Question

1. the real estate tax rate in 2018 in a small rural county increased by $\frac{1}{4}%$. in 2017, a family paid $1,200. which expression represents the real estate tax, in dollars, that the family will pay in 2018?

a. $1,200 + 1,200cdotleft(\frac{1}{4}
ight)$
b. $1,200cdot(1.25)$
c. $1,200cdot(1.025)$
d. $1,200cdot(1.0025)$

1. two inequalities are graphed on the same coordinate plane.

image of a coordinate plane with two lines and a shaded region
select all the points that are solutions to the system of the two inequalities.
a. $(4, -6)$
b. $(4, 6)$
c. $(-4, -6)$
d. $(-4, 6)$
e. $(6, -8)$
f. $(7, -9)$
g. $(-8, 6)$

Explanation:

Question 8

Step1: Convert % to decimal

$\frac{1}{4}\% = 0.25\% = \frac{0.25}{100} = 0.0025$

Step2: Find total tax multiplier

$1 + 0.0025 = 1.0025$

Step3: Calculate 2018 tax amount

$\text{2018 Tax} = 1200 \times 1.0025$

1. First, identify the inequalities from the graph:

• Solid line: Passes through $(-8,0)$ and $(0,-4)$, equation $y = -\frac{1}{2}x - 4$. The shaded region is below this line, so $y \leq -\frac{1}{2}x - 4$.
• Dashed line: Passes through $(0,8)$ and $(4,0)$, equation $y = -2x + 8$. The shaded region is below this line, so $y < -2x + 8$.

1. Test each point against both inequalities:

• A. $(4,-6)$: $-6 \leq -\frac{1}{2}(4)-4=-6$ (true); $-6 < -2(4)+8=0$ (true)
• B. $(4,6)$: $6 \leq -6$ (false)
• C. $(-4,-6)$: $-6 \leq -\frac{1}{2}(-4)-4=-2$ (true); $-6 < -2(-4)+8=16$ (true)
• D. $(-4,6)$: $6 \leq -2$ (false)
• E. $(6,-8)$: $-8 \leq -\frac{1}{2}(6)-4=-7$ (true); $-8 < -2(6)+8=-4$ (true)
• F. $(7,-9)$: $-9 \leq -\frac{1}{2}(7)-4=-7.5$ (true); $-9 < -2(7)+8=-6$ (true)
• G. $(-8,6)$: $6 \leq -\frac{1}{2}(-8)-4=0$ (false)

Answer:

D. $1,200 \cdot (1.0025)$

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Question 9