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Lemur [1.5K]
2 years ago
12

Dominic is deciding if he should become a member of his local ice rink.

Mathematics
1 answer:
babymother [125]2 years ago
6 0

After 4 visits, members would pay $160

After 4 visits, non-members would pay $80

After 6 visits, members would pay $168

After 6 visits, non-members would pay $120.

The equation that can be used to solve for the number of visits the cost would be equal is $144 + 4n = $20n

The total cost for members and non-members would be $180.

Dominic can guess the number of visits he plans to make in a year. If it would be greater than 9, he should pay for the membership. If not, he should not become a member.

<h3>What is the total cost for members and non members after 4 and 6visits?</h3>

Total cost for members = annual fee + (number of visits x cost per visit)

Total cost for non-members = (admissions + parking + cost of renting the ice skate) x number of visits

After 4 visits:

Total cost for members = $144 + (4 x 4) = $160

Total cost for non-members = (11 + 5 + 4) x 4 = $80

After 6 visits:

Total cost for members = $144 + (4 x 6) = $168

Total cost for non-members = (11 + 5 + 4) x 6 = $120

The equation that can be used to solve for the number of visits the cost would be equal is: $144 + 4n = $20n

In order to determine the value of n, take the following steps:

Combine similar terms: $144 = $20n - $4n

Add similar terms together : $144 = $16n

Divide both sides by 16 : 144 / 16

n = 9

Total cost = $20 x 9 = $180

To learn more about total cost, please check: brainly.com/question/25717996

#SPJ1

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yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.

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We will calculate the volume of both the beakers separately and then add them up together to get the volume of the beaker.

Given, π = 3.14

Beaker 1:

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Volume (V₁) = π r₁² h₁ = 3.14 x 2² x 3 = 37.68 cm³

Beaker 2:

Radius (r₂) = 6 cm
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Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?
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Answer:

  yes

Step-by-step explanation:

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For the first parabola, the point of intersection is ...

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The point of intersection is (1, -2).

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For the second parabola, the equation is the same, but with x and y interchanged:

  x^2 = 4(-x-1)

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  x = -2, y = 1 . . . . . one point of intersection only

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If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

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Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.

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