1. Name the point with the given coordinates.
(–4, 2)
A coordinate grid with four labeled points is shown.
Both the x- and y-axes are between negative 5 and 5, and each interval mark on the grid represents one unit. Four points are plotted.
· Point G is two units to the right of the y-axis and four units above the x-axis.
· Point H is four units to the right of the y-axis and two units below the x-axis.
· Point J is two units to the left of the y-axis and four units below the x-axis.
· Point K is four units to the left of the y-axis and two units above the x-axis.
(1 point)
H
K
J
G
J
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 (–12, 8), so you try a likely-looking spot 3 yards to the east and 11 yards to the south of the first spot. What are the coordinates of the second spot? (1 point)
(–9, 19)
(–9, –3)
(–15, 19)
(–15, –3)
(–9, –3)
3. Choose the function table that matches the given rule.
Output = Input – 3 (1 point)
Input
Output
–2
–5
1
–2
6
3
Input
Output
2
–1
–2
3
0
–6
Input
Output
5
2
2
–5
0
9
Input
Output
6
3
–6
–3
5
0
Input | Output
------|-------
–2 | –5
1 | –2
6 | 3
Function table:
Input | Output
------|-------
–2 | –5
1 | –2
6 | 3
4. Make a table and graph the function.
y = 3x + 2
(1 point)
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.
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.
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.
graphThe graph shows x values of 2, negative 1, 3, 1, and 2. The y values are 3, zero, 2, 3, and 8. The line passes through the points left-parenthesis 6 comma negative 1 right-parenthesis left-parenthesis 5 comma zero right-parenthesis left-parenthesis 4 comma 1 right-parenthesis left-parenthesis 3 comma 2 right-parenthesis.
Table:
x | y
--|--
-2| -4
-1| -1
0 | 2
1 | 5
2 | 8
Graph:
```
|
8 | ●
|
7 |
|
6 |
|
5 | ●
|
4 |
|
3 | ●
|
2 |
|
1 | ●
|
0 |
| ●
-1 |
|
-2 | ●
|
-------------
-2 -1 0 1 2
```
5. Solve the equation. 5x + 2 = 62 (1 point)
11.5
12
12.8
36
x = 12
6. Solve the equation.
Start Fraction x over 4 End Fraction + 1 = –6 (1 point)
2
–4
–22
–28
x = -28
7. Riverview Farms sold a combined total of 396 watermelons and cantaloupes. they sold 126 more watermelons than cantaloupes. Use n to represent the number of cantaloupes. Which equation could be used to solve for n? (Hint: First, think about the expression you would use to represent the number of watermelons, and then add the number of cantaloupes.) (1 point)
n + 126 = 396
n – 126 = 396
2n – 126 = 396
2n + 126 = 396
n + (n + 126) = 396 (since they sold 126 more watermelons than cantaloupes)
Simplifying:
2n + 126 = 396
So the equation that could be used to solve for n is:
2n + 126 = 396
8. Suppose you are driving to visit a friend in another state. You are driving 55 miles per hour. You must drive 440 miles total. If you have already driven 275 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 55h + 275 = 440. (1 point)
30 hours
2 hours
3 hours
1 hours
h = 3
9. Write an inequality for the situation.
Suzy scored at least 18 points. (1 point)
K ≤ 18
K < 18
K ≥ 18
K > 18
K ≥ 18 (since Suzy scored at least 18, this means the score is greater than or equal to 18)
10. Write an inequality for the following situation:
No more than 6 books are in your bag. (1 point)
x ≤ 6
x < 6
x ≥ 6
x > 6
x ≤ 6 (since the number of books cannot exceed 6, we use the less than or equal to symbol)
11. Which inequality does the graph represent?
A number line shows integers from negative 5 to 5. A solid dot is located at negative 2 and the line is darkened and bold from that point to the right. (1 point)
x ≤ –2
x ≥ –2
x < –1
x ≤ –1
x ≥ –2
12. Which inequality does the graph represent?
A number line is shown from negative 5 to 5, and each interval mark represents one unit. An open circle is drawn on negative 1 with a black ray drawn to the left of negative 1. (1 point)
x less than or equal to –1
x > –1
x greater than or equal to –1
x < –1
x < –1
13. Solve the inequality.
y + 5 greater than or equal to 7 (1 point)
yless than or equal to 2
yless than or equal to 12
ygreater than or equal to 2
ygreater than or equal to 12
y ≥ 2
14. Write an inequality for the sentence. Then solve the inequality.
Fifteen less than a number is at most 6. (1 point)
x + 15 ≤ 6; x ≤ –9
x – 15 ≤ 6; x ≤ 21
x – 15 ≥ 6; x ≥ 21
x – 15 ≥ 6; x ≥ 16
x - 15 ≤ 6 (since fifteen less than a number means we subtract 15 from the number, and "at most" means less than or equal to)
Simplifying:
x ≤ 21
So the inequality is x - 15 ≤ 6, and the solution is x ≤ 21.
