Given:
[tex]x=12[/tex]is given.
Required:
Which option is not appropriate.
Explanation:
Now we check all the option for this
[tex]\begin{gathered} \frac{x}{1}=12 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{4}=2 \\ x=8 \end{gathered}[/tex]which is not appropriate
[tex]\begin{gathered} \frac{x}{3}=4 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]which is appropriate
Final answer:
After the end of an advertising campaign, the daily sales of a product fell rapidly, with daily sales given by S=3800e−0.05x dollars, where x is the number of days from the end of the campaign.a. What were daily sales when the campaign ended?b. How many days passed after the campaign ended before daily sales were below half of what they were at the end of the campaign?
Since the given equation is
[tex]S=3800e^{-0.05x}[/tex]S is the amount of the daily sales from ending to x days
Since the form of the exponential function is
[tex]y=ae^x[/tex]Where a is the initial amount (value y at x = 0)
Then 3800 represents the daily sales when x = 0
Since x = 0 at the ending of the campaign, then
a. The daily sales when the campaign ended is $3800
Since the daily sales will be below half $3800 after x days
Then find half 3800, then equate S by it, then find x
[tex]\begin{gathered} S=\frac{1}{2}(3800) \\ S=1900 \end{gathered}[/tex][tex]1900=3800e^{-0.05x}[/tex]Divide both sides by 3800
[tex]\begin{gathered} \frac{1900}{3800}=\frac{3800}{3800}e^{-0.05x} \\ \frac{1}{2}=e^{-0.05x} \end{gathered}[/tex]Insert ln for both sides
[tex]\ln (\frac{1}{2})=\ln (e^{-0.05x})[/tex]Use the rule
[tex]\ln (e^n)=n[/tex][tex]\ln (\frac{1}{2})=-0.05x[/tex]Divide both sides by -0.05 to find x
[tex]\begin{gathered} \frac{\ln (\frac{1}{2})}{-0.05}=\frac{-0.05x}{-0.05} \\ 13.86294=x \end{gathered}[/tex]Since we need it below half 3800, then we round the number up to the nearest whole number
Then x = 14 days
b. 14 days will pass after the campaign ended
Orang has worked as a nurse at Springfield general hospital for 5 years longer than her friend Bill. Two years ago she had been at the hospital for twice as long. How long has each been at the hospital?
Answer:
• Bill = 3 years
,• Hoang = 8 years.
Explanation:
Let the time Bill had worked in the hospital = b years.
Hoang has worked for 5 years longer than her friend Bill, therefore:
• The time ,Hoang, had worked in the hospital = (b+5) years.
Two years ago:
• Bill's Time = (b-2) years
,• Hoang's Time = (b+5-2) years
Two years ago she had been at the hospital for twice as long as Bill.
[tex]\implies b+5-2=2b[/tex]Solve the equation for b:
[tex]\begin{gathered} b+5-2=2b \\ b+3=2b \\ 2b-b=3 \\ b=3 \end{gathered}[/tex]Hoang has been at the hospital for 8 years and Bill has been there 3 years.
Business is projected to be booming afterthe latest release of The Fast and theFurious 3.14159265359... Carver's AutoCustom must determine how many cansof paint and rims to stock at theirShanghai location.The Carver Family did choose WarehouseSpace A. The warehouse includes 8000sq. ft. of showroom and workshop space.One half of this warehouse space will beused to stock paint cans and rims. Thewarehouse has a height of 20 ft.Calculate the maximum numberof cylindrical paint cans thatCarver's Auto Custom can stock,if the paint comes in a 2-packhazmat box that measures 15<=>
Total Area = 8000 ft^2
Stock Area = 4000 ft^2
h = 20 ft
Stock's Volume = 4000*20 = 80000 ft^3
Boxes's Volume = 15*7*6 = 630 ft^3
Now he need to find how many boxes can stock in the warehouse space
80000/630 = 127 boxes. And if each box has two cans:
127 * 2 = 254 cans can be stored.
Lila's retirement party will cost $8 if she invites 4 guests. If there are 9 guests, how much will Lila's retirement party cost? Solve using unit rates.
