2(wl+hl+hw)
Now, insert values as follows:
A = 2(wl+hl+hw)
A = 2·(1·1+5·1+5·1)
A = 22 in²
Therefore, using the formula, we now know that the surface area of the rectangular prism is 22 in².
Know more about a rectangular prism here:
https://brainly.com/question/24284033
#SPJ1
At 1:00 p.m., the temperature in Arizona was 87o. Six hours earlier, the temperature was 20o cooler.
What was the temperature at 7:00 a.m?
The temperature at 7:00 a.m. was 67 degrees.
To find the temperature at 7:00 a.m., we need to consider that it was 20 degrees cooler than at 1:00 p.m.
1. Identify the given information: At 1:00 p.m., the temperature was 87 degrees, and it was 20 degrees cooler six hours earlier.
2. We need to find the temperature at 7:00 a.m., which is six hours before 1:00 p.m.
3. Since the temperature was 20 degrees cooler at 7:00 a.m.
we will subtract 20 from the temperature at 1:00 p.m.
4. Perform the subtraction:
87 degrees (1:00 p.m. temperature) - 20 degrees (cooler difference) = 67 degrees.
5. The result, 67 degrees, is the temperature at 7:00 a.m.
For similar question on temperature.
https://brainly.com/question/29503787
#SPJ11
Theo washed 6 cars last week. He washed each car in 34
hour. He washed the same cars this week in 23
hour each using his new pressure sprayer. How much longer did it take Theo to wash all the cars last week than this week?
Answer:
66 hours.
Step-by-step explanation:
6 cars x 34 hours per car = 204
6 cars x 23 hours per car= 138 hours
now subtract:
204 - 138 = 66
therefore, it took Theo 66 hours longer to wash all the cars last week than last week.
I need help with the Surface Area of Pyramids and Cones
Will give Brainliest
Answer:
Step-by-step explanation:
If you don't know, the Pythagorean Theorem states that a^2+b^2=c^2 in a right triangle where a and b are the legs and c is the hypotenuse.
Imagine unfolding a cone. It would become part of a circle. Therefore, to find the lateral surface area(the surface are not including bases), you have to find the surface area of this part of the circle. The circumference of the entire circle is 6*pi*sqrt10. The circumference of this partial circle is the circumference of the base of the cone which is 2*3*pi=6pi. therefore, the percent of the circle is 6*pi/6*pi*sqrt10=1/sqrt10. 1/sqrt10*90pi=90*sqrt10*pi/10=9*sqrt10*pi.
the area of the base is 3^2*pi=9pi. the answer is then 9pi(1+sqrt10)
A ball is thrown across the field from point A to point B. It hits the ground at point B. The path of the ball is shown in
the diagram below. The x-axis shows the horizontal distance the ball travels in feet, and the y-axis shows the height of
the ball in feet. Use the diagram to complete parts (a)-(f).
a.
b.
C.
d.
e.
f.
A
C
B
Suppose point A is approximately 6 feet above ground and that at time t=0 the ball is at point A. Suppose
the length of OB is approximately 88 feet. Include this information on the diagram.
Suppose that after 1 second, the ball is at its highest point of 22 feet (above point C) and has traveled a
horizontal distance of 44 feet. What are the approximate coordinates of the ball at the following values of
t: 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, and 2.
Use your answer from part (b) to write two predictions.
What is happening to the ball when it has coordinates (88, 0)?
Why do you think the ball is at point (0, 6) when t = 0? In other words, why isn't the height of the ball 0?
Does the graph allow us to make predictions about the height of the ball at all points?
Based on the information, the height of point A is 6 feet above ground and the length of OB is approximately 88 feet.
How to explain the valueb) At t = 0.25 seconds, the approximate coordinates of the ball are (11, 13.5).
At t = 0.5 seconds, the approximate coordinates of the ball are (22, 12).
At t = 0.75 seconds, the approximate coordinates of the ball are (33, 9).
At t = 1 second, the approximate coordinates of the ball are (44, 6).
At t = 1.25 seconds, the approximate coordinates of the ball are (55, 3).
At t = 1.5 seconds, the approximate coordinates of the ball are (66, 0).
