The number of bars which can be cut for the 1" X 1" and 2" X 2" square bars are; 117 and 29 units respectively.
How many bars can be cut from the pan in each case?The total area of the given pan can be evaluated as follows;
Area = length × width
= 9 × 13
= 117 square units.
Hence, the number of 1" X 1" bars can be cut which can be cut from the pan;
= 117/(1×1)
= 117 1" X 1" bars.
For the 2" X 2" square bars, we have;
= 117/(2×2);
29 remainder 1 square unit.
Ultimately, one square unit of the pan is wasted for the 2" X 2" square bars.
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Carbon Company provides the following information about resources.
Unused Resources Capacity Cost Driver Volume
Resources used
Materials $ 2,300 9,000 pounds
Energy 2,210 380 machine-hours
Setups 0 87 setups
Purchasing 7,800 80 purchase orders
Customer service 9,700 70 returns
Long-term labor 4,650 330 labor-hours
Administrative 5,950 450 labor-hours
Resources supplied
Materials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700
Sales revenue for Carbon Company is $600,000.
Required:
a. Prepare a traditional income statement.
b. Prepare an activity-based income statement.
a) The preparation of a traditional income statement for Carbon Company is as follows:
Carbon Company
Income Statement (Traditional)Sales revenue $600,000
Costs:
Materials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700 $253,750
Operating Income $346,250
b) The preparation of an activity-based income statement for Carbon Company is as follows:
Carbon Company
Income Statement (Activity-based)Sales revenue $600,000
Resources supplied Unused Resources Used Resources
Materials $ 101,300 $ 2,300 $99,000
Energy 21,590 2,210 19,380
Setups 24,360 0 24,360
Purchasing 26,200 7,800 18,400
Customer service 20,200 9,700 10,500
Long-term labor 29,400 4,650 24,750
Administrative 30,700 5,950 24,750
Total $253,750 $32,610 $221,140
Operating Income $378,860
Data and Calculations:Unused Resources Capacity Cost Driver Volume
Resources used
Materials $ 2,300 9,000 pounds
Energy 2,210 380 machine-hours
Setups 0 87 setups
Purchasing 7,800 80 purchase orders
Customer service 9,700 70 returns
Long-term labor 4,650 330 labor-hours
Administrative 5,950 450 labor-hours
Resources suppliedMaterials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700
Sales revenue $600,000
Activity-based Calculations:Resources supplied Unused Resources Used Resources
Materials $ 101,300 $ 2,300 $99,000
Energy 21,590 2,210 19,380
Setups 24,360 0 24,360
Purchasing 26,200 7,800 18,400
Customer service 20,200 9,700 10,500
Long-term labor 29,400 4,650 24,750
Administrative 30,700 5,950 24,750
Total $253,750 $32,610 $221,140
Thus, the traditional income statement for Carbon Company shows an operating income of $346,250, while the activity-based income statement shows an operating income of $378,860.
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jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
The required answers are calculated by using the simple interest formula:
a. She needs to deposit $793.65 in the account each month
b. The total money she put into an account for a year is $285,714.29
c. The total interest she earns is $514,285.71
What is the formula for simple interest?The formula for the simple interest is
A = P(1 + RT)
Where,
A - amount after T years
P - principal amount
R - the rate of interest
T - time (years)
Calculation:It is given that,
A = 8,00,000
T = 30 years
R = 6% = 0.06
So,
a. Finding the amount needs to deposit in the account each month:
We have A = P(1 + RT)
⇒ P = A/(1 + RT)
On substituting,
P = 8,00,000/(1 + 0.06×30)
= 8,00,000/2.8
= $285,714.29(per year)
Thus, the amount needs to deposit in the account for each month
= P/T×12
= 285,714.29/30×12
= $793.65
b. Finding the total money that she put into account:
That is nothing but,
P = A/(1 + RT)
On substituting,
P = 8,00,000/(1 + 0.06×30)
= 8,00,000/2.8
= $285,714.29(per year)
c. FInding the total interest:
We have I = A - P
⇒ I = 8,00,000 - 285,714.29
∴ I = $514,285.71
Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71
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How much is a one time investment of 250 be when invested at 6% for 40 years in compound annually
Answer:
600
Step-by-step explanation:
250/1 times 6/ 100 times 40/1
WILL GIVE BRAINLIEST
(04.01, 04.02 HC)
Jackie runs and dances for a total of 55 minutes every day. She dances for 25 minutes longer than she runs.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day. (5 points)
Part B: How much time does Jackie spend running every day? Show your work. (3 points)
Part C: Is it possible for Jackie to have spent 45 minutes dancing if she runs and dances for a total of exactly 55 minutes and dances for 25 minutes longer than she runs? Explain your reasoning. (2 points)