We are assuming that the party cost is directly proportional to the number of guests.
Then, if it will cost $8 for 4 guests, the unit rate is:
[tex]c=\frac{8\text{ dollars}}{4\text{ guests}}=2\text{ dollars per guest}[/tex]Then, we can use this unit rate to calculate the cost for 9 guests:
[tex]C(9)=2\frac{\text{ dollars}}{\text{ guest}}\cdot9\text{ guests}=18\text{ dollars}[/tex]The cost for 9 guests is $18.
¨do you know what complex numbers are? Can you divide two complex numbers? Give us an example here!¨
A complex number z is a number of the form z = a + bi where a and b are real numbers, and i is the imaginary number, defined as the solution for i² = - 1.
We can indeed divide complex numbers. Let's take the numbers 1 + i and 1 - 2i for example. Dividing the first number by the second, we have
[tex]\frac{1+i}{1-2i}[/tex]To solve this division, we need to multiply both the numerator and denominator by the complex conjugate of the denominator
[tex]\frac{1+\imaginaryI}{1-2\imaginaryI}=\frac{1+\imaginaryI}{1-2\imaginaryI}\cdot\frac{1+2i}{1+2i}=\frac{(1+i)(1+2i)}{(1-2i)(1+2i)}[/tex]Expanding the products and solving the division, we have
[tex]\frac{(1+\imaginaryI)(1+2\imaginaryI)}{(1-2\imaginaryI)(1+2\imaginaryI)}=\frac{1+3i-2}{1+4}=\frac{-1+3i}{5}=-\frac{1}{5}+\frac{3}{5}i[/tex]And this is the result of our division
[tex]\frac{(1+\imaginaryI)}{(1-2\imaginaryI)}=-\frac{1}{5}+\frac{3}{5}i[/tex]9.03 divided by 0.3
in order to divide
[tex]\frac{9.03}{0.3}[/tex]we must convert the decimal number to intergers. We can do that by multiplying by 100/100.
That is
[tex]\frac{9.03}{0.3}=\frac{9.03}{0.3}\cdot\frac{100}{100}[/tex]hence,
[tex]\frac{9.03}{0.3}=\frac{903}{30}[/tex]and now, we can apply the long division on 903/30:
Therefore, 9.03/0.3=30.1
What are the leading coefficient and degree of the polynomial?12 – 20u-u?Leading coefficient:Пx 5?Degree:
In a polynomial, the term with the highest power of the variable is the leading term. The coefficient of the leading term is the leading coefficient.
In the polynomial given;
[tex]12-20u-u^2[/tex]The leading term is
[tex]-u^2[/tex]The leading coefficient therefore is -1
The degree of the polynomial is the exponential power of the leading term. In the given polynomial, what we have is a second degree polynomial
ANSWER:
Leading coefficient = -1
Degree = 2
Please help 50 points!
1. A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
What is the volume of the jar?
The volume of the jar is 1130.4 in³. The number of marbles that is filled the jar is 56.
What is the cylindrical shape?
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers.
Given that the radius of cylindrical jar is 6 inches and the height is 10 inches.
The volume of a cylindrical shape is [tex]\pi r^2h[/tex].
Where r is the radius of the cylinder and h is the height of the cylinder.
Given that, the radius of the cylindrical jar is 6 inches and height is 10 inches.
The volume of a cylindrical shape is 3.14 × 6² × 10 = 1130.4 in³.
The number of marbles by which the jar can be filled is 1130.4/20 = 56.52 = 56 (approx.)
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You ordered from an online company. The original price of the item is $65. Theitem is on sale for 10%, and you have a coupon for an additional 15%. Applying onediscount at a time, what is the final price?$46.96$49.73$49.47$45.45
Given:
The original price, CP=$65.
The initial discount on sale, D1=10%.
The additional discount, D2=15%.
