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Delvig [45]
3 years ago
6

Dominic is deciding if he should become a member of his local ice rink. The $144 annual membership fee at the ice rink includes

admission and parking, members pay $4.00 per visit to rent ice skates. Non-members pay $11 admissions, $5.00 for parking and they also pay $4.00 per visit to rent ice skates. 1. When is it better to be a member? After 4 visits how much would each pay? Member: $_________ Non-Member: $__________ After 6 visits how much would each pay? Member: $_________ Non-Member: $__________
Mathematics
1 answer:
Alenkasestr [34]3 years ago
6 0

Answer:

1. members = $ 160 , non members = $ 80

2. members = $ 168 , non members = $ 120

Step-by-step explanation:

For members

Annual membership = $ 144

rent per visit charges = $ 4

For Non members

parking charges = $ 5

admission charges = $ 11

rent per visit = $ 4

(1) for 4 visits

Members pay = $ 144 + 4 x $ 4 = $ 160

Non members pay = 4 x $ 11 + 4 x $ 5 + 4 x $ 4 = $ 80

So, non member ship is better.    

(2) for 6 visits

Members pay = $ 144 + 6 x $ 4 = $ 168

Non members pay = 6 x $ 11 + 6 x $ 5 + 6 x $ 4 = $ 120

So, non member ship is better.    

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Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.
loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>
  • x^ax^b = x^{(a+b)}
  • \dfrac{x^a}{x^b} = x^{(a-b)}
  • (a^a)^b =x^{(a\times b)}
  • (xy)^a = x^ay^a
  • x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4

The solution of the expression is \dfrac{4x^4}{y^6}.

<h2>Explanation</h2>

Given to us

  • (16x^8y^{12})^{\frac{1}{2}}

Solution

We know that 16 can be reduced to 2^4,

=(2^4x^8y^{12})^{\frac{1}{2}}

Using identity (xy)^a = x^ay^a,

=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}

Using identity (a^a)^b =x^{(a\times b)},

=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})

Solving further

=2^2x^4y^{-6}

Using identity \dfrac{x^a}{x^b} = x^{(a-b)},

=\dfrac{2^2x^4}{y^6}

=\dfrac{4x^4}{y^6}

Hence, the solution of the expression is \dfrac{4x^4}{y^6}.

Learn more about Exponentiation:

brainly.com/question/2193820

8 0
2 years ago
Which of the following is equivalent to (5)^7/3? 5^-4<br> 5^4<br> ^7squroot5^3<br> ^3squroot5^7​
kvv77 [185]

Answer:

^7 squroot5^3

Step-by-step explanation:

5x2= 10

7÷ 3= 2.5

8 0
3 years ago
Sam is placing rope lights around the edge of a circular patio with a diameter of 18 feet. The lights come in lengths of 54 inch
andrew-mc [135]
You can find the circumference of the circle with the circumference equals 2pir.
circumference=2pi9
circumference=18pi
circumference=56.55 feet
you can then turn the feet into inches by multiplying by 12
(56.55 feet)x(12inches/foot)=678.58 inches
then divide 678.58 inches by 54 inches to find how many light strands are needed.
(678.58 inches)/(54 inches/strand)=12.57 strands
4 0
3 years ago
Read 2 more answers
Write the equation of the line that passes through the points (6,2) (4,1)
Alisiya [41]

Answer: y=1/2x-1

Step-by-step explanation:

To find the equation of the line that passes through the points, we need to find out slope, m.

m=\frac{y_{2} -y_{1} }{x_{2}-x_{1}  }

We plug our points into this formula to find slope.

m=\frac{1-2}{4-6} =\frac{-1}{-2} =\frac{1}{2}

Our slope is 1/2. To find our y-intercept, b, we would plug any point into the equation for slope-intercept form.

y=mx+b

y=1/2x+b

1=1/2(4)+b

1=2+b

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Now that we know b, our equation is y=1/2x-1.

6 0
3 years ago
In ΔPQR, the measure of ∠R=90°, the measure of ∠P=26°, and PQ = 8.5 feet. Find the length of QR to the nearest tenth of a foot.
Vitek1552 [10]

Answer:

3.7feet

Step-by-step explanations

Using the sin rule

A/sin a = B/sin b

Let A = PQ = 8.5feet

B = QR = x feet

a = R = 90°

b = P = 26°

Substitute the values into the Sin rule

8.5/sin90 = x/sin26

8.5×sin 26 = x × sin 90

8.5×0.4383 = x× 1

3.7255 = x

Hence the length of QR to the nearest tenth 3.7feet

5 0
3 years ago
Read 2 more answers
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