Answer:
x = 6 and x = 11.
Step-by-step explanation:
sqrt(x - 2) + 8 = x
sqrt(x - 2) = x - 8
(sqrt(x - 2))^2 = (x - 8)^2
x - 2 = x^2 - 16x + 64
x^2 - 16x + 64 = x - 2
x^2 - 17x + 66 = 0
We can use the discriminant to find whether there are solutions to the equation.
b^2 - 4ac; where a = 1, b = -17, and c = 66.
(-17)^2 - 4 * 1 * 66
= 289 - 264
= 25
Since the discriminant is positive, we know there are two valid solutions to the equation.
x^2 - 17x + 66 = 0
(x - 6)(x - 11) = 0
The solutions are when x - 6 = 0 and x - 11 = 0.
x - 6 = 0
x = 6
x - 11 = 0
x = 11
Hope this helps!
Answer: 15
√
2
Step-by-step explanation:
Equilateral triangles have three equal side lengths, three equal angles of 60 degrees, and three equal altitudes.
You would think that the height of an equilateral triangle would also be equal to it's sides, but it's not. The formula for height is: side/2 x √3
10√6 / 2 * √
3 = 15
√
2
The decimal form: 21.2
Answer:

Step-by-step explanation:
1) the equation of the given line in the slope-interception form is:
y= 3/5 x -2;
the equation of the required line is
y=slope*x+i;
2) if the required line is parallel to the given one, it means, the value of its slope is the same, it means 3/5;
then the equation of the required line is
y=3/5*x+i;
3) if the point (-4;-1) belongs to the required line, then it is possible to substitute its coordinates into the equiation of the required line
-1= 3/5*(-4)+i;
4) it is possible to calculate the value of 'i':
i=7/5;
5) if slope=3/5, i=7/5, then the required equation of the line in slope-interception form is:

Answer:
Step-by-step explanation:
<u>Given</u>
To find f(q+1),
<u>substitute x with q+1 in the given equation:</u>
- f(q + 1) = 6(q + 1) + 7 = 6q + 6 + 7 = 6q + 13
Distributive property: 3x3 and 3xn
So... 9x3n which becomes
27n