For given coordinates, the ordered pair describing the location of G'' is (3,-6).
What are coordinates?
Coordinates are a set of numbers that specify the position or location of a point or object in space, relative to a reference point or system. In two-dimensional space, coordinates are usually represented by a pair of numbers (x, y), where the first number represents the horizontal position of the point along the x-axis, and the second number represents the vertical position of the point along the y-axis. In three-dimensional space, coordinates are usually represented by a triple of numbers (x, y, z), where the first number represents the horizontal position of the point along the x-axis, the second number represents the vertical position of the point along the y-axis, and the third number represents the position of the point along the z-axis, which is perpendicular to the x-y plane.
Now,
When a point is reflected over the x-axis, the y-coordinate is negated. So the image of G(-3,6) over the x-axis is G'(-3,-6).
When a point is reflected over the y-axis, the x-coordinate is negated. So the image of G'(-3,-6) over the y-axis is G''(3,-6).
Therefore, the ordered pair describing the location of G'' is (3,-6).
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Jen is studying how years of drought conditions have caused the water level of Richland Reservoir to drop. At the start of the study, the water in the reservoir was 65 meters deep. Jen observed that the depth of the water dropped by about 0.8 meters the first month of the study. She wants to know what the depth of the water will be if it continues dropping at the same rate. You can use a function to approximate the depth of the water in the reservoir x months after the start of the study. Write an equation for the function.
The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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1. Identify and clearly label the slope and y-intercept for each equation in slope intercept form. Choose the correct answer from the choices below.
Y=-5
A. Slope is-5 and the y-intercept is (0,0)
B.Slope is zero and the y-intercept is (0,-5)
C. Slope is zero and the y-intercept is (0,0)
D. Slope is -5 and the y-intercept is (0,-5)
Slope is zero and the y-intercept is (0,-5)
What is slope ?
In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.
In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.
The formula for calculating slope is:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation Y = -5 to y = mx + b, we can see that:
The slope, m, is 0, since there is no x-term in the equation.
The y-intercept, b, is -5, since that is the constant value in the equation.
Therefore, the correct answer is:
B. Slope is zero and the y-intercept is (0,-5)
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Each of the lists below is in order from least to greatest
and has one number missing. List an example of a value
that could correctly complete the blank in each list.
I. -0.65,
2.
4.
/
3. 1.2%, 10%,
1
20'
12 13
4'5'2'2
,-0.6, -0.5, -0.4
6.2%,
/
1
16.7%, 40%
10.45
Answer:
-0.63
1/7
15%
10%
Step-by-step explanation:
hope this helps
Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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I really need to know how to solve this type of problems
Of the 250 total shirts about, the quantity of shirts that should be red would be = 125.
How to calculate the quantity of shirts that are red.?The total quantity of shirts that was ordered by Mr. Torres = 250 school t-shirts
The total quantity of red shirt selected at random = 5
The total quantity of blue shirt selected at random = 13
The total quantity of grey shirt selected at random = 12
Total selected at random = 30
Now if 5 red shirts = 30
X red shirts = 250
make X the subject of formula;
X = 15× 250/30
X = 3750/30
X = 125 red shirts.
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Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answer:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:
A = 2500(1 + 0.05/2)^(2*15)
A ≈ $5,551.33
Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.
Solve the problems. Show your work.
7
1. Mr. Nguyen had 7/8
pint of water in his water bottle. Then, he drank 2/3
pint. How much water is left in the bottle?
Answer:
7/8 - 2/3 = 5/8 pint of water left in the bottle.
Which of the following has the correct factored form AND the correct
solutions for the quadratic equation?
x²2x-3=0
(x − 1) (x+3) = 0 AND x = −1 and x = 3
(x + 1) (x − 3) = 0 AND x = −1 and x = 3
(x − 1) (x+3) = 0 AND x = 1 and x = −3
(x + 1)(x-3) = 0 AND x = 1 and x = −3
x²=22.136
Its the last one
I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. Royalty would be great.
By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.
How many halves they need in total?Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.
