What if the following is the sum of both solutions of the equation....

Mathematics

1 answer:

LuckyWell [14K]2 years ago

6 0

answer

D 2

factor

factor the equation $x^{2} - 2x - 8 = 0$ into (x + a) and (x + b) so that a + b = -2 and a * b = -8

the two numbers that meet these conditions are a = -4 and b = 2

$x^{2} - 2x - 8 = (x - 4)(x + 2)$

find solutions

set both (x - 4) and (x + 2) equal to zero to find your solutions

x - 4 = 0

x = 4

x + 2 = 0

x = -2

add solutions

since the two solutions are x = 4 and x = -2, add them together to get your final answer

4 + (-2) = 2

You might be interested in

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integr

prisoha [69]

Split up the interval [0, 2] into 4 subintervals, so that

$[0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right]$

Each subinterval has width $\dfrac{2-0}4=\dfrac12$ . The area of the trapezoid constructed on each subinterval is $\dfrac{f(x_i)+f(x_{i+1})}4$ , i.e. the average of the values of $x^2$ at both endpoints of the subinterval times 1/2 over each subinterval $[x_i,x_{i+1}]$ .

So,

$\displaystyle\int_0^2x^2\,\mathrm dx\approx\dfrac{0^2+\left(\frac12\right)^2}4+\dfrac{\left(\frac12\right)^2+1^2}4+\dfrac{1^2+\left(\frac32\right)^2}4+\dfrac{\left(\frac32\right)^2+2^2}4$

$=\displaystyle\sum_{i=1}^4\frac{\left(\frac{i-1}2\right)^2+\left(\frac i2\right)^2}4=\frac{11}4$

4 0

2 years ago

Which of the following equations best describes a square root function that is reflected across the x-axis and has a vertex of (

Minchanka [31]

Answer:

Step-by-step explanation:

Rather than picking, let's try to construct one from the description.

reflected over the x axis means - $\sqrt{x}$

the vertex is usually at (0,0), now how do we move a graph? or in other words translating it.

To move left and right you use $\sqrt{x-h}$ where if you subtract h you move right and if you add h you move left. we go from (0,0) to (-4,2). so 0 to -4 is 4 left, so that means we add 4.

To move up and down we use $\sqrt{x}+v$ Here if v is positive you move up and if v is negative you move down. going from (0,0) to (-4,2) it moves up 2