If the cost price(CP) of an item is given, then the selling price after the first discount is applied is,
[tex]SP=CP\times(\frac{1-First\text{ }Discount\text{ Percentage}}{100})[/tex]The additional discount is applied to the price after the first discount is applied. So, the final price after applying the second discount is,
[tex]SP^{\prime}=SP\times(\frac{1-Second\text{ }Discount\text{ Percentage}}{100})[/tex]Applying the first discount on the original price, the selling price is,
[tex]\begin{gathered} SP=CP\times\frac{(100-D1)}{100} \\ =65\times\frac{(100-10)}{100} \\ =58.5 \end{gathered}[/tex]Applying the second discount on the selling price, the final selling price is,
[tex]\begin{gathered} SP^{\prime}=SP_{}\times\frac{(100-D2_{})}{100} \\ =58.5_{}\times\frac{(100-15_{})}{100} \\ \cong49.73 \end{gathered}[/tex]Therefore, the final price is $49.73.
Note:
The direct formula for the final price if two successive discounts D1 and D2 are applied to a cost price CP is,
[tex]SP=CP\times(\frac{100-D1}{100})(\frac{100-D2}{100})[/tex]two mechanics worked on a car. the first mechanic worked for 5 hours and the second mechanic worked for 15 hours together they charged a total of $1,225 what was the rate charge per hour by each mechanic if the sum of the two rates was $125 per hour
Given : two mechanics worked on a car
The first : worked for 5 hours
The second : worked for 15 hours
Total charge for both = $1,225
Let the charge rate per hour for the first is x and for the second is y
So,
[tex]5x+15y=1225[/tex]the sum of the two rates was $125 per hour so,
[tex]x+y=125[/tex]so, we have the following system of equations :
[tex]\begin{gathered} 5x+15y=1225 \\ x+y=125 \end{gathered}[/tex]Form the second equation : y = 125 - x
Substitute at the first equation with y to find the value of x
so,
[tex]\begin{gathered} 5x+15\cdot(125-x)=1225 \\ 5x+1875-15x=1225 \\ 5x-15x=1225-1875 \\ -10x=-650 \\ \\ x=\frac{-650}{-10}=65 \\ \\ y=125-x=125-65=60 \end{gathered}[/tex]so, the rate of the first one who worked 5 hours = $65 per hour
And the rate of the second will be = $60 per hour
12 in.4 inShoe Box2 inWhat is the volume of the shoebox shown above in cubic inches?18 cubic inches48 cubic inches*96 cubic inches114 cubic inches
We have a shoebox with 3 dimensions, we are asked to find the volume of this shoebox
To do this we use the following volume formulation
[tex]V=l\cdot w\cdot h[/tex]Where the length is l=12, the width is w=2 and the height is h=4, now we replace a solve this
[tex]V=12\cdot2\cdot4V=96[/tex]In conclusion, the shoebox is 96 cubic inches
Solve the equation 4x2 + 8x + 1 = 0 by completing the square.
Let's compare the given equation with the notable product below:
[tex](a+b)^2=a^2+2ab+b^2[/tex]Since the first term is 4x², we have a = 2x.
Then, the second term is 8x, so since a = 2x, we have b = 2, this way 2ab = 8x
Now, since b = 2, we have b² = 4.
The constant term is just 1, so we need to add 3 units:
[tex]\begin{gathered} 4x^2+8x+1+3-3=0 \\ 4x^2_{}+8x+4-3=0 \\ (2x+2)^2=3 \\ 2x+2=\pm\sqrt[]{3} \\ 2x=-2\pm\sqrt[]{3} \\ x=\frac{-2\pm\sqrt[]{3}}{2} \end{gathered}[/tex]Therefore the correct option is the third one.
What is the difference between discrete and continuous data set?
Let's explain the difference between discrete and continuous data set.
• Discrete data set can be said to be a set of data with distinct and seperate values.
Discrete data contains finite values that are countable.
Discrete data set has clear sapces between values.
Examples of discrete data are:
• 10 kids
,• 7 laptops
,• 24 balls
• Continuous data set is said to be the set of data with random variables which may or may not be whole number.
Continuous data changes over time and can also have different values at different time intervals.
Continuous data can be any measured value.
Continuous data set falls on a continuos sequence.
