Answer: x = 3 - sqrt 17 / 2 , x = 3 + sqrt 17 / 2
Step-by-step explanation:
2x^2 = 4 + 6x
divide both sides by 2
x^2 = 2 + 3x
move expression to the left
x^2 - 2 - 3x = 0
reorder the terms
x^2 - 3x - 2 = 0
use the quadratic formula
x = - (-3) +- sqrt (-3)^2 - 4 x (-2) / 2 x 1
calculate
x = 3 +- sqrt 17 / 2
answer
x = 3 - sqrt 17 / 2 , x = 3 + sqrt 17 / 2
Answer:
<em>The old photo frame is still rectangular</em>
Step-by-step explanation:
<u>Rectangles</u>
The rectangle shape can be identified because it has 4 internal angles of 90° each. The diagonal forms with two adjacent sides a right triangle where the Pythagora's Theorem must stand. Being a and b the length of the sides of the rectangle and d the diagonal, then:

Vince's photo frame has dimensions of 8 inches and 6 inches, with a diagonal of 10 inches. If the above condition is met, then the frame is still rectangular.
Calculating:



Since the condition is met, the old photo frame is still rectangular
10 of the numbers are even. 4 more are odd multiples of 3. The probability of landing on even or a multiple of 3 is (10+4)/21 = 2/3.
Answer:
Step-by-step explanation:
Standard equation of an ellipse,

(h, k) is the center of the ellipse
Value of a = Distance of the center from the vertex
b = Distance of the center from the covertex
From the picture attached,
a = Distance of the center (h, k) from the vertex (2, -2) = 3 units
b = Distance of the center (h, k) from the co-vertex (-1, 0) = 1 unit
Center of the ellipse (h, k) = (-1, -2)