Answer:
<em>8(x2 + 2x) = –3
</em>
<em>8(x2 + 2x + 1) = –3 + 8
</em>
<em>x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot</em>
Step-by-step explanation:
<u>Solving Quadratic Equations
</u>
Sometimes it's preferred to solve quadratic equations without the use of the known quadratic formula solver. One of the most-used methods consists of completing squares and solving for x.
We have the equation
We separate variables from constants
Taking the common factor 8
Completing squares in the brackets and balancing the equation in the right side
Factoring the perfect square
Isolating x
We can clearly see the steps used to solve the quadratic equation are (in order and written like in the question)
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
So... first off, we sort the dividend, the numerator, in descending order... so, looking at the exponents in this one, is already sorted in descending order, from 4 down to 1, so that's done.
then the divisor, we have x+3, that means x + 3 = 0, x = -3,
so, we'll be using -3 for the synthetic division then.
and now, we'll use those coefficients, dropping the exponents of the polynomial by one, and the remainder, remains as a fraction with the divisior of x+3.
<h3>
Answer: x = 14</h3>
=============================================
Work Shown:
Refer to the diagram below. I've added a line segment and two variables y and z. This forms two isosceles triangles.
The central angle 56 degrees subtends the same arc as the inscribed angle y. By the inscribed angle theorem, this means y = 56/2 = 28. The inscribed angle is always half of the central angle (when both angles subtend the same arc).
Focus on the smaller isosceles triangle that has angles 56, z and z. Those three angles add to 180
z+z+56 = 180
2z+56 = 180
2z = 180-56
2z = 124
z = 124/2
z = 62
Now focus on the larger isosceles triangle (angles y = 28, x+z and x+z)
We'll use the same trick as before.
(x+z)+(x+z)+(y) = 180
(x+62)+(x+62)+(28) = 180 ... plug in z = 62 and y = 28
2x+152 = 180
2x = 180-152
2x = 28
x = 28/2
x = 14
Answer:
I think its going to be (b)
Answer:
Yes, y=5x is a direct variation and the constant of variation is 5 .
