The equation that translates the information is $282 = $150 + $6x where x to represent the number of guests at your party
The total charge for renting a roller rink for a birthday party is composed of two parts: a fixed cost of $150 and a variable cost of $6 per person. The variable cost depends on the number of guests, which we can represent with the variable x.
Therefore, the total cost equation can be written as:
Total cost = Fixed cost + Variable cost
Total cost = $150 + $6x
Here, Total cost = $282
So, equation is $282 = $150 + $6x
To find the total charge for a specific number of guests, we can substitute the value of x into the equation and simplify it. For example, if there were 22 guests at the party, the total cost would be:
Total cost = $150 + $6(22)
Total cost = $150 + $132
Total cost = $282
This means that the total charge for a party with 22 guests would be $282.
It's important to note that the fixed cost of $150 is the cost that remains the same no matter how many guests attend the party. On the other hand, the variable cost of $6 per person changes based on the number of guests.
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Solve each system of equations:
1. Y = x2
y = 4x - 4
solution:
2. Y = -x2 + 2x - 4
y = 3x - 2
solution:
3. Y = x2 - 3x - 5
y = -2x + 1
solution:
1) The solution is (2, 4).
2) The solutions are (-1, -5) and (2, 4).
3) The solutions are (3, -5) and (-2, 5).
1) Y = x^2 and y = 4x - 4
Substitute y from the second equation into the first equation to get:
x^2 = 4x - 4
Simplifying and rearranging:
x^2 - 4x + 4 = 0
(x - 2)^2 = 0
x = 2
Substitute x = 2 into the second equation to get:
y = 4(2) - 4 = 4
Therefore, the solution is (2, 4).
2) Y = -x^2 + 2x - 4 and y = 3x - 2
Substitute y from the second equation into the first equation to get:
-x^2 + 2x - 4 = 3x - 2
Simplifying and rearranging:
-x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1 or x = 2
Substitute x = -1 into the second equation to get:
y = 3(-1) - 2 = -5
Substitute x = 2 into the second equation to get:
y = 3(2) - 2 = 4
Therefore, the solutions are (-1, -5) and (2, 4).
3) Y = x^2 - 3x - 5 and y = -2x + 1
Substitute y from the second equation into the first equation to get:
x^2 - 3x - 5 = -2x + 1
Simplifying and rearranging:
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 or x = -2
Substitute x = 3 into the second equation to get:
y = -2(3) + 1 = -5
Substitute x = -2 into the second equation to get:
y = -2(-2) + 1 = 5
Therefore, the solutions are (3, -5) and (-2, 5).
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Please help me with this and explain how you got it because I don’t really understand this.
Answer:YES
Step-by-step explanation:
you should write 1 instead of every x and 5 instead of every y.
6*1+2*5=6+10=16
1+3*5=1+15=16
4.02 Lesson check ! (3)
The given sequence 22, 12, 2, -8 is arithmetic, and the common difference is -10.
How to determine if the sequence is arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if k is that common difference, we can write the recursive formula as:
a(n) = a(n - 1) + k
Here we have the sequence:
22, 12, 2, -8
Taking the differences between consecutive terms we get:
12 - 22 = -10
2 - 12 = -10
-8 - 2 = -10
The differences are all equal, then this is an arithmetic sequence, and the common difference is -10.
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Find cos R and cos S.
The value of the trigonometric identities are;
1. cos R = 15/17
cos S = 8/17
2. cos R = 12/13
cos S = 5/13
What are trigonometric identities?
Trigonometric Identities are simply seen as the equalities involving trigonometry functions.
It also holds true for all the values of variables given in the equation.
There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. They are;
sinetangentcosinecotangentsecantcosecantWe have cosine represented as;
cos θ = adjacent/hypotenuse
For the first triangle, we have;
cos R = 30/34 = 15/17
cos S = 16/34 = 8/17
For the second triangle;
cos R = 24/26 = 12/13
cos S = 10/26 = 5/13
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The dimensions of the inner square pyramid have a ratio 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid
a. The surface area of the outer square pyramid is 11.25 square centimeters. b. The side length of the inner square pyramid is 2.25 centimeters.
a. To find the surface area of the outer square pyramid, we need to calculate the area of each of its faces and add them together. The outer square pyramid has four triangular faces and a square base.
