Answer:
(x, y) ⟶ (x + 4, y + 2)
Step-by-step explanation:
If you shift a point four units to the right, x ⟶ x + 4.
If you shift it up two units, y ⟶ y + 2.
If you combine the two shifts into one transformation, the rule becomes
(x, y) ⟶ (x + 4, y + 2)
Answer:91 years
Step-by-step explanation:
3(9 - 8x - 4x) + 8(3x + 4) = 11
3(9 - 12x) + 8(3x + 4) = 11
27 - 36x + 24x + 32 = 11
59 - 12x = 11
-12x = 11 - 59
-12x = -48
x = 4
hope this helps, God bless!
Answer:
t > -7
Step-by-step explanation:
To solve for t, first add 5 to both sides:
-2t - 5 < 9
-2t < 14
Divide each side by -2, and flip the inequality because we are dividing by a negative number:
-2t < 14
t > -7
So, the solution is t > -7
F1 = 6*cos(30) i + 6*sin(30) j = 5.20 i + 3 j
<span>F2 = 0 i + 5 j </span>
<span>R = F1 + F2 </span>
<span>Add the 'i's together (x direction) and the 'j's together (y direction) </span>
<span>R = (5.20 + 0) i + (3 + 5) j = 5.2 i + 8 j </span>
<span>Magnitude: </span>
<span>||R|| = </span>√<span>(5.2^2 + 8 ^2) = </span>√<span>91 = 9.54 </span>
<span>Direction: </span>
Θ<span> = atan ( Rj / Ri ) = atan( 8 / 5.2 ) = 57.0</span>⁰
