Answer:
A) y = 2*0.8ˣB) y = 3.5*3ˣ-----------------------------------------
Part AUse the coordinates to determine the function.
Point (0, 2):
2 = a*b⁰ ⇒ 2 = aThe function becomes:
y = 2bˣIt has a multiplier of 0.8, so b = 0.8, so the function is:
y = 2*0.8ˣPart BUse the first point:
3.5 = a*b⁰ ⇒ 3.5 = aUse the second point:
31.5 = 3.5*b²9 = b²b = √9b = 3The function is:
y = 3.5*3ˣAnswer:
[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]
[tex]\text{b)} \quad y=3.5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question (a)Given:
y-intercept = (0, 2) ⇒ a = 2multiplier = 0.8 ⇒ b = 0.8Substitute the values of a and b into the exponential function formula:
[tex]\implies y=2(0.8)^x[/tex]
Question (b)The y-intercept is when x = 0. Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.
Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:
[tex]\implies 31.5=3.5b^2[/tex]
[tex]\implies b^2=9[/tex]
[tex]\implies b=3[/tex]
Substitute the values of a and b into the exponential function formula:
[tex]\implies y=3.5(3)^x[/tex]
To make a homemade all-purpose household cleaner, you can mix the ingredients shown in the table.
All-Purpose Cleaner
1 cup vinegar
12 cup rubbing alcohol
1 gallon water (16 cups)
Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need?
Samuel will need
______ containers.
The total solution will include
cup(s)_____of vinegar,
cup(s)_____of rubbing alcohol, and
cup(s)_____ of water, which is a total of
cups of solution. Five containers will hold 5 × 6, or 30 cups of solution. So, he will need _____ total containers to hold all of the solution.
3 containers, 1 cup, 12 cup, 16 cups
Samuel will need
3 containers.
The total solution will include
cup(s) 1 of vinegar,
cup(s) 12 of rubbing alcohol, and
cup(s) 16 of water, which is a total of
cups of solution. Five containers will hold 5 × 6, or 30 cups of solution. So, he will need 3 total containers to hold all of the solution.
What are ingredients?Ingredients refer to the materials or apparatuses combined together to have a single product. In other words, ingredients are the chemical makeups of a refined product which combine together to have new and entirely different product.
The ingredients for a homemade all-purpose household cleaner, in this case, are vinegar, rubbing alcohol, and water.
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How many real solutions does this system of equations have? x²+y²=36
3x-y+1=0
A.0
B. 2
C. 3
D. 1
Answer: A. 0
This system of equations has no real solutions. The equation x² + y² = 36 represents a circle with center (0,0) and radius 6, while the equation 3x - y + 1 = 0 represents a line in a 2-dimensional plane. Since a line and a circle do not intersect at exactly one point in general, this system of equations have no common point, and therefore no real solutions.
Step-by-step explanation:
Students in Mrs.Whites class took their Chapter 1 math test on Monday
Answer:
Step-by-step explanation:
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⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⣀⣀⣀⣀⣀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀
Identify the quadratic function(s). (Select all that apply.) 8 - 5x = 4(3x - 1) (4a + 2)(2a - 1) + 1 = 0 2y + 2(3y - 5) = 0 2b(b - 7) + b = 0
Answer: A quadratic function is a polynomial function of form f(x) = ax^2 + bx + c where a,b, and c are constants, and a is not equal to zero.
The given functions are:
8 - 5x = 4(3x - 1)
(4a + 2)(2a - 1) + 1 = 0
2y + 2(3y - 5) = 0
2b(b - 7) + b = 0
The quadratic function(s) among them are:
2. (4a + 2)(2a - 1) + 1 = 0
2b(b - 7) + b = 0
The first one 8 - 5x = 4(3x - 1) is linear and not a quadratic function, and the third one 2y + 2(3y - 5) = 0 is also linear, not a quadratic function.
Note that to identify a quadratic function, we can look for the pattern of x^2 or y^2 in the equation.
Also, we could expand the second degree polynomials in the form (ax^2+bx+c) and check if there are x^2 or y^2 term on both sides of the equation.
Step-by-step explanation:
Factorise (pls show steps)
12y^2 - 20y - 8
Answer:
12y( y-1 ) - 8( y+1 )
Step-by-step explanation:
12y^2-20y-8 = (12y^2- 12y) - (8y+8) = 12y( y-1 ) - 8( y+1 )
Finish the table that represents the relation.
