Tutor profile: Gianna C.
A right triangle has a side length of 7 cm and its hypotenuse is 10 cm. What is the length of the 3rd side?
For right triangles we can use the Pythagorean theorem to solve for a side length. The formula is a^2+b^2=c^2 where c is the length of the hypotenuse (the longest side). When we plug in our numbers given we have 7^2+b^2=10^2. If we multiply out the exponents we have 49+b^2=100. To solve for b, lets subtract 49 from both sides. What's left is b^2=100-49, or b^2=51. To get the b by itself, we must square root the b^2, and if we square root one side, it must be done to the other side. The square root of b^2 is just b, so our final answer is b=the square root of 51, or roughly 7.14 cm.
Subject: Basic Math
If 2x-10=20, what is x?
When solving for one variable in an equation, we want to isolate it or get it by itself. We start by moving as much as we can to the other side of the equal sign by adding or subtracting. In this case, we will add 10 to the other side so that 2x is by itself. We are left with 2x = 20+10, or simplified it would be 2x=30. To get x by itself, we can divide both sides by 2. Any time we multiply or divide we must do it to both sides. When we do this we get 2x/2=30/2, or our final answer of x=15.
If f(x)=3((x-2)^2)+12, what is f(4)?
When you substitute 4 in for every x value in the equation, you end up with f(4)=3((4-2)^2)+12. When you use PEMDAS, you start with the parentheses (P). 4-2 is 2. Next in PEMDAS are exponents (E), so 2^2 is 4. The M and D stand for multiplication and division, and wherever you see this in the equation you just work from left to right. 4*3 is 12. The last letters are A and S for addition and subtraction, and the same left-to-right rule applies. 12+12 is 24. The final answer is f(4)=24.
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