So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:
3*(1/2) + 8*(1/2) + 7*(1/2)
3/2 + 8/2 + 7/2
All of these have the same denominator so we can directly add them up:
3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2
(3 + 8 + 7)/2 = 18/2
18/2 = 9
You need 9 cupcakes for you and your friends.
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Complete question:
"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"
video
Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
The volume of the solid is approximately 0.558 cubic units.
To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.
We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:
d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2
The radius of each semi-circle is half of the diameter, which is:
r(a) = (ln(a) - a + 2) / 2
The area of each semi-circle is π times the square of its radius, which is:
[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]
To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:
V = ∫[e,2] A(a) da
V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]
V ≈ 0.558 (rounded to the nearest thousandth)
Therefore, the volume of the solid is approximately 0.558 cubic units.
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A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1728 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value 3.14 for X, and round up your answer to the next square meter.?
Answer:
1759 square meters
Step-by-step explanation:
You want the surface area of a cuboid with a half-cylinder top.
Lateral areaThe lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.
P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters
LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²
End areaThe end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.
EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²
Total areaThe total area of 1 mailbox is ...
LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²
Then the area of 1728 mailboxes is ...
1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²
About 1759 square meters of aluminum will be needed for the 1728 mailboxes.
__
Additional comment
This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.
A line has the equation y - 6 = 5x + 9 . work out the gradient and the y intercept of the line.
The gradient of the line is 5, and the y-intercept of the line is 15.
EquationsThe given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.
Rearranging the given equation, we get:
y - 6 = 5x + 9
Adding 6 to both sides, we get:
y = 5x + 15
Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.
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Find the area of the shaded sector of the circle
Answer:
32.67 square meters
Step-by-step explanation:
finding the area of the shaded region.
area of sector = (θ/360°) x πr²
where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.
Substituting the given values into the formula, we get:
area of sector = (60°/360°) x π(14m)²
area of sector = (1/6) x 3.14 x 196m²
area of sector = 32.67m² (rounded to two decimal places)
Therefore, the area of the section is 32.67 square meters
Can some one help with this problem
Step-by-step explanation:
Area of the trapezoid = height x average of bases
area = 4 x (8+13)/2) = 42 in^2
Area of triangle = 1/2 base * height = 1/2 (13-8) * 4 = 10 in^2
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T.A. =
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In a survey of women in a certain country (ages 20−29), the mean height was 63.7 inches with a standard deviation of 2.75 inches. Answer the following questions about the specified normal distribution.
(a) What height represents the 95th percentile?
(b) What height represents the first quartile?
a) The height that represents the 95th percentile is approximately 68.1 inches.
b) the height that represents the first quartile is approximately 65.5 inches.
Percentile and Quartile Heights(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.
The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.
Now we can use the formula for z-scores to find the corresponding height:
z = (x - mu) / sigma
where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).
Rearranging the formula, we get:
x = mu + z * sigma
Plugging in the values, we get:
x = 63.7 + 1.645 * 2.75 ≈ 68.1
Therefore, the height that represents the 95th percentile is approximately 68.1 inches.
(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.
The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.
Using the formula for z-scores and the same values for mu and sigma, we get:
x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5
Therefore, the height that represents the first quartile is approximately 65.5 inches.
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PLEASE HELP ME WITH THIS PLEASE!!
Answer:
Step-by-step explanation:
sto p cheating ur too bad
(btw its 1d * 4r pi / 28)
What is the domain of the square root function graphed below?
If the graph of a polynomial function P(x) has -intercepts at x = - 4, x = 0, x * 1 point
= 5, which of the following must be true for P(x)?
• (x + 5) is a factor of the polynomial.
• (x-4) is a factor of the polynomial.
•' The degree of the polynomial is 3.
• The degree of the polynomial is greater than or equal to 3.
(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
What is a functiοn ?Functiοn can be define in which it relates an input tο οutput.
If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.
Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.
Thus, the cοrrect statement is:
(x + 5) is nοt necessarily a factοr οf the pοlynοmial.
(x-4) is a factοr οf the pοlynοmial.
