50 POINTS URGENT

Use the quadratic formula to find the correct solutions.

The solutions to the equations in order are

1. x = , x= -1,

2. x = , x = -3,

3. x = 4 + √10, x= 4 - √10, 4.

4. x = 8 + √40/ 2, x = 8 - √40 / 2 and

6. x= 1/2 + √5/3, x= 1/2 - √5/3.

Step-by-step explanation:

Step 1; For a quadratics equation ax² + bx + c = 0, the product of the solution terms is a×c and the product of the terms is b.

For 5x² + 6x + 1 = 0, the sum is 6 and the product is 5. The terms are 5 and 1.

5x² + 6x + 1 = 5x² + 5x + x + 1 = 5x (x + 1) + 1 (x + 1) = (5x + 1)(x + 1) = 0.

5x + 1 = 0 and x + 1 = 0 so x = , x= -1.

Step 2; For 2x² + 5x - 3 = 0, the sum is 5 and the product is -6. The terms are 6 and -1.

2x² + 5x - 3 = 2x² - 1x + 6x - 3 = x (2x - 1) + 3 (2x - 1) = (x + 3)(2x - 1) = 0.

x + 3 = 0 and 2x - 1 = 0 so x = , x = -3.

Step 3; For x² + 2x - 8 = 0, the sum is 2 and the product is -8. The terms are 4 and -2.

x² + 2x - 8 = x² - 2x + 4x - 8 = x (x - 2) + 4 (x - 2) = (x + 4)(x - 2) = 0.

x + 4 = 0 and x - 2 = 0 so x = -4 and x = 2.

Step 4; For equations that cannot be seperated into its factors.Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

x² - 8x + 6, here a = 1, b = -8, c = 6.                                                               x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(1)(6) / 2(2) = 8 ± √64 - 24/2.     So x= 8 ± √40 / 2 so x = 8 + √40/ 2, x = 8 - √40 / 2

Step 5; 9x² - 6x - 4, here a = 9, b = -6, c = -4.                                                x =-b ± √b² - 4ac / 2a =-(-6) ± √(-6)² - 4(9)(-4) / 2(9) = 6 ± √36 + 144/18. 180 can also be written as 5 × 36 and √36 = 6. So                                   x= 1/2 + √5/3, x= 1/2 - √5/3.

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answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq