2x + y ≤ 10
<span>y ≤ - 2x + 10 → you can see the line in red </span>
<span>As the sign is ≤, you keep only the part below the red line, included the red line </span>
<span>2x - 4y < 8 </span>
<span>- 4y < - 2x + 8 </span>
<span>y > (- 2x + 8)/- 4 </span>
<span>y > - (1/2)x - 2 → you can see the line in blue </span>
<span>As the sign is >, you keep only the part above the blue line
</span><span>A, C, D, K</span>
Q = d - 12
q = 28 - d
d - 12 = 28 - d
d + d = 28 + 12
2d = 40
d = 40/2
d = 20 <== 20 dimes
q = d - 12
q = 20 - 12
q = 8 <== 8 quarters
The last choice, f(x)=1/4(4ˣ⁻⁻¹)-4, is correct.
Substituting our values for x, we have:
f(2) = 1/4(4²⁻¹)-4 = 1/4(4¹) - 4 = 1/4(4) - 4= 1 - 4 = -3
f(3) = 1/4(4³⁻¹)-4 = 1/4(4²) - 4 = 1/4(16) - 4 = 4 - 4 = 0
f(4) = 1/4(4⁴⁻¹)-4 = 1/4(4³) - 4 = 1/4(64) - 4 = 16 - 4 = 12
All of the data points fit.
