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2 years ago

Find the product xy if2^(x)+3^(y)=5,2^(x+2)+3^(y+1)=18

Mathematics

1 answer:

Marina86 [1]2 years ago

5 0

The solution to the system of equation is (0, 1)

<h3>System of equations</h3>

Given the following system of equation as shown below

2^(x)+3^(y)=5,

2^(x+2)+3^(y+1)=18

Rewrite

2^(x)+3^(y)=5,

2^x*2^2 + 3^y*3^1 = 18

___________

2^(x)+3^(y)=5,

4(2^x) + + 3(3^y) = 18

Let a = 2^x and b = 3^y

Substitute

a + b = 5

4a + 3b = 18

a = 5 - b

Substitute

4(5-b) + 3b = 18

20 - 4b + 3b = 18

-b = -2

b = 2

since a = 5 - b

a = 5 - 2

a = 3

Recall that a = 2^x and b = 3^y

2^x = 2

x = 0

Similarly

3^y = 3

y =1

Hence the solution to the system of equation is (0, 1)

Learn more on system of equation here: brainly.com/question/25976025

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3 years ago

Complete the square to determine the minimum or maximum value of the function defined by the expression.

FrozenT [24]

Answer:

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3 years ago

40% of the memberships sold by Gym A were gold memberships.

Aneli [31]

Answer:

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

Step-by-step explanation:

Here is the complete question: 40% of the memberships sold by Gym A were gold memberships. 25% of the memberships sold by Gym B were gold memberships.

Which statement must be true?

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

b) If both gyms sold the same number of memberships, Gym A sold 15 more gold membership.

c) Gym A sold more gold membership than Gym A did.

d) If Gym B sold 50 membership, 25 would be gold memberships.

Given: Gym A have sold 40% gold membership of total membership.

Gym B have sold 25% gold membership of total membership.

Lets take option A first to find if it is true statement.

As per option A, There are total number of membership is 80.

∵ Gym A has sold 40% gold membership.

∴ Gym A gold membership= $40\% \times 80$

⇒ Gym A gold membership= $\frac{40}{100} \times 80= 32 member.$

∴ Gym A gold membership= 32.

Now, Gym B

∵ Gym B has sold 25% gold membership.

∴ Gym B gold membership= $25\% \times 80$

⇒ Gym B gold membership= $\frac{25}{100} \times 80=20 member.$

∴ Gym B gold membership= 20.

Next finding difference gold membership for Gym A and Gym B

$32-20= 12 \ membership$

Hence, we can say option A is correct as Gym A have sold 12 more gold membership, if total number of membership sold by both Gym is 80.

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3 years ago