Area of a triangular face = (1/2) x base x height
Area of a triangular face = (1/2) x 1.5 cm x 3 cm = 2.25 cm²
The area of the square base can be found using the formula for the area of a square:
Area of square base = side length²
Area of square base = 1.5 cm x 1.5 cm = 2.25 cm²
Therefore, the total surface area of the outer square pyramid is:
Surface area = 4 x area of triangular face + area of square base
Surface area = 4 x 2.25 cm² + 2.25 cm²
Surface area = 11.25 cm²
Therefore, the surface area of the outer square pyramid is 11.25 square centimeters.
b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. Let's call the side length of the inner square pyramid "x". Since the ratio of the dimensions is 2:3, we know that the side length of the outer square pyramid is (3/2)x.
The volume of a square pyramid can be calculated using the formula:
Volume = (1/3) x base area x height
Since the two pyramids are similar, the ratio of their volumes is the cube of the ratio of their corresponding side lengths:
Volume of inner pyramid / Volume of outer pyramid = (x / (3/2)x)³ = (2/3)³
We also know that the volume of the outer pyramid is:
Volume of outer pyramid = (1/3) x base area x height
The height of the two pyramids is the same, since they are stacked on top of each other, so we can write:
Volume of inner pyramid / Volume of outer pyramid = (1/3) x base area of inner pyramid / (1/3) x base area of outer pyramid
Simplifying this expression, we get:
(x / (3/2)x)³ = (1/3) x² / (1/3) (3/2x)²
Solving for x, we get:
x = (3/2)²
x = 2.25
Therefore, the side length of the inner square pyramid is 2.25 centimeters.
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The complete question is :
a. For the outer square pyramid, the side length of the base is 1.5 centimeters and the height of one of the triangular faces is 3 centimeters. What is the surface area of the outer square pyramid?
b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid?
4. Kiran says that a solution to the equation x + 4 = 20 must also be a solution to the equation 5(x + 4) = 100. Write a convincing explanation as to why this is true.
Kiran is correct in saying that a solution to the equation x + 4 = 20 must also be a solution to the equation 5(x + 4) = 100. This is because the second equation is simply the first equation multiplied by 5. To see this, we can distribute the 5 on the left side of the second equation to get 5x + 20 = 100. We can then subtract 20 from both sides to get 5x = 80, and finally divide both sides by 5 to get x = 16.
Since x = 16 satisfies the first equation, it must also satisfy the second equation. This is because if we substitute x = 16 into the first equation, we get 16 + 4 = 20, which is true. If we substitute x = 16 into the second equation, we get 5(16 + 4) = 100, which is also true. Therefore, any solution to the first equation will also be a solution to the second equation when the second equation is just the first equation multiplied by a constant factor.
Answer:
Kiran is correct. To see why, let's first simplify the second equation, 5(x + 4) = 100, by multiplying both sides by 1/5:
5(x + 4) = 100
⇒ (1/5) * 5(x + 4) = (1/5) * 100
⇒ x + 4 = 20
Now we can see that the second equation simplifies to the first equation, x + 4 = 20. This means that any solution that satisfies the first equation (x + 4 = 20) will also satisfy the second equation (5(x + 4) = 100).
In other words, if we find a value of x that makes x + 4 = 20 true, then substituting that value of x into 5(x + 4) = 100 will also make it true. Therefore, any solution to the equation x + 4 = 20 will also be a solution to the equation 5(x + 4) = 100.
Step-by-step explanation:
Willie’s Widgets has created a demand function for its widget, where q is the quantity demanded and p is the price of one widget.
Q = -112p + 4,500
Let E = 3.00q + 18,000, and find the total expense if 2 widgets are produced.
The total expense for producing 2 widgets is $18,006.00.
