Is a triangle with side lengths of 9cm, 40 cm, and 41 cm a right triangle?
To answer this question we need to know the Pythagorean Theorem which states that a^2+b^2=c^2. This means that the two sides of the triangle squared equal the hypotenuse of the triangle squared. For this problem, you would have to set 9^2 + 40^2=41^2 This equation simplifies to be 81 +1600=1681 and 1681=1681 so this would be a right triangle.
Evaluate the expression 8(6-3) + 4
This is an order of operations problem. To solve this type of problem we need to remember the rules on order of operations. We do parenthesis first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. I would first subtract 6-3 because it is inside of parenthesis, this gives me 3. Then I would multiply by 8 because it is on the outside of the parenthesis which means to multiply, this would give me 24. Then I would add the four to 24 which is 28.
Solve the equation -5x + 13 = 38 for x
To solve the equation for x I need to isolate the variable x. To do this I need to first subtract 13 from both sides of the equation. The reason I need to do this is so I can have the -5x alone on one side. By subtracting 13 on both sides the equation is still balanced because of the subtraction property of equality. This will leave us with -5x= 25. To finish solving the equation I will need to divide each side by -5 to solve for x. When I do this I get x is equal to -5 because -5x divided by -5 leaves us with x and 25 divided by -5 gives us an answer of -5. I can check my answer by substituting -5 into the original equation. I would have -5*-5 +13 =38 and this is true.