{(-2, 3) , (2, -1) . (3, 3) , (5, -4) , (9, 12)}
The table that represents the relation are out put 3 input 3, input 2 out put -1, input 5 out put -4.
How can you locate a table that illustrates a function?Find out if a table of input and output values is a representation of a function. The input and output values should be noted.
Verify that every input value is matched with just one output value. Consequently, the table is a function in that case.
A relation is a rule that links the constituents of one set to those of another. Relationships can be visualized using graphs, ordered pairs, tables of values, equations, or mapping diagrams. Every input in a relation results in one or more outputs.
According to question:-
out put 3 input 3
input 2 out put -1
input 5 out put -4.
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Recall that the standard form of a linear equation is Ax+By=C. Rewrite this equation in slope intercept form.
Answer:
y = [tex]\frac{-A}{B}[/tex] x + [tex]\frac{C}{B}[/tex]
y = 6/5 x + 9/5
Step-by-step explanation:
Ax + By = C Subtract Ax from both sides
Ax - Ax + By = -AX + C
By = -AX + C Divide both sides by B
y = [tex]\frac{-A}{B}[/tex] x + [tex]\frac{C}{B}[/tex]
-6x + 5y = 9 Add 6x to both sides
-6x + 6x + 5y = 6x + 9
5y = 6x + 9 Divide both sides by 5
y = 6/5 x + 9/5
The table shows how the amount of Ariel’s bank account changed over several weeks.
Help
By how much did Ariel’s account change from week `1` to week `6`?
Make sure to show whether the change is positive or negative.
The amount by which Ariel’s bank account changed from week `1` to week `6` is -$365.80.
What are the changes that occurred in Ariel's account?The changes over the six-week period in Ariel's bank account are as follows:
At the end of week 1:
$337.5 - $360 = -$22.50
At the end of week 2:
$182.35 - $337.5 = -$155.15
At the end of week 3:
$-41.4 - $182.35 = -$223.75
Balance at the end of week 4:
-$41.4 + $40 = -$1.40
At the end of week 5:
-$5.80 - (-$1.4) = -$4.40
Week 6 balance = -$5.80
Changes that occurred = -$22.50 + (-$155.15) + (-$223.75) + (-$1.40) + $40 + (-$4.40)
Changes that occurred = -$365.80
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i don’t understand:(
The measure of the exterior angle is 70° .
What is the measure of the exterior angle ?Exterior angle = Sum of two opposite interior angles of a triangle.
(2x- 8)° = x° + 31°
2x- x = 31 +8
x = 39
So, Substituting the value of x in the exterior angle.
(2x- 8)° = 78 - 8
= 70°
What is the exterior angle of a triangle?One side of a triangle can be extended to form an external angle. An exterior angle is the angle formed by the extended side and the adjacent side. According to the external angle theorem, when a triangle's side is extended, the resulting exterior angle is equal to the sum of the measurements of the triangle's two opposed internal angles. A triangle's unknown unknown angle can be measured using the theorem.To use the theorem, we must first determine the triangle's exterior angle and then its two remote interior angles. Exterior angles are those created between a polygon's side and its extended neighbouring side.To learn more about exterior angle , refer:
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write a word problem for 5x5.
Answer: The answer is 5x5=25 rows of crops.
Step-by-step explanation:
A farmer has 5 acres of land and wants to plant 5 rows of crops on each acre. How many total rows of crops will the farmer have planted?
The answer is 5x5=25 rows of crops.
Answer: There were 5 groups of cats, and there 5 cats in each group. How many cats are there in total?
1) In the given figure, name (a) the vertex opposite A to side AB (b) the angle opposite to side AC (c) the angle made by the sides CB and CA.
In this case, the arms of $angle ABC$ are represented by AB and AC, which are two rays that unite to make an angle. The vertex of angle $angle ABC$ is B in this case. It is the common terminal point where rays meet to form an angle.
What is vertex in angle ABC?The vertex and arm of the provided ABC must be found in this question. Vertex information is required for this puzzle. Angles are formed when two rays share a terminal. The vertex is the term for the shared endpoint. Alternatively, vertex refers to the shared terminal point where two rays converge to form an angle. Likewise, we must understand what an angle's arm is. An angle's arm is made up of the two rays that unite to make it. Here, an angle of ABC was provided. Specifically, we must identify the angle's vertex and arm.The arms of the ABC formula are represented by AB and AC, two rays that unite to make an angle.The vertex of ABC is the common terminal point where rays converge to form an angle. In this case, B is the vertex.AB and AC make up the arms of ABC, and B serves as the vertex.To Learn more About vertex of angle Refer To:
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you have 53 dollars. your brother has 23 fewer dollars than you . How many dollars does your brother have
Answer:
The brother has 30 dollars.