A. The pair of linear equations are: x + y = 55 and y = x + 25
B. Number of time she spend running everyday is: 15 minutes.
C. It is not possible.
How to Write a System of Linear Equations?A system of equations consist of linear equations that have unknown variables whose values make the linear equations in the system true.
Part A: To write a pair of linear equations, do the following,
Let x represent the time Jackie runs
Let y represent the time Jackie dances
We are given that, Jackie runs and dances for a total of 55 minutes every day, therefore, the first linear equation would be:
x + y = 55 --> equation 1
We are also given that Jackie dances for 25 minutes longer than she runs, therefore, the second linear equation would be:
y = x + 25 --> equation 2
Therefore, the two pair of linear equations that shows the relationship between the number of minutes Jackie runs and dances everyday are:
x + y = 55
y = x + 25
Part B: Substitute y = (x + 25) into equation 1
x + y = 55 --> equation 1
x + x + 25 = 55
2x + 25 = 55
2x = 55 - 25
2x = 30
x = 15
Therefore, the number of time she spend running everyday is: 15 minutes.
Part C:
If she spent 45 minutes dancing (y = 45), and x = 15, substitute the values into x + y = 55 to find out if it is possible.
15 + 45 = 55
60 = 55 (not true)
Therefore, it is not possible.
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PLEASE I NEED THIS FAST a three dight number has one more ten than it has hundreds, and it also has one more than twice as many units as tens the sum of the number and that number reversed is 31 less than 10 cubed find the reverse number
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
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Pls help w this question
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
According to given figure,
Angle 11, Angle 20 and Angle 16 forms angles of a triangle,
so, by angle sum property of a triangle :
[tex]\qquad❖ \: \sf \: \angle11 + \angle20 + \angle16 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +66 + 43 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +109 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 = 180 \degree - 109[/tex]
[tex]\qquad❖ \: \sf \: \angle11 =71 \degree [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correct18. What is the probability that the student plays football?
(a) 35 /66 (b) 20 /33 (c) 13 /33 (d) 3 /22
The probability that the student plays football is 20/33.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that the student plays football = total number of students who play football / total number of students
total number of students who play football = 26 + 3 + 5 + 6 = 40 total number of students = 26 + 3 + 5 + 6 + 9 + 7 + 10= 66The probability that the student plays football = 40/66 = 20/33
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Factor completely 4x^2 − 32
Answer: [tex]4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]
Step-by-step explanation:
We can first take out the common factor of 4, as both 4x² and -32 are divisible by 4.
[tex]4(x^2-8)[/tex]
From here, we can assume that x²-8 is a difference of two squares even though 8 is not a perfect square.
For review, a difference of two squares [tex]a^2-b^2[/tex] can be factored into [tex](a+b)(a-b)[/tex].
[tex]4(x^2-8)\\4(x+\sqrt{8})(x-\sqrt{8})\\4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]
Enter the correct answer in the box.
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 1/3 What is the equation of function g?
Substitute a numerical value for k into the function equation.
Using translation concepts, the equation for function g is given by:
g(x) = 7x/3 + 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Supposing that we have a function f(x), a horizontal compression by a factor of a is equivalent to finding f(ax).
In this problem, the function is:
f(x) = 7x + 1.
For the horizontal compression by a factor of 1/3, we have that:
g(x) = f(1/3x) = 7x/3 + 1.
