Question

1. what ordered pair represents a reflection of the point ( 3, 5) across the y - axis?
2. during a weekend, the manager of a mall gave away gift cards to every 80th person who visited the mall.

• on saturday, 1,210 people visited the mall.
• on sunday, 1,814 people visited the mall.

how many people received a gift card?
what is the distance between the points ( 1, 3) and (4, 3) in the coordinate plane?

1. a school has 109 students signed up for a science workshop. the school will buy every student attending the workshop a pencil, a folder, and an eraser.

• a package of 12 erasers is $0.75. only whole packages of erasers can be bought
• folders are $0.10 each
• a package of 8 pencils is $0.50. only whole packages of pencils can be bought

how much will the school spend?

1. kevin, carl, and tom played a game.

• kevin had 4 more points than carl.
• tom had 2 fewer points than carl

how many more points did kevin have than tom?

Explanation:

Question 1

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Apply the rule to the point \((3,5)\)

For the point \((3,5)\), when we reflect it across the \(y\) - axis, we change the sign of the \(x\) - coordinate. So \(x = 3\) becomes \(x=-3\) and the \(y\) - coordinate remains \(y = 5\).

Step1: Calculate number of gift cards on Saturday

To find the number of gift cards given on Saturday, we divide the number of people who visited the mall on Saturday (\(1210\)) by \(80\). So we calculate \(\lfloor\frac{1210}{80}
floor\) (the floor function gives the greatest integer less than or equal to the quotient). \(\frac{1210}{80}=15.125\), so the number of gift cards on Saturday is \(15\).

Step2: Calculate number of gift cards on Sunday

We divide the number of people who visited the mall on Sunday (\(1814\)) by \(80\). \(\frac{1814}{80}=22.675\), so the number of gift cards on Sunday is \(22\).

Step3: Calculate total number of gift cards

We add the number of gift cards given on Saturday and Sunday. So \(15 + 22=37\).

Step1: Recall the distance formula for horizontal points

For two points \((x_1,y)\) and \((x_2,y)\) (since they have the same \(y\) - coordinate, the line segment between them is horizontal), the distance \(d\) is given by \(d=\vert x_2 - x_1\vert\).

Step2: Apply the formula to the points \((1,3)\) and \((4,3)\)

Here, \(x_1 = 1\), \(x_2 = 4\) and \(y = 3\). So \(d=\vert4 - 1\vert=\vert3\vert = 3\).

Answer:

\((-3,5)\)

Question 2