Step-by-step explanation:
Alright
So if you have 53 dollars
And your brother has 23 less dollars than you.
You subtract.
53-23=
Which will give you 30
So in the end
Your brother has 30 dollars.
Confusing question:
Please help quickly!
The value of angle x based on the information given is 45°.
How to determine the value of angle x?Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life
From the image ∠BEC = 160°, ∠FED = 115° and ∠AEF = x°
∠AEC = 180 - 160 = 20° (sum of angles on a straight line)
∠DEB = ∠AEC (vertically opposite angles)
∠DEB = 20°
It should be noted that vertically opposite angles are equal just as denoted above.
x = 180 - ∠DEB - ∠FED (sum of angles on a straight line)
It should be noted that the sum of angles that are on a straight line is 180°.
x = 180 - 20 - 115
x = 45°
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Determine the intercepta of the line. Do not round your answers. -6x+3y=-7
Please help!!!
x=7<
Step-by-step explanation:
7x4=77iuiiiiiiiiii
Three vertices of DEFG are D(1, 1), E(5, 2), and F(1, 8). Find the coordinates of the remaining vertex.
The coordinates of the remaining vertex if the other 3 vertices of DEFG are D(1, 1), E(5, 2), and F(1, 8) is G(12,2)
What is a coordinate?A spherical or elliptical coordinate system known as the geographic coordinate system is used to measure and transmit positions on Earth as latitude and longitude. Of all the several spatial reference systems in use, it is the most basic, traditional, and generally used. It serves as the foundation for the majority of
How do coordinates work?Latitude and longitude are the two components of the geographic coordinate system. Each longitude line measures the number of degrees east or west of the prime meridian and travels north to south. Values fall between -180° and +180°. Latitude lines travel from east to west and count the degrees north or south of the equator.
According to the given question, we see that
The coordinates of the remaining vertex if the other 3 vertices of DEFG are
D(1, 1), E(5, 2), and F(1, 8) is G(12,2)
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The model represents a division equation.
Determine whether each statement is true or fa
Select True or False for each statement.
Please double check my work!
50 points!!!
The above statements are
A) True
B) True
C) False
D) False
What is the division equation?
The division equation is a mathematical operation that represents the process of determining the number of times one number, called the divisor, can be subtracted from another number, called the dividend, without going negative.
A) The whole bar represents 4/5 -> TRUE
B) The model is divided into 1/8 equal parts -> TRUE
C) The model is divided into parts each worth 1/10. -> FALSE
D) The model represents the division equation 4/5 ÷ 1/10= 8 -> FALSE.
Hence, the above statements are
A) True
B) True
C) False
D) False
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Let's be any real number such that 4 < √ s <9. Which of the following is a possible value of s?
A. 2.5
B. 7.6
C. 12.7
D. 39.3
E. 82.4
The possible real number for the variable s is 39.3 (letter D).
Power and Square RootsIt is common in math solutions, you multiply a number by itself. See the examples below.
2 x 2 =4
3 x 3 = 9
4 x 4 = 16
In math, you can use the power to represent a multiply a number by itself using the operation power. Let's consider the previous example for a better understanding.
2 x 2 = 2²
3 x 3 = 3²
4 x 4 = 4²
Therefore, the power represents the number of times the numeral repeats in a product. It is important to know that the inverse operation of power is the root. Thus,
2²=4 and [tex]\sqrt{4}[/tex]= 2
The question asks you the possible value of s.
If [tex]4 < \sqrt{s}[/tex], you can apply power operation on both sides, for eliminating the root.
[tex](4)^2 < (\sqrt{s})^2\\ \\ 16 < s[/tex]
Another inequality is [tex]\sqrt{s} < 9[/tex]. Then, one more time you will apply power operation on both sides, for eliminating the root.
[tex](\sqrt{s})^2 < (9)^2 \\ \\ s < 81[/tex]
Combining the intervals you have: 16< s< 81. Now, let's analyze the given options.
A. 2.5 - It is not contained in the given range 16< s< 81.
B. 7.6 - It is not contained in the given range 16< s< 81.
C. 12.7 - It is not contained in the given range 16< s< 81.
D. 39.3 - It is contained in the given range 16< s< 81.
E. 82.4 - It is not contained in the given range 16< s< 81.
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Select the expressions that have a
quotient of 9.