How to find the total expense for producing 2 widgets?To find the total expense for producing 2 widgets, we need to find the total revenue from selling 2 widgets and then subtract the total expense of producing them.
The total revenue from selling 2 widgets is simply the price per widget times the quantity demanded at that price. Since the price is not specified in the problem, we can use the demand function to find it.
We know that the quantity demanded when 2 widgets are produced is:
q = 2
So we can solve the demand function for p:
q = -112p + 4,500
2 = -112p + 4,500
-112p = -4,498
p ≈ 40.16
Therefore, the price per widget is approximately $40.16.
The total revenue from selling 2 widgets at this price is:
revenue = price × quantity demanded
revenue = $40.16 × 2
revenue = $80.32
Now we need to find the total expense of producing 2 widgets. The problem gives us an expression for the total expense:
E = 3.00q + 18,000
Substituting q = 2, we get:
E = 3.00(2) + 18,000
E = $18,006.00
Therefore, the total expense for producing 2 widgets is $18,006.00.
Finally, we can calculate the profit as the difference between the revenue and the expense:
profit = revenue - expense
profit = $80.32 - $18,006.00
profit ≈ -$17,925.68
Since the profit is negative, Willie's Widgets would not make any profit from producing 2 widgets at this price. They would lose money.
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Alberto compro 2 melones del mismo tamaño y juntos pesan 6kg.¿Cuántos gramos pesarán 7 melones iguales a los que compró Alberto?
Based on the above, the 7 melons together will weigh about 21,000 grams.
What is the melon about?We know that 2 melons of the same size together weigh 6 kg, therefore each melon weighs:
6kg / 2 = 3kg
To know how many grams the 7 melons weigh, we first need to know how many grams a kilogram weighs:
1kg = 1000g
So each melon weighs 3 kg * 1000 g/kg = 3000 g.
Therefore, 7 melons equal to the ones Alberto bought will weigh:
7 * 3000g = 21,000g
Therefore, the 7 melons together will weigh 21,000 grams.
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See text below
Alberto bought 2 melons of the same size and together they weigh 6 kg. How many grams will 7 melons equal to the ones Alberto bought weigh?
How do you find the surface area of the cone?
Answer:
A=[tex]\pi[/tex]r(r+h2+r2)=[tex]\pi[/tex]·7·(7+122+72)≈459.44884
rounded off to 500 square millimetres
Step-by-step explanation:
The total surface area of a cone is the combination of the curved surface as well as the base area of a cone. The formula to calculate the total surface area of the cone is:
TSA of cone = [tex]\pi[/tex]r^2 + [tex]\pi[/tex]r l = r (l + r) square units.
A triangle has sides 8 cm and 5 cm and an angle of 90° between them. Calculate the smallest angle of the triangle.
Step-by-step explanation:
let the smallest angle = x
tan x = 5/8
x = arctan 5/8
x = 32°
Answer: The smallest angle of the triangle is 32°
Step-by-step explanation:
Given:
one side of the triangle= 8 cm
The other side of the triangle = 5 cm
Angle between AB and BC = 90°
⇒ ∠ABC = 90°
ΔABC is a right angled triangle
Use trigonometric function: For X
tanx= AB/CB
tanx= 8/5
x=tan-1 (8/5)
x= 58°
Use trigonometric function: For Y
tany= BC/AB
tany=5/8
y=tan-1 (5/8)
y = 32°
Making 32° be the smallest angle of the triangle
Jethro has sat 5 tests Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74 Jethro has to sit one more test that is also to be marked out of 100 Jethro wants his mean mark for all 6 tests to be at least 77 Work out the least mark that Jethro needs to get for the last test
Jethro must get a mark of 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.
To work out the least mark that Jethro needs to get for the last test, we can use the Mean formula: Mean = (Sum of all scores) / (Number of scores).
We know that the Mean of the 5 tests that Jethro has already sat is 74, so we can calculate the sum of the 5 test scores by multiplying the mean by the number of tests (74 x 5 = 370). We also know that Jethro wants his mean mark for all 6 tests to be at least 77, so the sum of all 6 test scores must be higher than (77 x 6 = 462).
