Tutor profile: Liz C.
Solve the equation -10 + 3e^x = -6
The first step in solving our equation is to move the -10 to the other side of the equal sign. We need to perform the opposite operation, so we should add 10 to the -6 to get 4. Next, divide by 3 to get the e term by itself. We get e^x = 4/3. In order to eliminate the e, we find the natural log of both sides, since e and ln are inverses of each other. This eliminates the e on the left and gets the x by itself. The natural log of 4/3 is 0.2877, so this is the solution for x.
A right triangle has legs of length 5 cm and 7 cm. Find the missing hypotenuse.
We use Pythagorean Theorem to find missing side lengths in a right triangle. The theorem is a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. In this triangle, a and b are 5 cm and 7 cm. Plug these into the formula and we get 25 + 49 = c^2. Add 25 and 49 to get 74. To find c, we need to take the square root of 74. 74 does not have a perfect square root, so we can round the answer to 8.6 cm.
Solve the equation by factoring: x^2 + 7x = 8
In order to solve by factoring, the equation must be set equal to zero. So we need to move the 8 over to the left hand side of the equal sign. When we move it, we perform the opposite operation, so we must subtract 8. The equation is now x^2 + 7x - 8 = 0. To factor, we should look for factors of -8 that add up to 7. That would be 8 and -1. Set up our 2 sets of parentheses with these factors. Remember that since our leading term is x^2, the leading term in each set of parentheses must be x. So we have (x + 8) (x - 1) = 0. Now set each of those factors equal to zero and solve for x. X + 8 = 0, so x = -8, and x - 1 = 0, so x = 1. Our 2 solutions are -8 and 1.
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