A ladder is placed 5 feet away from at billboard. If the top of the ladder meets at the ledge of the billboard that is 12 feet tall how long is the ladder?
The first thing is you need to realize that the figure formed is a triangle and it is a right triangle. When you are given two sides of a right triangle you can always find the third side of the triangle with the pythagorean theorem which is a^2+b^2=c^2. In this case we would draw the situation and we would see that the ladder would be the hypothenuse and that the hypothenuse is c in the pythagorean theorem. So all we have to do is plug in the numbers give after we do so algebra. The opposite of a squared is the squared root so c=sqroot(a^2+b^2)=sqroot(5^2+12^2)=sqroot(169)=13
Balance the following equation: Fe+ H2SO4 ---> Fe2(SO4)3+ H2
First thing in balancing equation is knowing that the equation needs to have the same number of element on each side even though its in a different compound. You first want to write what elements you have on each side. Fe H S O Once written down you can know use it as you table to help count the number of each element. So with out adding any coefficients to the equation the numbers would look like this. 1 Fe 2 2 H 2 1 S 3 4 O 12 the right answer is 2 Fe+ 3 H2SO4 ---> Fe2(SO4)3+ 3 H2 2 Fe 2 6 H 6 3 S 3 12 O 12
Solve for x. (2-x)^2=2x^2+8
4-4x+x^2=2x^2+8 0=x^2+4x+4 0=(x+2)(x+2) x=-2 You first need to foil out (2-x)^2. You do this by (2-x)(2-x) and distribute the first number then the outer numbers the inners then the last. If i would use letters to describe this I would (a-b)(c-d)= ac+a(-d)+(-b)c+(-b)(-d). This would then be set to the rest of your equation. The next set would be to subtract on side to the other to get the equation to equal zero and combine like terms. now you are going to factor into to find two number when added together they make 4 as well as when they are multiplied. In our case it was 2 so it came out to be 0=(x+2)^2. We then solve for x by knowing 0=x+2 x=-2 we do this by subtraction 2 from each side.