To calculate the least mark Jethro needs to get for the last test, we can combine these two facts. We know the sum of the 5 test scores is 370, so the sum of all 6 test scores must be 462 or higher. This means the least mark Jethro needs to get for the last test must be (462 – 370) = 92. This means that Jethro must get a mark of at least 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.
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Write vector a in terms of other vectors using the following image:
Answer:
Step-by-step explanation:
2a = -b - d + c
= c - b - d
x = c/2 - b/2 - d/2
The vector a in terms of other vectors for the given vectors in the image is c/2 - b/2 - d/2.
A vector is a quantity that determines both an object, its magnitude, and its direction.
The resultant vector is obtained when the tail of one vector is attached to the head of another vector such the resultant vector is formed from the sum of the two vectors.
Let a be the total vector of the given figure.
The vectors are written as:
2a = -b - d + c
a = c - b - d
a = c/2 - b/2 - d/2
Hence, the vector a in terms of other vectors is c/2 - b/2 - d/2.
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there are two concentric circles, the radii for the circles are 15CM and 7CM. A diameter AB of the larger circle intersects the smaller circle at C and D. Find two possible values for AC.
Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.
In mathematics, what do circles represent?An assortment of similarly spaced out points in a plane make up a circle. The center is where the point is located, but the radius is the distance from the center. Two times the radius equals the diameter.
We can see that triangle ADC is a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem to find AC:
AC² = AD² - CD²
Since AD is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:
AC² = 15² - 7²
AC² = 176
AC = √(176)
AC ≈ 13.266 cm
So one possible value for AC is approximately 13.266 cm.
Now let's consider the other intersection point, D. We can see that triangle BDC is also a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem again to find BD:
BD² = BC² + CD²
Since BC is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:
BD² = 15² - 7²
BD² = 176
BD = √(176)
BD ≈ 13.266 cm
Since BD is a diameter of the larger circle, we have:
AC + BD = 2 * 15 = 30
So the other possible value for AC is:
AC = 30 - BD
AC ≈ 16.734 cm
Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.
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(Explain) the probability of the following event happening: rolling a 9 on a number cube with sides labeled 1-6.
Choose one of the following:
impossible, less likely, somewhat likely, highly likely, or certain
Answer:
Step-by-step explanation:
Impossible. Using simple logic skills, the only possible outcomes from rolling a dice are 1,2,3,4,5,6. Hence, rolling a 9 is an impossible outcome.
Need help with answer, than you!
What is the value of x?
Answer:
x = 18
Step-by-step explanation:
[tex]\frac{6}{7}=\frac{x}{21} \\\\6*21=7*x\\\\126=7x\\\\x=18[/tex]
The graphs below show the speed of a car over four different time periods. Which graph indicates the car slowing down and then stopping?
Answer:
(D)
Step-by-step explanation:
You want the graph that shows speed decreasing to zero.
Slowing"Slowing down" means speed is decreasing. On a graph of speed that is indicated by a negative slope.
StoppedWhen an object is stopped, its speed is zero. On a graph of speed, points on the horizontal axis indicate the speed is zero.
GraphThe attached graph shows the speed of a car that is slowing to a stop.
If A+B=O
then what's the relation between A and B
Suppose you bought a car for $63,765 and the value of the car has decreased by 44%. What is the new value of the car? Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
If the value of the car has decreased by 44%, it still retains 56% of its value. Thus, the solution for the depreciation is 63,765(.56) = $35,708.40
7. (01. 03 MC)
Stephen's current hourly pay is $9. 45. If he receives a 5% hourly pay increase each year, what will his hourly pay be in two years? (4 points)
O $9. 92
O $10. 25
$10. 42
O $11. 00
Stephen's hourly pay will be $10.42 in two years, calculated by plugging the principal amount of $9.45, the rate of interest of 5%, and the number of times interest is compounded per year of 1 into the compound interest formula.