The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.
Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
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What is the center and radius of a circle with the following equation
Answer:
Center: (1, -3); radius: 2
Step-by-step explanation:
(x - h)² + (y - k)² = r²
(x - 1)² + (y + 3)² = 4
(x - 1)² + (y - (-3))² = 2²
Center: (1, -3); radius: 2
To solve using square roots, your quadratic must be in which format?
Answer:
0=-ax^2+bx+c
Step-by-step explanation:
100 Points!!! Algebra question, only looking for answer to last two. Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached. Thank you!
1) y = -3x and y = -3x + 2: inconsistent system of equations.
2) y = x - 5 and -2x + 2y = - 10: consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.
Explain about the consistent and inconsistent system of equations?If there is at least one solution, an equation system is considered consistent. If there is no solution, a system is inconsistent.If one equation is a multiple of the other in a pair of equations that have two variables, both equations are dependant. Every point in dependent systems is a potential solution, giving them an endless number of solutions.The given equation are:
The graph for each system of equations is plotted.
1) y = -3x and y = -3x + 2
From the graph 1 it is shown that the lines for the each equation form the parallel lines.
Thus, system of equations are inconsistent.
2) y = x - 5 and -2x + 2y = - 10
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
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For a given recipe 8 cups of flour are mixed with 12 cups of sugar how many cups of flour should be used if 27 cups of sugar are use
Therefore, if we are using 27 cups of sugar, we also need 18 cups of wheat.
What does an arithmetic ratio mean?An ordered combination of integers a and b, rendered as a / b, is a ratio if b is not equal to 0. A percentage is an expression that sets two numbers at the same value. For instance, you could put the percentage as follows: 1: 3 if it's 1 male and 3 girls. (for every one boy there are 3 girls)
If 8 cups of flour are mixed with 12 cups of sugar, then the ratio of flour to sugar is:
8 : 12
Simplifying this ratio by dividing both numbers by 4, we get:
2 : 3
This means that for every 2 cups of flour, we need 3 cups of sugar.
If we are using 27 cups of sugar, we can set up a proportion to find out how much flour we need:
2/3 = x/27
Multiplying both sides by 27:
2 × 27 / 3 = x
Simplifying:
x = 18
Therefore, we need 18 cups of flour if we are using 27 cups of sugar.
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A truck is traveling due north at 60km/hr approaching a crossroad. On a perpendicular road a police car is traveling west toward the intersection at 75km/hr. Both vehicles will reach the crossroad exactly one hour. Find the vector currently representing the displacement of the truck with respect to the police car.
Displacement d=
In the given problem, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
How to Solve the Problem?To solve this problem, we can use vector addition. Let's assume that the police car is at the origin, and let the positive x-axis point west and the positive y-axis point north. Then, the initial position of the truck can be represented by the vector (-d, 0), where d is the distance between the police car and the crossroad.
Since the truck is traveling due north, its velocity vector is (0, 60). Similarly, the velocity vector of the police car is (-75, 0). We know that both vehicles will reach the crossroad at the same time, which means that their displacement vectors will have the same magnitude and direction.
Let's call the displacement vector we're looking for "D". Using the formula for displacement, we can write:
D = vt
where v is the average velocity of both vehicles, and t is the time it takes for them to reach the crossroad (which is one hour). The average velocity is given by the vector sum of the velocities of the truck and the police car:
v = (0, 60) + (-75, 0) = (-75, 60)
Substituting in the values for v and t, we get:
D = (-75, 60) * 1 = (-75, 60)
Therefore, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
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Mr. Kwesi Oppong was appointed Financial Controller of Dukes Limited on an annual salary scale of GH¢85,000 X GH¢5,000 – GH¢130,000 on 1/7/2019. In addition, he was entitled to the following allowances:Acting Allowance GH¢5,000 per annumMedical Allowance GH¢300.00 a monthTransport Allowance GH¢250.00 a monthThe company provided him with a furnished accommodation at Hydrafon Estates and a vehicle with an official driver and free fuel.He has a Life Insurance Policy with the following details:Company Capital Sum Premium paid GH¢ GH¢Star Assurance 70,000.00 8,000.00 He is married with three children. The eldest son is in the University of South Africa (UNISA). His other son is in Adonten Senior High School in Aburi and the daughter is in Akosombo International School. He maintains all the children in addition to a 61 year old mother. He contributes 5.5% of his salary to Social Security.RequiredCalculate his chargeable income for the year of assessment 2022.