Examples of continuous data are:
• 4.84 miles
,• 84.3 meters
,• 8 kg
The monthly rents for five apartments advertised in a newspaper were $650, $650, $750, $1650, and $850.the mean, median, and mode of the rents to answer the question. Which value best describes the monthlyrents?
SOLUTION
Given the question in the image, the following are the solution steps to get the correct answer
Step 1: Write the monthly rents
[tex]\text{\$}650,\text{\$}650,\text{\$}750,\text{\$}1650,\text{\$}850[/tex]We need to calculate the mean, median and moce of these data to allow us choose the best answer
Step 2: Calculate the mean
a
[tex]\begin{gathered} \text{\$}650,\text{\$}650,\text{\$}750,\text{\$}1650,\text{\$}850 \\ \operatorname{mean}=\frac{sum\text{ of monthly rents}}{number\text{ of monthly rents}} \\ \operatorname{mean}=\frac{\text{\$}650+\text{\$}650+\text{\$}750+\text{\$}1650+\text{\$}850}{5}=\frac{4550}{5}=\text{\$}910 \end{gathered}[/tex]Step 3: Calculate the median
The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number.
[tex]\begin{gathered} By\text{ rearrangement},\text{ we have} \\ \text{\$}650,\text{\$}650,\text{\$}750,\text{\$}850,\text{\$}1650 \\ \operatorname{median}=\text{\$}750 \end{gathered}[/tex]Step 4: Calculate the mode
The mode is the number in a data set that occurs most frequently.
[tex]\begin{gathered} \text{data}=\text{\$}650,\text{\$}650,\text{\$}750,\text{\$}850,\text{\$}1650 \\ \mod e=\text{\$}650 \end{gathered}[/tex]Hence, the value that best describe the rents is mean because $910 is the average rent
Option A
Please Help! I will give brainliest! Need the correct answer!
Answer:
HL
Step-by-step explanation:
The two triangles are rectangle and have a congruent hypotenuse and a congruent leg
kiruiand kariuki formed a trading partnership .in the first month kirui contributed 1/12 of his salary towards the cost of the company kariukis contribution was 1/10 of his monthly salary giving a total of ksh 980 .their respective contributions the following month were 1/8 and 1/6 of their salaries .if a total contribution for the second month was cash 1550, what were their monthly salaries
kirui's monthly salary is 6000 and kaiuki's monthly salary is 4800.
Let
kirui's salary =x
kariuki's salary=y
Given,
In first month,
Total contribution=980
kirui's contribution=[tex]\frac{x}{12}[/tex]
kariuki's contribution=[tex]\frac{y}{10}[/tex]
In second month,
Total contribution=1550
kirui's contribution =[tex]\frac{x}{8}[/tex]
kariuki's contribution=[tex]\frac{y}{6}[/tex]
Equation for first month,
[tex]\frac{x}{12} +\frac{y}{10} =980\\\\5x+6y=58800....i[/tex]
Equation for second month,
[tex]\frac{x}{8} +\frac{y}{6} =1550\\\\3x+4y=37200....ii[/tex]
Solving eq.
[tex]5x+6y=58800= > 15x+18y=176400\\3x+4y=37200= > 15x+20y=186000\\\\Subtracting the equations,\\\\15x+18y=176400\\15x+20y=186000\\---------\\-2y=-9600\\\\y=4800[/tex]
Substituting y in eq.[tex]ii[/tex]
[tex]3x+4(4800)=37200\\\\3x=18000\\\\x=6000[/tex]
Thus, kirui's monthly salary is 6000 and kaiuki's monthly salary is 4800.
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Help find the indicated functional value for the floor function
We need to find the greates integer less than f(-0.75):
In this case the integer nearest to -0.75 is -1.
The table shows the highest maximum temperature for the month of October in Philadelphia Pennsylvania over the yearsPart A identify the independent and dependent quantity in their units of measure?Part B identify the equation of line of best fit using the data table.what is the slope and y-intercept of the line and what do they represent?
Answers:
A. Independent = Year
Dependent = Temperature
B. Temp = 0.6733(Year) - 1293.61
Explanation:
The independent variable is the variable that is not affected by the other, in this case, no matter the temperature, the year is given, so the independent variable is the year and the dependent variable is the highest temperature because it changes depending on the year.