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Factor x² - 4x + 5.
Prime
O(x + 5)(x - 1)
O(x - 5)(x - 1)
(x+5)(x + 1)
Answer:
(x-5)(x+1)
Step-by-step explanation:
x² - 4x + 5 = (x-5)(x+1)
Consider rolling a six-sided die. Let A be the set of outcomes where the roll is an even number. Let B be the set of outcomes where the roll is greater than 3. Calculate and compare the sets on both sides of De Morgan’s law.
1. [tex](A \cup B)^c = A^c \cap B^c[/tex]
2. [tex](A \cap B)^c = A^c \cup B^c[/tex]
Answer:
See below
Step-by-step explanation:
[tex]A = \{2, 4, 6\}[/tex]
[tex]A^c =\{1, 3, 5\}\\B = \{4, 5, 6\}\\B^c = \{ 1,2, 3\}[/tex]
To prove 1 we have
[tex](A \bigcup B) = \{2, 4, 6\} \bigcup \{4, 5, 6\} = \{2, 4, 5, 6\}\\(A \bigcup B) ^c =\bold{\{1,3\}}\\A^c \bigcap B^c = {\{1, 3, 5\} \bigcap \{1, 2, 3\} =\bold{\{1,3\}}\\[/tex]
Hence proved
To prove 2
[tex](A \bigcap B) = \{2, 4, 6\} \bigcap \{4, 5, 6\} = \{4, 6\}\\\\(A \bigcap B)^c = \bold{\{1,2, 3, 5\}}\\A^c \bigcup B^c = \{1, 3, 5\} \bigcup \{1, 2, 3\} = \bold{\{1,2,3,5\}}\[/tex]
Hence proved
Notes
The complement of a set is the set of all elements not in the set
Here the set of all outcomes is {1, 2, 3,4,5, 6}
So if A = {2, 4, 6} then the complement of A s=is the set of outcomes not in A ie the set {1, 3, 5} which is the set of odd numbers on a die throw
The union of two sets is the set of all elements in both sets without duplication
The intersection of two sets is the set of all elements common to both sets
D₁ vide using x² - 2x² 2× +3× -5 by ×-3 using synthetic division.
Answer:
Step-by-step explanation:
I think you are trying to use synthetic division for
[tex]x^{4} -2x^{3} -2x^{2} +3x-5[/tex] divided by x-3
First
x -3 = 0 , make it equal to 0 and add 3 to both sides
x = 3
Then we write all the coefficients and continue with
a pattern of multiply by 3 and add to the next coefficient.
See attachment.
The average telephone bill in a locality is $70, with a standard deviation of $40. In a sample of 50 randomly selected phone connections, what is the probability that the sample average will exceed $75?
Using the normal distribution, there is a 0.1894 = 18.94% probability that the sample average will exceed $75.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 70, \sigma = 40, n = 50, s = \frac{40}{\sqrt{50}} = 5.66[/tex]
The probability that the sample average will exceed $75 is one subtracted by the p-value of Z when X = 75, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (75 - 70)/5.66
Z = 0.88
Z = 0.88 has a p-value of 0.8106.
1 - 0.8106 = 0.1894.
0.1894 = 18.94% probability that the sample average will exceed $75.
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Write the expression. Then, check all that apply. twice the difference of a number and six A 2-column table with 4 rows. Column 1 is labeled Key Words with entries twice, the difference of, a number, six. Column 2 is labeled Replace with entries 2 times, (minus), n, 6. Replace “a number” with the variable, n. The two operations are multiplication and addition. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6). The expression is written as 2 × 6 – n.
The statements that apply to the algebraic expression are
Replace “a number” with the variable, n. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6)How to determine the algebraic expression?The complete question is added as an attachment
The statement is given as:
Twice the difference of a number and six
Represent the number with n.
So, the statement becomes
Twice the difference of a n and six
Twice means 2 *
So, we have
2 * difference of a n and six
Express difference as minus i.e. -
So, we have
2 * (n - 6)
Hence, the expression is written as 2(n - 6)
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please help i would really appreciate it pallas athena
The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D
Long division9√4.000
= 4.000/9
= 0.444
Approximately,
= 0.4
Fraction
This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.