Mr. Oppong's chargeable income for the year of assessment 2022 is GH¢109,100.
What sort of revenue is charged, for instance?Taxes must generally be paid on all types of income, even those derived from a business or profession. Employment. Dividends.
We must take into account Mr. Kwesi Oppong's salary, benefits, and any deductions when determining his chargeable income for the assessment year of 2022.
Let's start by figuring out his gross revenue for 2022. The annual wage scale for Mr. Oppong is GH85,000 X GH5,000 - GH130,000, which denotes a salary range of GH85,000 to GH130,000. To make things easier, we might suppose that his pay is the midpoint of the range, or GH107,500.
His annual acting allowance is GHC 5,000, so the following would be his total income from salary and allowances:
GH107,500 plus GH5,000 plus (GH300 x 12) plus (GH250 x 12) equals GH114,500.
Next, we must look at his advantages. Mr. Oppong is given a vehicle with a designated driver and free fuel, as well as a furnished place to stay. They are taxable benefits, but in order to estimate their worth, we need more details.
Mr. Oppong also holds a life insurance policy with a GHC 70,000 capital and GHC 8,000 yearly premium. This is not a necessary component of his chargeable income.
Let's now explore the inferences made by Mr. Oppong. 5.5% of his income is put into Social Security by him. Since the Social Security rate is set at GH450 every month, Mr. Oppong can only contribute a maximum of GH5,400 (GH450 x 12) in a given year.
As a result, the following would be Mr. Oppong's chargeable income for the year of assessment 2022:
GH114,500 minus GH5,400 equals GH109,100.
Thus, GH 109,100 will be Mr. Oppong's chargeable income for the assessment year 2022.
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7 x 10 the the power of -5
Answer:
0.00005
Step-by-step explanation:
you move 5 decimal places left starting from 7 and right it as a decimal.
Ans=0.00007
Ella has an offer to buy an item with a sticker price of $12,300 by paying $420 a month for 36 months. What interest rate is Ella being offered?
Answer:
To calculate the interest rate, we can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r)^(-n)) / r]
where:
PV = present value
PMT = monthly payment
r = interest rate per period
n = number of periods
In this case, we have:
PV = $12,300 (the sticker price)
PMT = $420
n = 36 (36 months)
Substituting these values into the formula, we get:
12,300 = 420 x [(1 - (1 + r)^(-36)) / r]
Simplifying this equation algebraically is not possible, so we need to use numerical methods to solve for r. One way to do this is to use a financial calculator or spreadsheet program, which can find the interest rate that makes the equation true. Using Excel's RATE function, for example, we get:
=RATE(36,-420,12300)
This gives us an interest rate of approximately 3.33% per month or 39.96% per year.
Therefore, Ella is being offered an interest rate of 3.33% per month or 39.96% per year.
Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters x and y as necessary.)
2x − 4y = 40
−x + 2y = −20
(x, y) =
The solution to the system of equations 2x - 4y = 40 and -x + 2y = -20 is infinitely many solutions. The solution can be expressed as (x, y) = (2y + 20, y), where y can be any real number.
is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x is first angle
y is second angle
and z is third angle
Step-by-step explanation:
This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.
If m∠ A=5x+6 and m∠ B= 7x-18 Find m∠C
Answer:
We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:
m∠A + m∠B + m∠C = 180
Substitute the given values:
5x+6 + 7x-18 + m∠C = 180
Combine like terms:
12x-12 + m∠C = 180
Add 12 to both sides:
12x + m∠C = 192
Subtract 12x from both sides:
m∠C = 192 - 12x
Therefore, m∠C is equal to 192 minus 12 times x.