Stephen's current hourly pay is $9.45. In order to calculate his hourly pay in two years time, we need to use the compound interest formula. The formula is A = P (1 + r/n)^nt, where A is the amount after n years, P is the principal or initial amount, r is the rate of interest, and n is the number of times interest is compounded per year. In this case, the principal is $9.45, the rate of interest is 5%, and the number of times interest is compounded per year is 1. Plugging these into the formula yields A = 9.45(1 + 0.05/1)^2*1, which equals $10.42. That means Stephen's hourly pay will be $10.42 in two years.
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A plant grows at a constant rate. Lalita records the height of the plant each week. The unite rate is measured in inches per week. What is the constant of proportionality
A.1/2
B.3
C.7
D.2
The constant of proportionality between the plant's height and time in weeks is 2 inches/week. So,correct answer is (D) 2.
Define constant of proportionality?The constant of proportionality is a factor that relates two variables that are directly proportional, indicating the ratio of change between them.
We can use the given information to determine the constant of proportionality between the plant's height and time in weeks.
The plant's height increased by 6 - 0 = 6 inches in the first three weeks (from week 0 to week 3). Therefore, the rate of growth during this period was 6 inches / 3 weeks = 2 inches/week.
Similarly, the plant's height increased by 10 - 6 = 4 inches during the next two weeks (from week 3 to week 5), so the rate of growth during this period was 4 inches / 2 weeks = 2 inches/week.
Finally, the plant's height increased by 14 - 10 = 4 inches during the last two weeks (from week 5 to week 7), so the rate of growth during this period was also 4 inches / 2 weeks = 2 inches/week.
Since the plant grows at a constant rate, we can assume that the rate of growth was 2 inches/week throughout the entire period from week 0 to week 7.
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HELP ME PLEASE(HELP WITH BOTH PLEASE)
As a result, the answer to the following question, As a result, the length triangle of side JS is 18.
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
We must apply the Pythagorean theorem to answer question 19. We know that JN is the hypotenuse of a right triangle with legs of 6 and 8 lengths. As a result, we may apply the formula:
[tex]JN^2 = 6^2 + 8^2\\JN^2 = 36 + 64\\JN^2 = 100\\JN = square root (100)\\JN = 10\\[/tex]
As a result, the length of side JN is 10.
JS/NS = JM/JN
When we substitute the provided values, we get:
12/10 = JS/NS
When we simplify the left side, we get:
6/5 = JS/NS
When we multiply both sides by NS, we get:
JS = (6/5)NS
We also know that NS is 15, therefore we may substitute that number for:
[tex]JS = (6/5) * 15\sJS = 18[/tex]
As a result, the length of side JS is 18.
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For what value of C is the function one-to-one?
(1,2) (2,3) (3,5) (4,7) (5,11) (6,C)
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
The basic definition of a one-to-one function is the mapping of two sets. If each element in the range of a function g matches precisely one in the domain of g, then the function g is one-to-one. 1-1 is another way to represent one-to-one. A function or formula, such as f() connects the values of two variables in such a way that the values of the first variable's elements determine the values of the second variable in exactly the same ways.
We have:
{(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)}
We can see the number of the 2nd position is prime and in sequence so, we can easily determine that 2, 3, 5, 7, 11, and next will be 13.
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
When every element in a function's range and domain match exactly one another, the function is said to be one-to-one. 1-1 is also used to indicate one-to-one. A function or formula, such as f() links the elements and values of one variable to those of another in such a way that the elements of the first variable exactly predict the elements of the second variable.
The complete question is-
For what value of c is the function one-to-one?
{ (1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c) }
a)2
b) 5
c)11
d)13
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Challenging y’all a little
If LI = 25 cm and AC = 24 cm , what is the length of BC?
The length of the missing side of the given triangle ABC which is similar to triangle ILN would be = 7cm
How to calculate the length of the missing side of the given triangle?Given that triangle ILN and ABC are similar this shows that their sides are equal in measurement too.