At t = 1.75 seconds, the approximate coordinates of the ball are (77, -3).
At t = 2 seconds, the approximate coordinates of the ball are (88, -6).
The height of the ball will be negative when it reaches point B again after traveling from A to B, assuming it follows the same path.
The time it takes for the ball to reach its maximum height and return to the ground will be approximately 2 seconds.
When the ball has coordinates (88, 0), it has reached the ground at point B, and its horizontal distance traveled is 88 feet.
At t = 0, the ball is at point A, which is 6 feet above the ground. This is because it was thrown from that height, and the time elapsed is not enough for gravity to affect its height yet.
Yes, the graph allows us to make predictions about the height of the ball at all points. However, the accuracy of the predictions may depend on the assumptions and approximations made about the ball's initial velocity, air resistance, and other factors.
Learn more about graph on
https://brainly.com/question/25184007
#SPJ1
solve[tex]\sqrt{-4=4[/tex]
The radical expression √(-4x) = 4 when evaluated has a value of x = -4
Evaluating the radical expressionFrom the question, the equation is given as
√(-4x) = 4
We can start by squaring both sides of the equation to eliminate the square root:
(√(-4x))^2 = 4^2
So, we have
-4x = 16
Dividing both sides by -4, we get:
x = -4
However, we need to check if this solution satisfies the original equation.
√(-4x) = √(-4(-4)) = √(16) = 4
So, the only solution to the equation is x = -4.
Read more about radical expression at
https://brainly.com/question/20070575
#SPJ1
I need help answering this question, please tell me how you got the answer
The properties of the conic section are Ellipse, Domain = [-2, 2] and the range is [-3, 3]
Identifying the properties of the conic sectionFrom the question, we have the following parameters that can be used in our computation:
The conic section
From the graph, we have
The conic section is an ellipse
The domain of this equation is all possible values of x and the range is for y
From the graph, we have
x values = -2 to 2
y values = -3 to 3
These are the domain and the range
Read more about conic section at
https://brainly.com/question/9702250
#SPJ1
Susan rolled a die 702 times. Which of the following would be a good estimate of the number of times she rolled the number 3 on the die?
Times Rolled: 702
Need estimation of: 3
Numbers on the dice: 6
702/6 = 117
Answer: 117
Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5.25 hours and charged him $116 for parts. The total was $719.75. Which equation could be used to determine cc, the cost of labor per hour?
Forest bought a box of chocolates for himself last week. However, by the time forest got home he had eaten 1/3 of the box. As Forest was putting the groceries away, he at 1/4 of what was left. There are now 12 chocolates left in the box.
How many chocolates were in the box to begin?
Be sure to show and explain all your reasoning.
Answer:
There were 24 chocolates in the box to begin with.
Step-by-step explanation:
Let's use working backwards to solve this problem.
We know that there are 12 chocolates left in the box. Let's call the number of chocolates that were in the box to begin with "x".
After eating 1/4 of what was left, Forest had 3/4 of the chocolates left. So, we can set up an equation:
3/4 (x - 1/3x) = 12
We can simplify this equation by multiplying both sides by 4/3:
x - 1/3x = 16
Multiplying both sides by 3:
2x = 48
x = 24
Therefore, there were 24 chocolates in the box to begin with.
The solution to 15 + a2 − 1 = 5 2a − 2 is a =___. The extraneous solution is a =____.
The solution to the equation is a = 6 and a = 4.
There is no extraneous solution.
To find the solution for the given equation, follow these steps:
1. Rewrite the equation: [tex]15 + a^2 - 1 = 5(2a - 2)[/tex].
2. Simplify both sides: [tex]a^2 + 14 = 10a - 10.[/tex]
3. Move all terms to one side:[tex]a^2 - 10a + 24 = 0.[/tex]
4. Factor the quadratic equation: (a - 6)(a - 4) = 0.
5. Set each factor equal to zero: a - 6 = 0 or a - 4 = 0.
6. Solve for 'a': a = 6 or a = 4.
Now, we need to check if both solutions are valid or if there is an extraneous solution.
Since there are no restrictions on the domain of the original equation, both solutions are valid.
For similar question on extraneous.
https://brainly.com/question/30092430
#SPJ11