We can create a system of equations with the information we know.
J = 4L
J + L - 6 = 64
The first equation is pretty self-explanatory. Jack is 4 times as old as Lucy. The second equation is just adding their ages together. We subtract 6 because the sum of their ages was 64 three years ago. Three years ago, both Jack and Lucy were 3 years younger (total of 6).
Substitute 4L in for J in the second equation and solve.
4L + L - 6 = 64
5L = 70
L = 14
If Lucy is 14, then Jack is 14*4 = 56.
Let's simplify step-by-step.
<span><span><span><span>x−<span>3<span>(<span><span>2x</span>−1</span>)</span></span></span>−9</span>+<span>8x</span></span>+5
</span>Distribute:
<span>=<span><span><span><span><span><span>x+<span><span>(<span>−3</span>)</span><span>(<span>2x</span>)</span></span></span>+<span><span>(<span>−3</span>)</span><span>(<span>−1</span>)</span></span></span>+</span>−9</span>+<span>8x</span></span>+5
</span></span><span>=<span><span><span><span><span><span><span>x+</span>−<span>6x</span></span>+3</span>+</span>−9</span>+<span>8x</span></span>+5
</span></span>Combine Like Terms:
<span>=<span><span><span><span><span>x+<span>−<span>6x</span></span></span>+3</span>+<span>−9</span></span>+<span>8x</span></span>+5
</span></span><span>=<span><span>(<span><span>x+<span>−<span>6x</span></span></span>+<span>8x</span></span>)</span>+<span>(<span><span>3+<span>−9</span></span>+5</span>)
</span></span></span><span>=<span><span>3x</span>+<span>−<span>1</span></span></span></span>
Answer:
B
Step-by-step explanation:
The sum of the 3 interior angles of a triangle = 180°
Check the sums of the given sets of angles
90° + 42° +58° = 190° ≠ 180° ← not valid
60° + 60° + 60° = 180° ← Valid
100° + 48° + 42° = 190° ← not valid
31° + 75° + 70° = 176° ← not valid
This is true, because there is an infinite amount of real numbers in both, and they are both countably infinite (so these infinities are equal). Hope this helps!