Question

6 select all the values that are equivalent to -\frac{12}{7}.
\\(\square a. -\frac{-12}{-7}\\) \\(\square b. - 5\frac{1}{7}\\) \\(\square c. -1\frac{5}{7}\\)
\\(\square d. 1\frac{5}{7}\\) \\(\square e. \frac{-12}{-7}\\)
7 find the pattern. describe what you see.
predict how many blocks would be on image 43. (hint: make a table if that is useful to you!)
darcy pays $37.95 for a 25.3 - kilometer taxi ride.
how much does darcy pay, in dollars, per kilometer?
what is the value, in degrees, of x?

Explanation:

Question [6]

Step1: Simplify option A

$-\frac{- 12}{-7}=-\frac{12}{7}$

Step2: Convert option B to improper - fraction

$-5\frac{1}{7}=-\frac{5\times7 + 1}{7}=-\frac{36}{7}$

Step3: Convert option C to improper - fraction

$-1\frac{5}{7}=-\frac{1\times7+5}{7}=-\frac{12}{7}$

Step4: Convert option D to improper - fraction

$1\frac{5}{7}=\frac{1\times7 + 5}{7}=\frac{12}{7}$

Step5: Simplify option E

$\frac{-12}{-7}=\frac{12}{7}$

1. Use the unit - rate formula:

• The unit rate (cost per kilometer) is calculated by dividing the total cost by the total distance.
• Let \(C\) be the total cost and \(d\) be the total distance. The cost per kilometer \(r=\frac{C}{d}\).
• Given \(C = 37.95\) dollars and \(d = 25.3\) kilometers.
• \(r=\frac{37.95}{25.3}\)
• \(37.95\div25.3 = 1.5\) dollars per kilometer.

Answer:

A. $-\frac{-12}{-7}$, C. $-1\frac{5}{7}$

Question [7]

1. Find the pattern:

• Let's assume the number of the image is \(n\).
• For the first image (\(n = 1\)), the number of blocks \(a_1=3\).
• For the second image (\(n = 2\)), the number of blocks \(a_2 = 5\).
• For the third image (\(n = 3\)), the number of blocks \(a_3=7\).
• We can observe that this is an arithmetic - sequence with the first term \(a_1 = 3\) and the common difference \(d = 2\).
• The formula for the \(n\)th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\).

1. Predict the number of blocks for \(n = 43\):

• Substitute \(a_1 = 3\), \(d = 2\), and \(n = 43\) into the formula \(a_n=a_1+(n - 1)d\).
• \(a_{43}=3+(43 - 1)\times2\)
• First, calculate the value inside the parentheses: \(43−1 = 42\).
• Then, multiply: \(42\times2=84\).
• Finally, add: \(a_{43}=3 + 84=87\).