Answer:
Both boats will be 54 miles apart after 3 hours.
Step-by-step explanation:
Given that from a point on a river, two boats are driven in opposite directions, one at 7 miles per hour and the other at 11 miles per hour, to determine how many hours they will be 54 miles apart, the following calculation must be performed :
54 / (11 + 7) = X
54/18 = X
3 = X
Therefore, both boats will be 54 miles apart after 3 hours.
Answer: A
<u>Step-by-step explanation:</u>
f(x) = x³ + 4x² + 7x + 6
possible rational roots are ±{1, 2, 3, 6}
Try x = -2
-2 | 1 4 7 6
<u>| ↓ -2 -4 -6</u>
1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0
The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.
a=1, b=2, c=3
The factors are:
![(x - 2)[x - (-1 + i\sqrt{2})][x - (-1 - i\sqrt{2})]](https://tex.z-dn.net/?f=%28x%20-%202%29%5Bx%20-%20%28-1%20%2B%20i%5Csqrt%7B2%7D%29%5D%5Bx%20-%20%28-1%20-%20i%5Csqrt%7B2%7D%29%5D)
Answer:
1/3
Step-by-step explanation:
Rolling a die has the possible outcomes of 1,2,3,4,5,6 = 6 total
P(3 or 5) = number of 3 or 5's / total
= 2/6
= 1/3
Answer:
D.) It has rotational symmetry with an angle of rotation of 90 degrees.
Step-by-step explanation:
i) the shape shown in the figure has reflectional symmetry with four lines of symmetry. There are four lines of symmetry such that each line when drawn divides the shape into two exact halves such that if each half were too be folded across the line of symmetry it would produce the other half exactly.
Therefore Option A.) and Option B.) are not true
ii) It has point symmetry which means if the shape is rotated by 180 degrees the shape does not change. Therefore Option C.) is not true.
iii) the shape has rotational symmetry because if the shape is rotated though any between 0 degrees and 360 degrees the shape appears to be unchanged.
Therefore the correct options are
D.) It has rotational symmetry with an angle of rotation of 90 degrees.
