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kvv77 [185]
3 years ago
15

Math whizzes assemble! this is a tough one, this is a question on my study guide its a screenshot, any help would be appreciated

.

Mathematics
1 answer:
arsen [322]3 years ago
5 0

Answer:

x = 6   y = -9   (I took a complicated route so if my explanation doesn't make sense It's fine)

Step-by-step explanation:

DAY = FUN

F = (7x+2y) = 24

If DAY = FUN then D = F making (7x + 2y) = 24

This means A = U so you have to find U with 24+126=150

A triangle is 180 degrees so you would do 180-150=30

U = 30

This also makes (8x+2y) = 30

8x + 2y = 30

-8x           -8x

2y = 30 - 8x

Divide everything by 2

y = 15 - 4x

Doing this you can take 7x + 2y = 24 and plug in 7x + 2(15 - 4x) = 24

Multiply it 7x + 30 - 8x = 24

Add like terms -x + 30 = 24

Subtract 30      -x = -6

Divide by -1       x = 6

Now take one of the equations and plug it in 7(6) + 2y = 24

Multiply 42 + 2y = 24

Subtract 2y = -18

Divide by 2    y = -9

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Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership wit
valkas [14]

She spent 8 months in the 1st gym and 4 months in the 2nd gym

Step-by-step explanation:

Jan spends part of her year as a member of a gym.

  • She then finds a better deal at another gym so she cancels her membership with the first gym after x months
  • She spends the rest of the year, y months, with the second gym
  • The membership to the first gym costs $75 per month, while the membership for the second gym costs $45 per month
  • She ended up spending a total of $780 over the course of the year

We need to find how much time she spent at each gym

∵ She spent x months in the 1st gym

∵ She spent y months in the 2nd gym

∵ Her course is a year

- There are 12 months in a year

∴ x + y = 12 ⇒ (1)

∵ The membership to the first gym costs $75 per month

∵ The membership to the second gym costs $45 per month

∵ She ended up spending a total of $780 over the course

∴ 75x + 45y = 780 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -45 to eliminate y

∵ -45x - 45y = -540 ⇒ (3)

- Add equations (2) and (3)

∴ 30x = 240

- Divide both sides by 30

∴ x = 8

- Substitute the value of x in equation (1) to find y

∵ 8 + y = 12

- Subtract 8 from both sides

∴ y = 4

She spent 8 months in the 1st gym and 4 months in the 2nd gym

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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svet-max [94.6K]

The sum of the inner angles of any triangle is always 180°, i.e. you have


\alpha + \beta + \gamma = 180


In the particular case of an equilater triangle, all three angles are the same, so

\alpha = \beta = \gamma


and the expression becomes


\alpha + \beta + \gamma = \alpha + \alpha + \alpha = 3\alpha = 180


which implies \alpha = 60


So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.


Of course, this is equivalent to a clockwise rotation of 120 degrees.


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