Question

1. robert is planning a trip. he uses his map and notices the legend at the bottom of the map has 1 inch = 250 miles. he measures the distance between destinations to be 4.5 centimeters. the two destinations are about how many miles apart?

a) 440 miles
b) 443 miles
c) 141 miles
d) 2857 miles

solve the system of equations.

1. 3x - 2y = -2

-x + 3y = 3
a) (-1, 0)
b) (0, 1)
c) (1, 0)
d) (0, -1)

state the vertex to the following quadratic equation.

1. y = x² - 3x - 4

a) (1.5, 6.25)
b) (-1.5, 6.25)
c) (1.5, -6.25)
d) (-1.5, -6.25)

1. rosie has her favorite numbers in a bag. they are 7, 12, 15, 21, and 52. what is the probability that she will select a number with a factor of 7?

a) \\(\frac{2}{7}\\)
b) \\(\frac{2}{5}\\)
c) \\(\frac{1}{7}\\)
d) \\(\frac{5}{7}\\)

Explanation:

Question 13

Step1: Convert cm to inches

1 inch = 2.54 cm, so 4.5 cm = $\frac{4.5}{2.54} \approx 1.7717$ inches.

Step2: Calculate miles

1 inch = 250 miles, so distance = $1.7717 \times 250 \approx 442.925 \approx 443$ miles.

Step1: Multiply second equation

Multiply $-x + 3y = 3$ by 3: $-3x + 9y = 9$.

Step2: Add to first equation

Add to $3x - 2y = -2$: $(3x - 2y) + (-3x + 9y) = -2 + 9$ → $7y = 7$ → $y = 1$.

Step3: Substitute y=1

Substitute into $-x + 3(1) = 3$ → $-x + 3 = 3$ → $x = 0$.

Step1: Find x-coordinate of vertex

For $y = ax^2 + bx + c$, vertex x = $-\frac{b}{2a}$. Here, a=1, b=-3, so x = $\frac{3}{2} = 1.5$.

Step2: Find y-coordinate

Substitute x=1.5 into $y = (1.5)^2 - 3(1.5) - 4$ = $2.25 - 4.5 - 4 = -6.25$.

Answer:

b) 443 miles

Question 14