Then, to identify the equation of the line of best fit, we will use the following:
First, we need to calculate the mean of both variables, so:
[tex]\begin{gathered} \text{Mean Year = }\frac{2008+2009+2010+2011+2012+\cdots+2017}{10} \\ \text{Mean Year = }2012.5 \\ \text{Mean Temperature = }\frac{64.9+53.1+61+54+\cdots+66.9}{10} \\ \text{Mean Temperature=}61.47 \end{gathered}[/tex]Then, we need to fill the following table:
Now, the slope of the line can be calculated as the sum of the values in the row (Year - Mean Year) x (Temp - Mean Temp) divided by the sum of the row (Year - Mean Year)^2. So, the slope of the line is:
[tex]m=\frac{55.55}{82.5}=0.6733[/tex]Finally, the y-intercept can be calculated as:
[tex]\begin{gathered} b=\text{Temp Mean - Slope x Year Mean} \\ b=61.47-0.6733(2012.5) \\ b=-1293.61 \end{gathered}[/tex]So, the equation of the line that best fits the data table is:
[tex]\text{Temp}=0.6733(\text{Year)}-1293.61[/tex]q (3.2r – 7)Write an equivalent expression by combining like terms
From the problem, we have the expression :
[tex]q(3.2r-7)[/tex]By distributive property, multiply q to the parenthesis.
[tex]3.2qr-7q[/tex]Since the terms are NOT like terms, we cannot combine them.
Therefore, the answer is :
3.2qr - 7q
To find the angle of rotation θ between the previous x and y axes and the new x′ and y′ axes, we use the formula: cotangent of 2 theta equals A minus C all over B , where 2θ lies on the interval (0°, 180°).TrueFalse
The equation is the given one:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Which is the same as:
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]And the interval of the angle θ must be (0°,90°) so, 2θ must be (0°,180°).
So the statement is True.
What number must be added to the expression below to complete the
square?
x²-x
O A. -1/1
4
O B. /
O C. - 12/2
O D.
-12
Answer:
1/4
Step-by-step explanation:
Completing the square
x^2 -x
Take the coefficient of the x term
-1
Divide by 2
-1/2
Square it
(-1/2) ^2 = 1/4
Add this to each side
Juan has already run 6 miles this month. He plans to run an additional 2 miles per day. At this rate, how long will it take Juan to run 40 miles?Hint: Write and solve a 2-step equation
ANSWER
[tex]17\text{ days}[/tex]EXPLANATION
We want to find how long it will take Juan to run 40 miles.
To do this, we have to set up an equation that describes the situation.
We have that Juan has already run 6 miles and he wants to run an additional 2 miles per day.
This implies that after d days, he would have run:
[tex]6+2d[/tex]For Juan to run 40 miles, it implies that:
[tex]6+2d=40[/tex]Solve that for d:
[tex]\begin{gathered} 2d=40-6=34 \\ d=\frac{34}{2} \\ d=17\text{ days} \end{gathered}[/tex]That is how long it will take Juan to run 40 miles.
Lynn had an opening balance of $179.30 in her checking account.She made deposits of $432 and had bank charges of $5.35. If herclosing balance was $353.82, how much did she write in checks?a. $625.89b. $258.05c. $262.83d. $252.13
Given:
Opening balance $179.30 then she deposits $432 and had bank charges $5.35
Closing balance is $353.82
[tex]\text{Amount written in the check = 179.30+432-5.35-353.82}[/tex][tex]\text{Amount written in the check = \$}252.13[/tex]Therefore, Option d is the correct answer.
Bonnie is searching online for airline tickets two weeks ago the cost to fly from Orlando to Denver was $200 .now the cost is $345. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with with the new ticket price?
Answer:457
Step-by-step explanation:
Show your steps when solving the problem below. Container A has 800 mL of water and is leaking 6 mL per minute. Container B has 1,000 mL of water and is leaking minute. How many minutes will it take for the two containers to have the same amount of water?
