Answer:
- A"(-1, -2)
- B"(6, 0)
- C"(3, 3)
- (x, y) ⇒ (x+1, y+1)
Step-by-step explanation:
Translation vectors add, and the addition is commutative and associative.
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The first translation adds (-1, 2) to the original coordinates. The second translation adds (2, -1) to the original coordinates. The two translations together add ...
(-1, 2) +(2, -1) = (-1+2, 2-1) = (1, 1)
to the original coordinates.
The single rule representing this translation is ...
(x, y) ⇒ (x +1, y +1)
Then the doubly-translated coordinates are ...
A(-2, -3) ⇒ A"(-1, -2)
B(5, -1) ⇒ B"(6, 0)
C(2, 2) ⇒ C"(3, 3)
Answer:
.82 x 4 = $3.28
.82 = 1/4 pound, so you multiply by 4 (the reciprocal of 1/4) to get a whole.
Hope this helps <3
1/3x + 5 = -2 is the way to set up the equation…. You got this!
<h3>
Answer:</h3>
(2x + 1)(x + 3)
<h3>
Step-by-step explanation:</h3>
It is probably easier to try the answer choices than to try to factor the expression yourself.
(2x + 2)(x + 1) = 2x² +4x +2
(2x + 3)(x + 1) = 2x² +5x +3
(2x + 1)(x + 3) = 2x² +7x +3 . . . . . correct choice
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<em>Constructed solution</em>
If you want to factor this yourself, you can look for factors of "ac" that add to give "b". That is, you want factors of 2·3 = 6 that add up to give 7. You don't have to look very far.
... 6 = 1·6 = 2·3 . . . . . . the first factor pair adds to give 7
Now, rewrite the x term using the sum of these numbers.
... 2x² +(1 +6)x +3
... 2x +x +6x +3 . . . . eliminate parentheses
... (2x +x) +(6x +3) . . . . group pairs of terms
... x(2x +1) +3(2x +1) . . . . factor each pair
... (x +3)(2x +1) . . . . . . matches the last selection
