A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?
Step 1: Assign variables: Let x = length of the equal side Sketch the figure Step 2: Write out the formula for the perimeter of the triangle. Perimeter = sum of the three sides Step 3: Plug in the values from the question and from the sketch. 50 = x + x + x+ 5 Combine like terms 50 = 3x + 5 Isolate variable x 3x = 50 – 5 3x = 45 x =15 Be careful! The question requires the length of the third side. The length of third side = 15 + 5 =20 Final Answer: The length of third-side is 20
Do the addition or subtraction. You can use the calculator, but be careful with the signs! -987- -654
Remember that when you see two negatives next to each other, you can turn them into one big plus sign. This makes it easier to remember that subtracting a negative turns a negative to a positive. By doing this, your new equation is -987+654 which is -333. All you do is subtract 987 from 654 then add a negative sign since 987 is greater than 654.
For what value of the constant K does the equation Kx2 + 2x = 1 have two real solutions?
Rewrite the given quadratic equation in standard form: Kx 2 + 2x - 1 = 0 Discrimant = 4 - 4(K)(-1) = 4 + 4K For the equation to have two real solutions, the discriminant has to be positive. Hence we need to solve the inequality 4 + 4K > 0. The solution set to the above inequality is given by K > -1 for which the given equation has two real solutions.