Decimal
This is a number expressed in the decimal system (base 10).
Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.
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The guy wire is approximately blank feet long
Answer: The guy wire = 393.4 ft
Step-by-step explanation:
Given images:
Refer to the attachment below (I apologize for the bad writing on the computer)
Given information:
Height of the tower = 175 ft
Height of the wire = 15 ft from the top (Opposite)
Angle with the ground = 24°
Length of wire = Unknown (Hypotenuse)
Determine the trigonometric function:
The primary choice will be the Sine function because the angle is opposite to the height and the wire is the hypotenuse of the system.
Determine the equation:
sin θ = (Opposite) / (Hypotenuse)
sin (24°) = (175 - 15) / (Length)
Simplify value in parenthesis
sin (24°) = (160) / (Length)
Multiply the Length of wire on both sides
sin (24°) * (Length) = (160) / (Length) * (Length)
sin (24°) * (Length) = (160)
Divide sin (24°) on both sides
sin (24°) * (Length) / sin (24°) = (160) / sin (24°)
Length = 160 / sin (24°)
[tex]\Large\boxed{Length~=~393.4~ft}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
3x - 2(2x - 5) = 2(x + 3) - 8
Answer:
x = 4
Step-by-step explanation:
Hello!
We can solve for x by expanding the parentheses and isolating x.
Solve for x3x - 2(2x - 5) = 2(x + 3)-83x - 4x + 10 = 2x + 6 - 8-x + 10 = 2x - 210 = 3x - 212 = 3xx = 4The value of x is 4.
A small motorboat travels 12mph in still water. It takes 2 hours longer to travel 46 miles going upstream than it does going downstream. Find the rate of the current
Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
v = d/t
A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:
12 + r = 46/t
r = 46/t - 12
Downstream, the time is of t + 2 hours, hence:
12 - r = 46/(t + 2)
r = 12 - 46/(t + 2)
Hence, equaling the values for r:
46/t - 12 = 12 - 46/(t + 2)
46/t + 46/(t + 2) = 24
[tex]\frac{46t + 92 + 46t}{t(t + 2)} = 24[/tex]
92t + 92 = 24t² + 48t
24t² - 44t - 92 = 0
Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:
r = 46/t - 12 = 46/3 - 12 = 3.33 mph.
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if a set of test scores has a large range but a small standard deviation, describe what this means about students' performance on the test.
a. Most of students' test scores are around the mean, except that few students got scores much less than the mean.
b. Most of students' test scores are around the mean.
c. Most of students' test scores are around the mean, except for the students who got scores much greater than the mean and a few students who got scores much less than the mean.
d. Most of students' test scores are around the mean, except for the students who got scores much greater than the mean.
Answer:
C
Step-by-step explanation:
Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.
The correct option is:
b. Most of students' test scores are around the mean.
A large range indicates that there is a significant difference between the highest and lowest scores in the set.
On the other hand, a small standard deviation indicates that the data points (test scores) are clustered closely around the mean.
When the range is large but the standard deviation is small, it means that most of the students' test scores are relatively close to the mean, and there are no extreme values that are significantly far from the mean. In other words, the majority of students performed similarly on the test, with only a few outliers having scores much higher or much lower than the mean.
Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.
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A rectangular tank 60cm long, 50cm wide and 24cm height was 1/3 filled with water at first. A tap was turned on to completely fill the tank. The rate of water flowing from the tap into the tank was 3 litre per minute. How long did it take to fill the tank completely? Give your answers in minutes.
-y(-6y-3) I need to combine like terms and simplify. I got 6y^2 + 3y by distributing. It's wrong and in the explanation it says use the distributive property to remove the parentheses and it gave -6y -3 -y as the first step answer. How the heck did they remove the parentheses or use the distributive property correctly?
if any number or variable is outside a parenthesis it will go to all the number rin the parenthesis.
in this case -y is outside the parenthesis so it will got to both the sides :
-y(-6y-3) = -6y x y - 3 x y
= -6y² -3y//
PLEASE HELP URGENT
Which equation could be solved using this application of the quadratic formula?