The correct option is: x – 15 ≤ 6; x ≤ 21
15. The maximum weight allowed per car on The Twister carnival ride is 263 pounds. Your friend weighs 86 pounds. To be able to ride in a car together, how much can you weigh? Write and solve the inequality. (1 point)
x + 177 ≤ 263; at most 86 pounds
x – 86 ≤ 263; at most 177 pounds
x + 86 ≤ 263; at most 177 pounds
x + 86 ≤ 177; at most 263 pounds
x + 86 ≤ 263 (since the total weight allowed is the weight of the car plus the weight of the riders, and we want to find how much can you weigh to ride together, we add your friend's weight to the maximum weight allowed)
Simplifying:
x ≤ 177
So the inequality is x + 86 ≤ 263, and the solution is x ≤ 177.
The correct option is: x + 86 ≤ 263; at most 177 pounds.
16. Complete the function table. Then write a rule for the function.
A two column table is shown. The first column is titled 'Input' and contains negative 3, negative 2, negative 1, 0, and 1 from top to bottom. The second column is titled 'Output' and contains an empty box, negative 4, an empty box, an empty box, and negative 1 from top to bottom.
Input | Output
------|-------
-3 |
-2 | -4
-1 |
0 |
1 | -1
The rule for the function is: Output = Input - 1, except when Input = -2, then Output = -4.
well what is the output for the missing ones
Based on the rule Output = Input - 1, we can find the missing values in the function table:
Input | Output
------|-------
-3 | -4
-2 | -4
-1 | -2
0 | -1
1 | -2
Write an inequality to represent the situation: The temperature stayed above –15°.
The inequality that represents the situation is:
temperature > -15
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the inequality and describe the solution set.
y
–
6
≥
12
The inequality is:
y - 6 ≥ 12
Adding 6 to both sides, we get:
y ≥ 18
So the solution set is all real numbers greater than or equal to 18. We can write this in interval notation as:
[18, ∞)
but ist this subraction
Apologies for the confusion. It could be a formatting error. If the inequality is actually y over 6 ≥ 12, then we would solve it as follows:
y/6 ≥ 12
Multiplying both sides by 6 (since dividing by 6 is the same as multiplying by 1/6), we get:
y ≥ 72
So the solution set is all real numbers greater than or equal to 72. We can write this in interval notation as:
[72, ∞)
i dont understand how would that work is it not y - 6 shout it not be 12 - 6
You are absolutely right, I apologize for my mistake. If the inequality is y - 6 ≥ 12, we would solve it as follows:
y - 6 ≥ 12
Adding 6 to both sides, we get:
y ≥ 18
So the solution set is all real numbers greater than or equal to 18. We can write this in interval notation as:
[18, ∞)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the equation.
c
4
−
5
=
4
The equation is:
c/4 - 5 = 4
Adding 5 to both sides, we get:
c/4 = 9
Multiplying both sides by 4, we get:
c = 36
So the solution to the equation is c = 36.
are you sure
Yes, I am sure.
The steps to solve the equation are:
c/4 - 5 = 4
Adding 5 to both sides, we get:
c/4 = 9
Multiplying both sides by 4, we get:
c = 36
I hope this clears up any confusion.
why do need to add 5 to both sides
We need to add 5 to both sides to isolate the variable term, which in this case is `c/4`.
When we add 5 to both sides of the equation, we get:
c/4 - 5 + 5 = 4 + 5
The -5 and +5 on the left side cancel out, leaving us with:
c/4 = 9
Then, to solve for `c`, we multiply both sides by 4 to get:
c = 36
how doesnt it mean that c/4 is meant to be the same as 9
Yes, exactly.
In the step where we have `c/4 - 5 = 4`, we added 5 to both sides to isolate the term involving `c/4`.
Adding 5 to both sides gives us:
`c/4 - 5 + 5 = 4 + 5`
The -5 and +5 on the left side cancel out, leaving us with `c/4` on the left side.
So we get:
`c/4 = 9`
This is because we want to find the value of `c` that satisfies the given equation. Since we have `c/4` in the equation, we need to isolate this term to find the value of `c`.
To do this, we multiply both sides by 4 to find `c`:
`c = 36`
Therefore, `c/4 - 5 = 4` is equivalent to `c = 36`.