Therefore, LI = 25cm = AB = c
AC = 24 cm = LN = b
BC = X = IN = a
Using the Pythagorean formula;
C² = a² + b²
25² = a² + 24²
625 = a² + 576
625 -576 = a²
a² = 49
a = √49
a = 7cm
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Jazmin takes a ride share service home from the airport. The ride share service charges $5 as an initial cost to pick her up, and $2. 25 for every mile to her final destination. Jazmin's ride home cost a total of $38. 75. Write an equation to represent the situation. Let m represent the number of miles to her home
Answer ! :)
If Jazmin spent $38.75 on all
Then it would 15miles ( 15m ) to get home.
As your adding the extra $5 which starts the process.
Basically a equation could be:
(5 + 2.25 = 7.25) + ( 2.25 x 14 )
Extra info if needed more explanation: ( 2.25 x 14 = 31.5 ) Which 31.5 + 7.25 = 38.75
Info on counting:
7.25, 9.50, 11.75, 14, 16.25, 18.50, 20.75, 23, 25.25, 27.50, 29.75, 32, 34.25, 36.50, 38.75
3×4+(-7)×9 the answer
Answer:
-51 would be the answer for this equation.
Step-by-step explanation:
A crow is holding a 0.11 kg clam above a rocky beach from a height of 11.5 m. What is the potential energy clam?
(show work please!!)
Answer:
The potential energy (PE) of an object is given by:
PE = mgh
where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s² near the Earth's surface), and h is the height of the object above a reference level.
In this case, the mass of the clam is 0.11 kg, the height above the beach is 11.5 m, and the acceleration due to gravity is 9.8 m/s². Therefore, the potential energy of the clam is:
PE = (0.11 kg) × (9.8 m/s²) × (11.5 m) ≈ 12.7 J
So the potential energy of the clam is approximately 12.7 Joules.
A cinema sells adult tickets and child tickets.
The cost of 2 adult tickets and 2 child tickets is £38.
The cost of 2 adult tickets and 5 child tickets is £59.
Work out how much the following cost:
a) 6 adult tickets and 6 child tickets.
b) 4 adult tickets and 7 child tickets.
c) 3 child tickets.
a) 6 adult tickets and 6 child tickets cost is £102. b) 4 adult tickets and 7 child tickets cost is £77 c) 3 child tickets cost is £21
Describe Elimination Method?The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.
Let x be the cost of one adult ticket and y be the cost of one child ticket.
From the given information, we can write two equations:
2x + 2y = 38 (equation 1)
2x + 5y = 59 (equation 2)
To solve for x and y, we can use elimination method.
Multiplying equation 1 by 5 and equation 2 by 2, we get:
10x + 10y = 190
4x + 10y = 118
Subtracting equation 2 from equation 1, we get:
6x = 72
x = 12
Substituting x = 12 into equation 1, we get:
2(12) + 2y = 38
2y = 14
y = 7
Therefore, one adult ticket costs £12 and one child ticket costs £7.
a) 6 adult tickets and 6 child tickets:
Cost = 6(£12) + 6(£7) = £102
b) 4 adult tickets and 7 child tickets:
Cost = 4(£12) + 7(£7) = £77
c) 3 child tickets:
Cost = 3(£7) = £21
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The terminal side of an angle of 7 radians is in which quadrant?
According to the given information, the terminal side of an angle of 7 radians is in the second quadrant.
What is the terminal angle?
The terminal angle is the angle formed by the terminal side of an angle in standard position (i.e., with its initial side along the positive x-axis) and the nearest x-axis. It is typically measured in a counterclockwise direction from the positive x-axis.
An angle of 7 radians is greater than 2π radians (which is approximately 6.28 radians), so it corresponds to more than one full revolution around the unit circle.
To find the terminal side of an angle of 7 radians, we can subtract 2π radians (or 360 degrees) from 7 radians until the result is between 0 and 2π radians. We have:
[tex]$$7 \text{ radians} - 2\pi \text{ radians} \approx 1.716 \text{ radians}$$[/tex]
Since 1.716 radians is less than π radians (which is approximately 3.14 radians), the terminal side of an angle of 7 radians is in the second quadrant.
The terminal side of an angle of 7 radians is in the second quadrant.
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