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jenyasd209 [6]
3 years ago
15

Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee. Lian correctly wrote

and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?
a. One gym charges $75 per month.
b. Each gym charges $75 per month.
c. Both gyms charge the same monthly rate and the same membership fee.
d. Both gyms charge the same monthly rate, but not the same membership fee.
Mathematics
2 answers:
Alex_Xolod [135]3 years ago
8 0

Answer:

Both gyms charge the same monthly rate and the same membership fee.

Step-by-step explanation:

lapo4ka [179]3 years ago
3 0
The resulting equation 75 = 75 is an identity; this tells that the two equations of the system are equivalent, this is they both represent the same function. So, Lian can conclude that (option c) both gyms charge the same monthly rate and the same membership fee<span>.</span>
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Sylvie folds a large piece of paper in half. The fold divides the paper into two equal parts. She folds it in half again. When s
Nikolay [14]
Each time you fold a paper it will double the amount of parts. When you think about it, it's just multiplying by 2 a bunch of times.

One fold is 2 times 1, which is 2.
The second fold is 2 times 2, which is 4.
The third fold is 4 times 2, which is 8.

Using this process, we can simplify that into exponents. If the amount of times you fold is x and the parts double for each fold, then the amount of parts can be represented by:

2^{x}

So if the amount of parts is given and we need the amount of folds, just keep doubling until you get to 64. The amount of times you doubled is the number of times Sylvie folded.

Later you will learn that the opposite of an exponent is a logarithm, which would look like this:

log_{2}(64) = ?

But don't worry about that yet.
6 0
3 years ago
Find the total value of an investment of $1030 at 4% for 2 years to the nearest dollar.
mel-nik [20]

Answer:

1114$

Step-by-step explanation:

3 0
3 years ago
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7nadin3 [17]
28°

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3 0
3 years ago
The point (16, 12) lies on the terminal side of an angle. find cos, tan, and sin
frez [133]
The terminal side means that it's 16 to the right and 12 up. Which means that the triangle made from this has the sides of 16 and 12 and the hypotenuse is 20 units long. Theta, in this case, would have 16 as it's adjacent and 12 as it's opposite.
Therefore, using the Pythagorean identities:
<span>sin(\theta) = \frac{12}{20} = \boxed{\frac{3}{5}} \\\ cos(\theta) = \frac{16}{20} = \boxed{\frac{4}{5}} \\\ tan(\theta) = \frac{12}{16} = \boxed{\frac{3}{4}} </span>
8 0
3 years ago
Find the volume of a right circular cone that has a height of 11.1 cm and a base with a diameter of 17.2 cm. Round your answer t
vovangra [49]

Answer:

2577.8\text{ cm}^3

Step-by-step explanation:

GIVEN: A right circular cone that has a height of 11.1 cm and a base with a diameter of 17.2 cm.

TO FIND: Volume of cone.

SOLUTION:

radius of cone =\frac{\text{diameter}}{2}=\frac{17.2}{2}=8.6\text{ cm}

height of cone =11.1\text{ cm}

Volume of cone =\frac{1}{3}\pi r^2h

putting values we get

Volume of cone =\frac{1}{3}\times3.14\times8.6\times8.6\times11.1

                           =2577.8\text{ cm}^3

Hence the volume of cone is 2577.8\text{ cm}^3

3 0
3 years ago
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