x = 
± 
i
rearrange the equation and equate to zero
2x² - 6x = - 5 ⇒ 2x² - 6x + 5 = 0
this doesn't factor with integers, hence use the quadratic formula to solve
with a = 2, b = - 6 and c = 5
x = (6 ± √(36 - 40 ) )/4
= (6 ± √(-4) ) / 4
= (6 ± 2i ) / 4
x = ± i
Answer:
Step-by-step explanation:
Let us find the acceleration of box .
v² = u² + 2as
Putting the values
7² = 3² + 2 a x 14
a = 1.43 m /s²
If coefficient of friction be μ
force of friction = μ mg
= μ x 10 x 9.8
= 98μ
Net force pushing the box
= 85 - 98μ
Applying newton's second law
85 - 98μ = 10 x 1.43
98μ = 85 - 14.3
μ = .72
Answer:
P' = (4, 4)
Step-by-step explanation:
T(x, y) is a function of x and y. Put the x- and y-values of point P into the translation formula and do the arithmetic.
P' = T(8, -3) = (8 -4, -3 +7) = (4, 4)
_____
<em>Comment on notation</em>
The notation can be a little confusing, as the same form is used to mean different things. Here, P(8, -3) means <em>point P</em> has coordinates x=8, y=-3. The same form is used to define the translation function:
T(x, y) = (x -4, y+7)
In this case, T(x, y) is not point T, but is <em>a function named T</em> (for "translation function") that takes arguments x and y and gives a coordinate pair as a result.
Answer: k = 1, -6
Explanation: Slove the answer using the Quadratic formula.
A regular octagon has 8 sides, so it would coincide exactly each time the vertices fall into the same places. In one full 360-degree rotation, any "selected" vertex would fall into all 7 other vertices one after the other, before going back to its original position. Therefore, there would be 8 times during the rotation that the octagon coincides with the preimage.
