2. You start a search for a buried object by marking the center of a field as (0, 0), with coordinates giving distances in yards. Coordinates to the north or east are positive, and coordinates to the south or west are negative. You find nothing at (-10, 6), so you try a likely looking spot 3 yards to the east and 12 yards to the south of the first spot. What are the coordinates of the second spot? (1 point)
The coordinates of the second spot are ( -7, -6).
You start at (0, 0) and move 3 yards to the east, so the x-coordinate becomes -3. Then you move 12 yards to the south, so the y-coordinate becomes -12.
Therefore, the coordinates of the second spot are (-3, -12) relative to the starting point of (0, 0). To get the absolute coordinates, we add -3 to the x-coordinate of the first point (-10) and -12 to the y-coordinate of the first point (6):
-10 + (-3) = -13 (the new x-coordinate)
6 + (-12) = -6 (the new y-coordinate)
So the absolute coordinates of the second spot are (-13, -6).
You start a search for a buried object by marking the center of a field as (0, 0), with coordinates giving distances in yards. Coordinates to the north or east are positive, and coordinates to the south or west are negative. You find nothing at (–10, 6), so you try a likely looking spot 3 yards to the east and 12 yards to the south of the first spot. What are the coordinates of the second spot?
A. (–7, –6)
B. (12, –6)
C. (–13, –9)
D. (5, –3)
The correct answer is A. (-7, -6).
To get to the second spot, you move 3 yards to the east and 12 yards to the south from (-10, 6).
Moving 3 yards to the east changes the x-coordinate from -10 to -10 + 3 = -7.
Moving 12 yards to the south changes the y-coordinate from 6 to 6 - 12 = -6.
Therefore, the coordinates of the second spot are (-7, -6).
Choose the function table that matches the given rule.
Output = Input – 3
There are multiple correct answers to this question, but here's one example of a function table that matches the rule "Output = Input - 3":
| Input | Output |
|-------|--------|
| 0 | -3 |
| 1 | -2 |
| 2 | -1 |
| 3 | 0 |
| 4 | 1 |
In this table, each output (i.e. the result of "Input - 3") is equal to the input minus 3. For example, when the input is 2, the output is 2 - 3 = -1. This matches the given rule.
Question 4 of 17
Make a table and graph the function.
y = 3x + 2
A. graphThe graph shows x values of negative 2, negative 1, zero, 1, and 2. The y values are negative 4, negative 1, 2, 5, and 8. The line passes through the points left-parenthesis negative 2 comma negative 4 right-parenthesis left-parenthesis negative 1 comma negative 1 right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 1 comma 5 right-parenthesis.
B. graphThe graph shows x values of negative 2, negative 1, zero, 1, and 2. The y values are 6, 1, 2, 3, and 8. The line passes through the points left-parenthesis negative 2 comma negative 2 right-parenthesis left-parenthesis negative 1 comma zero right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 1 comma 4 right-parenthesis.
C. graphThe graph shows x values of zero, negative 1, 3, 1, and 2. The y values are 6, zero, 2, 3, and 8. The line passes through the points left-parenthesis negative 6 comma negative 1 right-parenthesis left-parenthesis negative 5 comma zero right-parenthesis left-parenthesis negative 4 comma 1 right-parenthesis left-parenthesis negative 3 comma 2 right-parenthesis.
A. The graph shows x values of negative 2, negative 1, zero, 1, and 2. The y values are negative 4, negative 1, 2, 5, and 8. The line passes through the points (-2, -4), (-1, -1), (0, 2), (1, 5), and (2, 8).
Solve the equation. 5x + 2 = 62
To solve the equation 5x + 2 = 62, we want to isolate the variable x on one side of the equation by itself.
First, we'll subtract 2 from both sides of the equation:
5x + 2 - 2 = 62 - 2
Simplifying the left side:
5x = 60
Next, we'll divide both sides of the equation by 5:
5x/5 = 60/5
Simplifying:
x = 12
So the solution to the equation 5x + 2 = 62 is x = 12.
Start Fraction x over 4 End Fraction + 2 = –2
Starting with the equation:
(x/4) + 2 = -2
We want to isolate the variable x on one side of the equation. First, we'll subtract 2 from both sides:
(x/4) + 2 - 2 = -2 - 2
Simplifying the left side by canceling out the 2's:
(x/4) = -4
Next, we'll multiply both sides of the equation by 4 to get rid of the fraction:
4 * (x/4) = 4 * (-4)
Simplifying the left side by canceling out the 4's:
x = -16
So the solution to the equation (x/4) + 2 = -2 is x = -16.
Smallside Farms sells Delicious and Empire apples. One August they sold 162 more Empire than Delicious apples. The total number of apples sold was 424. Which equation could be used to solve for n, the number of Delicious apples sold?
Let's use the variable "D" to represent the number of Delicious apples sold.
If Smallside Farms sold 162 more Empire apples than Delicious apples, then the number of Empire apples sold can be represented as "D + 162".
The total number of apples sold was 424, so we can set up the equation:
D + (D + 162) = 424
Simplifying the left side by combining like terms:
2D + 162 = 424
Now we want to solve for "D", so we'll subtract 162 from both sides:
2D + 162 - 162 = 424 - 162
Simplifying the right side:
2D = 262
Finally, we divide both sides by 2:
D = 131
Therefore, the equation that could be used to solve for the number of Delicious apples sold would be:
D + (D + 162) = 424
Or, after simplifying:
2D + 162 = 424
Suppose you are driving to visit a friend in another state. You are driving 65 miles per hour. You must drive 520 miles total. If you have already driven 195 miles, how long will it take you to reach your destination? Use h to represent the number of hours it will take to reach your destination. Use the equation 65h + 195 = 520.
The equation that represents the situation is:
65h + 195 = 520
We want to solve for the variable "h", which represents the number of hours it will take to reach the destination.
First, we'll isolate the term with "h" by subtracting 195 from both sides:
65h = 520 - 195
Simplifying the right side:
65h = 325
Now, we want to solve for "h", so we'll divide both sides of the equation by 65:
65h/65 = 325/65
Simplifying:
h = 5
Therefore, it will take 5 hours to reach the destination.
Write an inequality for the situation.
Sam scored at least 26 points.
One possible inequality for this situation is:
s ≥ 26
In this inequality, "s" represents Sam's score, and the symbol "≥" means "greater than or equal to".
Alternatively, we could write the inequality as:
26 ≤ s
Both of these inequalities express the same idea: Sam's score is at least 26 points.
Write an inequality for the following situation:
No more than 6 books are in your bag
One possible inequality for this situation is:
b ≤ 6
In this inequality, "b" represents the number of books in your bag, and the symbol "≤" means "less than or equal to".
Alternatively, we could write the inequality as:
b < 7
Both of these inequalities express the same idea: the number of books in your bag is no more than 6.
Which inequality does the graph represent?
A number line shows integers from negative 5 to 5. A solid dot is located at negative 1 and the line is darkened and bold from that point to the right.
A. x ≤ –2
B. x < –1
C. x ≤ –1
D. x ≥ –1
The answer is C. x ≤ -1.
The solid dot at -1 on the number line indicates that -1 is included in the shaded region, so it is not less than -1 (as in option B). The boldened line to the right of -1 indicates that all values less than or equal to -1 are included in the shaded region, which is represented by the inequality x ≤ -1. Therefore, the answer is C.
Which inequality does the graph represent?
A number line shows integers from negative 5 to 5. A small open circle is located at 2 and the number line is darkened and bold from that point to the left.
A. x > 2
B. x ≤ 2
C. x ≥ 2
D. x < 2