1.35 ÷ 1.5
1.35 0.15
13.5 ÷ 1.5
13.5+ 0.15
Answer:
1.35/0.15
13.5/1.5
Step-by-step explanation:
We know the first and last ones are incorrect. The last is incorrect because it uses addition when the question is asking for the quotient. The first is incorrect because 1.35/1.5 = 0.9. The quotient (or answer) for the rest all equal 9.
1.35/0.15 = 9
13.5/1.5 = 9
Before you add fractions, they must have the same:
A basketball team played 6 games. In those games, the team won by 7 points, lost by 5 points, won by 8, won by 11, lost by 3, and won by 6. What was the mean difference in game scores over the 6 games?
Answer:
6-7-8-5-11-8=-33
Step-by-step explanation:
Answer: 6-7-8-5-11-8=-33
Step-by-step explanation:
Mr. Felkamp planted 8 rows of tomato plants. There were 96 plants in a row. How many tomato plants were there in all?
The total number of tomato plants is given as follows:
768 tomato plants.
How to obtain the total number of tomato plants?The total number of tomato plants is obtained according to the proportions in the context of this problem.
The use of the proportion is because the total number of tomato plants is given by the multiplication of the number of plants by the number of rows.
The parameters for this problem are given as follows:
8 rows.96 plants per row.Hence the total number of tomato plants is obtained as follows:
96 * 8 = 768 plants.
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The measure of one angle of a right triangle is 34∘ more than the measure of the smallest angle. Find the measure of the smallest angle. Please Help me and solve ASAP.
Answer:
28°
Step-by-step explanation:
You want the smallest angle in a right triangle if the difference from the larger one is 34°.
Sum and differenceThis is one of a class of problems in which you want to find values that have a particular sum and a particular difference. They all have the same generic solution:
the smaller value is half the difference of the sum and differencethe larger value is half the sum of the sum and differenceApplicationHere, the sum of the two acute angles in a right triangle is 90°. The problem statement tells you their difference is 34°. That means the smaller angle is ...
smaller angle = (90° -34°)/2 = 56°/2 = 28°
The smallest angle is 28°.
__
Additional comment
The largest acute angle is (90° +34°)/2 = 124°/2 = 62°. You will notice this is the complement of the 28° angle found above, and differs by ...
62° -28° = 34° . . . . as required by the problem statement
If you don't want to just jump to the answer, you can write an equation for the smallest angle (x). The larger will be (x+34).
x +(x +34) = 90 . . . . . the two acute angles are complementary
2x = 90 -34
x = (90 -34)/2 = 56/2 = 28 . . . . . this should look familiar
Use the Quadratic Formula to solve the equation 4x^2+1=10x
Using the Quadratic Formula to solve the equation 4x² + 1 = 10x, we get x₁ = 0.104 and x₂ = 2.395.
What is Quadratic Formula?The term "quadratic equation" refers to an equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers and a0 is an imaginary number. The quadratic equation's roots are the values of the unknown variable x that satisfy the given quadratic equation.
A + b + c, for instance, equals zero if is a root of the quadratic equation ax² + bx + c = 0. Additionally, the act of locating roots is referred to as solving a quadratic equation.
The quadratic formula is
[tex]$ {\displaystyle \text x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
We have given the quadratic equation 4x²+ 1 = 10x
= 4x² -10x + 1
Pouting the values in the formula we get
[tex]{\displaystyle \text x={\frac {-(-10)\pm {\sqrt {(-10)^{2}-4(4)(1)}}}{2(4)}}}[/tex]
On solving we get
[tex]$ \text x_1 = \frac{5-\sqrt{21} }{4}[/tex] and [tex]$ \text x_2 = \frac{5+\sqrt{21} }{4}[/tex]
Approximately,
x₁ = 0.104
x₂ = 2.395
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Question 6(Multiple Choice Worth 2 points)
(Linear Relationships LC)
Which of the following tables represents a linear relationship that is also proportional?
x y
0 0
4 2
8 4
x y
0 1
2 3
4 5
x y
0 2
3 5
6 8
x y
0 3
6 5
12 7
Table 1 is the correct answer.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given: Table 1
x y
0 0
4 2
8 4
Clearly here x=2y which is proportional equation with 2 being the constant with x varying directly with the value of y
Hence, Table 1 is the correct answer.
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A line passes through the points (5,9) and (4,6). What is it's equation in slope-intercept form?
A line passes through the points (5,9) and (4,6) is y=3x-6.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
The given coordinate points are (5,9) and (4,6).
