<span>A quadratic equation of the form ax^2 + bx + c has a general solution of the form
x = - b +- b^2 - 4ac/2a
We shall use the expression under the radical in the formular method. The expression under the radical is called the discriminant.
If the discriminant D = b^2 - 4ac > 0 then the quadratic has two distinct real number solutions since the square root of any positive number is it self a positive number.
If D = b^2 - 4ac = 0 then we get expressions of the form (-b + 0) and (-b - 0). Regardless we end up with -b. This means when D = 0 we have one solution.
If D < 0 the quadratic equation has a conjugate pair of complex roots of the form a + bi</span>
<span>1. 10 square units.
2. 16.9 units
1. The area of a triangle is 1/2bh where b is the base and h is the height of the triangle. Any of the 3 sides of the triangle may be the base. So looking at the 3 points, I'll consider the line segment DE to be the base since both D and E have an X value of 3, so the length of the base is 3 - (-1) = 4. Since the base of the triangle is a vertical line with X = 3, the height of the triangle will be the absolute value of the X value of vertex F minus 3. So abs(-2 - 3) = abs(-5) = 5. We now have a base of 4 and height of 5 and using the 0.5bh formula, that gives us 0.5 * 4 * 5 = 10.
2. I'll call the points A(-2,-2), B(3,-3), C(4,-6), D(1,-6), and E(-2,-4). Using the pythagorean theorem, we can calculate the length of each side. SO
length AB = sqrt((-2 - 3)^2 + (-2 - (-3))^2) = sqrt(-5^2 + 1^2) = sqrt(25 + 1) = sqrt(26) = 5.099
length BC = sqrt((3 - 4)^2 + (-3 - (-6))^2) = sqrt(-1^2 + 3^2) = sqrt(1 + 9) = sqrt(10) = 3.162
Do the same for the lengths of CD, DE, and EA getting 3.000, 3.606, and 2 respectively.
Now just add them together. So
5.099 + 3.162 + 3.000 + 3.606 + 2.000 = 16.867, which rounds to 16.9</span>
Answer:
?
Step-by-step explanation:
Answer:
Step-by-step explanation:
7(x-4)-3(x+5)
7x-28-3x-15
4x-43
Didnt feel like doing them all , i only attempted to answer the first one which is " a " ( -6 ) hope i helped :)