Step 1 : Let's review the information given to us to answer the problem correctly:
• Container A = 800 ml - 6 ml per minute
,• Container B = 1,000 ml - 10ml per minute
Step 2: Let's write the equation to solve the problem, as follows:
Let x to represent the number of minutes both containers have the same amount of water
Container A = Container B
800 - 6x = 1,000 - 10x
Like terms:
-6x + 10x = 1,000 - 800
4x = 200
Dividing by 4 at both sides:
4x/4 = 200/4
x = ?
I think you can calculate the value of x without problems.
7. Solve the following set of equations: 3x - 7y=-4 and 2x - 5y = -3a. (1, 2)b. (2, 1)c. (-2,-1)d. (1, 1)e. (-1,-1)
We will have the following:
First, we solve both expressions for "y", that is:
[tex]\begin{gathered} 3x-7y=-4\Rightarrow-7y=-3x-4 \\ \Rightarrow y=\frac{3}{7}x+\frac{4}{7} \\ \\ and \\ \\ 2x-5y=-3\Rightarrow-5y=-2x-3 \\ \Rightarrow y=\frac{2}{5}x+\frac{3}{5} \end{gathered}[/tex]Now, we equal both expressions:
[tex]\begin{gathered} \frac{3}{7}x+\frac{4}{7}=\frac{2}{5}x+\frac{3}{5}\Rightarrow\frac{1}{35}x=\frac{1}{35} \\ \\ \Rightarrow x=1 \end{gathered}[/tex]Now, we determine the value of y:
[tex]y=\frac{2}{5}(1)+\frac{3}{5}\Rightarrow y=1[/tex]So, the solution is:
[tex](1,1)[/tex]Right to sleep as a fraction by the Y intercept as well
Given:
The points (0,3) and (2,0) lie on the line.
Required:
We need to find the slope and y-intercept of the given line.
Explanation:
The y-intercept is the point where the line crosses the y-axis.
The given line crosses the y-axis at 3.
y-intercept=(0,3).
Consider the slope formula,
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitu\text{te }y_2=0,y_1=3,x_2=2\text{ , and }x_1=0\text{ in the formula.}[/tex][tex]slope=\frac{0-3}{2-0}[/tex][tex]slope=\frac{-3}{2}[/tex]Final answer:
[tex]slope=\frac{-3}{2}[/tex]y-intercept=(0,3).
Subtract 5y^2-6y-11 from 6y^2+2y+5?
Subtract 5y^2 - 6y - 11 from 6y^2 + 2y + 5
They are both quadratic expression
6y^2 + 2y + 5 - (5y^2 - 6y - 11)
Firtstly, use the negative sign to open the parentheses
6y^2 + 2y + 5 - 5y^2 + 6y + 11
Secondly, collect the like terms
6y^2 - 5y^2 + 2y + 6y + 5 + 11
since y^2 is common, factorize it out
y^2(6 - 5) + y(2 + 6) + 26
y^2(1) + y(8) + 26
y^2 + 8y + 26
The answer is y^2 + 8y + 26
does the number line below present the solution to the equivalent X < -1?
On a number line, if we choose a number a, all the numbers to the right of a are greater than a, while all the numbers to the left are lower than a.
In this case, the inequality is:
[tex]x<-1[/tex]So, the solution in the number line would be all the numbers to the left of -1.
Therefore, this number line does not represent the solution to x<-1 because everything is to the right instead of to the left.
If x varies inversely as y and x=16 when y=5, find x when y=20.
Since x varies inversely as y, then it can be represented as the expression below:
[tex]y=\frac{1}{a}\cdot x[/tex]Where a is the proportionality constant. We need to find a to determine the value of x when y is 20. For that we will use the two values given as shown below:
[tex]\begin{gathered} 5=\frac{1}{a}\cdot16 \\ 5\cdot a=16 \\ a=\frac{16}{5}=3.2 \end{gathered}[/tex]The expression is:
[tex]y=\frac{1}{3.2}\cdot x[/tex]If y is 20, then x must be:
[tex]\begin{gathered} 20=\frac{1}{3.2}\cdot x \\ x=3.2\cdot20 \\ x=64 \end{gathered}[/tex]The value of x must be 64.