Here, slope m=(6-9)/(4-5) =3
Substitute m=3 and (x, y)=(5, 9) in y=mx+c, we get
9=3×5+c
9-15=c
c=-6
Substitute m=3 and c=-6 in y=mx+c, we get
y=3x-6
Therefore, equation in slope-intercept form is y=3x-6.
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An odd integer is represented by x. Which expression represents the next consecutive odd integer?
The expression which represent consecutive odd integer is 2x+1.
What is odd integer?
Any integer that cannot be divided by two is referred to as an odd number. In other words, integers that take the form 2k+1, where k , are referred to be odd numbers. Integers or sets of integers on a number line can be either odd or even, it should be noted.
Here let us take the odd integer as x.
Now the expression which expression consecutive odd integer is,
=> 2x+1 .
Here x is a real number.
Hence the expression which represent the next consecutive odd integer is 2x+1.
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The expression which represent consecutive odd integer is 2x+1.
What is odd integer?Any integer that cannot be divided by two is referred to as an odd number. In other words, integers that take the form 2k+1, where k , are referred to be odd numbers. Integers or sets of integers on a number line can be either odd or even, it should be noted.
Here let us take the odd integer as x.
Now the expression which expression consecutive odd integer is,
=> 2x+1 .
Here x is a real number.
Hence the expression which represent the next consecutive odd integer is 2x+1.
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in order to graph your solutions solve for the variable be sure to show your work
Variable x isb5 is the answer to the equation 6 is 3x - 9 in the given situation.
The equation is what?A mathematical statement is considered to be an equation if it contains at least two terms with equal amounts of variables or integers.
We can start by focusing on the variable on one side of equation 6 = 3x - 9 in order to find a solution. We may accomplish this by adding 9 to both sides, giving us:
6 + 9 = 3x
Simply put, this means:
15 = 3x
The next step is to divide the equation's two sides by 3, which will yield the answer to the question "what is x?"
15/3 = 3x/3
We obtain 5 = x by simplifying.
Consequently, x = 5 is the answer to the variable.
The complete question is,
Locate the answer to the variable in the following equation. Use entire sentences to describe the problem-solving procedure you used to come up with a solution, and be sure to present all of your efforts. Include two words from the word bank at the very least.
6 = 3 x - 9.
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Gwen buys 3 identical pairs of shoes at store A. She pays $110.25 after the discount. What is the regular price of each pair?
The regular price of each shoe pair is $36.75
How to find the regular price?To find the regular price of each pair of shoes before the discount, we need to use algebra. Let x be the regular price of each pair of shoes. We know that:
3x = regular price of 3 pairs of shoes
We also know that Gwen paid $110.25 after the discount, so we can set up the following equation:
3x - discount = 110.25
We don't know the discount, so we can't solve for x yet.
But we can use the fact that Gwen bought 3 pairs of identical shoes to find the discount.
discount = regular price of 3 pairs of shoes - price paid after discount
= 3x - 110.25
Now we can substitute this expression for the discount into the first equation:
3x - (3x - 110.25) = 110.25
Simplifying this equation gives:
110.25 = 110.25
So x = regular price of each pair of shoes = $110.25/3 =
$36.75
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:p confused on how to do this
Answer: C
Step-by-step explanation:
Same thing as before(I believe I answered a similar question).
Substitute the values for the variables.
Do that, and you get
(1/2)^2+2/5
= 1/4+2/5
= 5/20+8/20
= 13/20
The answer is C.
van someone help w this paper
Assume that
x is the total number of hours that you and your pals skate at Sam's or Brad's Skate Park, and y is the cost of skating as a whole.Sam's Skate Park charges $3 to enter the facility, $1 for each hour of skating, $1 for a total of x hours, and y=(3+x).Brad's Skate Park costs $5 to enter, $0.50 per hour of skating, then $0.5 per hour for a total of y=(5+0.5x).First gap: y=(3+x)
Second gap: y=(5 + 0.5 x)
x represents the total number of hours you and your pals skate at Sam's or Brad's Skate Park, and y represents the cost of skating. Compare the two expressions:3+x=5+0.5x,
x-0.5x=5-3,
0.5x=2,
5x=20,x=4.
When skating for 4 hours, the total costs in the two parks are equal.The cost for three hours at Sam's skate park is $(3+3)=$6, whereas the cost at Brad's skate park is $(5+30.5)=$6.5. The best deal is at Sam's Skate Park where admission is $6–$6.5.To know more about Find the Value for X and Y refer to :
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