Answer:
Step-by-step explanation:
D because the quadratic formula is basically [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]±
so if we place the equation D into the formula
a = 1
b = +3
c = +24
we can clearly say that D eq is correctly used and can be.
A total load of 28,800 watts is distributed equally over 15 circuits. What is the load per circuit in watts? i need help with solving this, need a step by step for later on
Answer:
1,920 watts per circuit
Step-by-step explanation:
To find the load for 1 circuit (per circuit) we can divide 28,800 watts by 15 circuits
28800/15 = 1,920 watts per circuit
Someone please help me with this question! How can I prove it?
Answer:
TS=QV
Step-by-step explanation:
To prove SAS congruence, you need to prove that two lines and the angle between them are all respectively equal.
In the diagrams we already have RS=WV and ∠RST=∠WVQ, so it follows that we need to prove that TS=QV.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For triangles to be congruent by SAS congruency criteria, one angle and the two adjacent sides to the angle should be equal to corresponding angle and it's adjacent aides of another triangle.
And we have already been given the angle and one of the side. so the third side that need to be equal in both side to pe proved congruent are :
TS = QV[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option is 1The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
750 - y(y-5) = 0
Step-by-step explanation:
Area is Length times width. In a rectangle we have two lengths and 2 widths.
We can use y to represent the length. The width would be y-5.
Area = LW
750 = y(y-5) or another way to write this is
750 - Y(y-5) = 0
8. The probability that Ava gets promoted is 7/10. Find the odds in favor of Ava getting promoted.
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3?
A.–6
B.–5
C.5
D.7
The y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C
How to determine the coordinatesLet's the point that divides the line segment as point S.
We have that,
Point S divides the line segment into ratio 2:3
The ratio 2:3 means that we are to divide the line segment into;
= 2+3
= 5 equal parts.
We then have that the horizontal distance between the two coordinates is 5
The vertical distance between the two coordinates is 10
Now, let's divide both vertical and horizontal distance into five equal parts,
Horizontal distance = 5/5 = 1
Vertical distance = 10/ 5 = 2
The horizontal distance is 1
The vertical distance is 2
For every one unit move to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.
The coordinate of point S that divides the line segment into 2 parts and 3 parts is (-5,5)
Thus, the y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C
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What is the slope of the graph shown below?
Answer:
Option 3: -2
Step-by-step explanation:
The slope of the graph is negative, and the only option with a negative term for the slope is -2.
So the slope of the graph is -2.
Wich solutions are correct
Answer:
Rhoda and Ming are both correct, but Ming's prediction is closer because the result is accurate to two decimal places.
Step-by-step explanation:
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLU X = 6 X = -x + 6 = x - 6 Identify any extraneous solution. (If there is no extraneous solution, enter NO SOLUTION.) 2
Taking squares on both sides leads to
[tex]\sqrt{-x + 6} = x - 6[/tex]
[tex]\left(\sqrt{-x + 6}\right)^2 = (x - 6)^2[/tex]
[tex]-x + 6 = x^2 - 12x + 36[/tex]
[tex]x^2 - 11x + 30 = 0[/tex]
[tex](x - 5) (x - 6) = 0[/tex]
Solving for [tex]x[/tex], we get
[tex]x - 5 = 0 \text{ or } x - 6 = 0[/tex]
or
[tex]x = 5 \text{ or } x = 6[/tex].
Evaluating both sides of the starting equation at these solutions, we have
[tex]\sqrt{-6 + 6} = 6 - 6 \implies 0 = 0[/tex]
which is true, so [tex]\boxed{x=6}[/tex] is a valid solution. However,
[tex]\sqrt{-5 + 6} = 5 - 6 \implies \sqrt1 = -1 \implies 1 = -1[/tex]
which is not true, so [tex]\boxed{x=5}[/tex] is an extraneous solution.