An isosceles right triangle has a hypotenuse with the value of 9. Find the value of the legs
A right isosceles triangle has angle values 45-45-90. Using special right triangles we know the side opposite the 90 degree angle (the hypotenuse) is equal to s times the square root of 2. To solve special right triangles, the goal is to solve for s based on the given side. Here we can say that s times the square root of 2 is equal to 9. To solve for s, we divide both sides by the square root of two, giving s = 9 divided by the square root of two. We must now rationalize the denominator by multiplying both the top and bottom by the square root of 2. This gives 9 times the square root of 2 all over the value of 2. In a 45 - 45 - 90 triangle, both legs are congruent and have the value of "s", so here, both legs are equal to 9 times the square root of 2 all over the value of 2.
Solve the equation to find the value of x. 5x + 8 = 3x - 7 - x
When solving an equation you must first combine the like terms on each side of the equation. The left side is simplified here, but on the right side, the terms "3x" and "-x" can be combined. The equation is now 5x + 8 = 2x - 7. You must now isolate the variable x by using opposite operations to get the x variable alone on one side of the equation, and the numbers on the other side. We can start by subtracting 2x from both sides (the 2x is positive so subtraction is the opposite operation). We must do the same operation to both sides to balance the equation. We are now left with 3x + 8 = - 7. Next we must move the 8. The 3x can not be broken apart until there is only one unit/monomial on that side (nothing else being added or subtracted). We subtract the 8 from both sides and are left with 3x = - 15. Now the 3x is isolated so we can break it apart and move the 3 over by dividing both sides by 3 (the 3 and x are multiplied so the opposite operation in division). We are now left with our solution that x = - 5
A museum membership costs $75 a year with a $5 admission charge per visit. Write an equation and solve to find how many times Brooke visited the museum if she paid $125 for the year.
The variable (v) in this problem is the amount of times Brooke visited the museum over the given year. The fixed fee is the $75 membership charge and the variable fee is the $5 PER visit. Look for keywords like "per" and "each" to help guide you to the variable fee. These amounts equal the total (T) spent for the year. The basic equation for this problem is 5v + 75 = T or, if using x and y variables, y = 5v + 75 In this problem, the total paid is $125 so we set the equation to this amount. The other side of the equation represents the fees that added up to this amount: 5v + 75 = 125 To solve the equation, subtract both sides by 75 and then divide both sides by 5. Your answer should be 10, which represents that Brooke visited the museum 10 times throughout the year.