1. 3(y + 1) for y = 2 (1 point)
6
9
7
8
2. start fraction lower d plus lower g over lower h end fraction for d = 45, g = 18, and h = 9 (1 point)
6
7
3
4
3. The cost in dollars of a class party is 59 + 13n, where n is the number of people attending. What is the cost for 44 people? (1 point)
$116
$587
$767
$631
4. Write a word phrase for p ÷ 3. (1 point)
a number plus 3
the product of a number and 3
the quotient of a number and 3
a number decreased by 3
5. A major league baseball player chews 17 pieces of gum per game. Write an algebraic expression to show how many pieces of gum he might chew in n games. (1 point)
n + 17
start fraction n over 17 end fraction
17n
17 – n
Use mental math to solve the equation.
6. x – 14 = 13 (1 point)
27
–27
1
–1
7. Jamie owns about 3 times as many books as Carly. Jamie owns 42 books. Write an equation and use it to estimate the number n of books Carly owns. (1 point)
3n = 42; about 14 books
n + 2= 42; about 40 books
n ÷ 3 = 42; about 126 books
n – 2 = 42; about 44 books
8. –13x = –78 (1 point)
6
–6
1,014
–1,014
9. Solve.
start fraction r over 8 end fraction equals negative 6 (1 point)
negative 48
negative eight-sixths
negative start fraction 1 over 48 end fraction
48
10. 12.4x + 7.7 = 82.1 (1 point)
0.7
7
0.6
6
11. Gabriella owned so many CDs that she gave 64 of them away. After donating the CDs, she still had 147 left. Write and solve an equation to find the number of CDs c Gabriella had originally. (1 point)
c + 64 = 147; 83 CDs
c + 147 = 64; 83 CDs
c + 147 = 64; 211 CDs
c – 64 = 147; 211 CDs
Graph the solution of the equation.
12. b – 5 = –8 (1 point)
A number line with numbers ranging from negative 5 to 5 is shown. A closed circle is on negative 3.
A number line with numbers ranging from negative 5 to 5 is shown. A closed circle is on 3.
A number line with numbers ranging from negative 5 to 5 is shown. A closed circle is on negative 4.
A number line with numbers ranging from negative 5 to 5 is shown. A closed circle is on 4.
Use number sense to solve the equation.
13. 5x + 10 = 15 (1 point)
3
1
5
25
14. Suppose you are driving to visit a friend who lives far away. You are driving at an average rate of 55 miles per hour. You must drive a total of 295 miles. If you have already driven 20 miles, how long will it take you to reach your destination? (1 point)
2 hours
5 hours
3 hours
4 hours
15. Find a solution to the inequality x > 7. (1 point)
9
5
1
7
Write the inequality for the graph.
16. A number line is shown from negative 7 to 7 with interval marks representing one unit. A solid dot is drawn at 3, and a ray is drawn pointing to the left of 3. (1 point)
x > 3
x < 3
x ≥ 3
x ≤ 3
17. Write an inequality to model the situation: The number n of people who applied for the job was at least 6. (1 point)
n > 6
n < 6
n ≥ 6
n ≤ 6
Solve the inequality.
18. x + 17 ≤ –5 (1 point)
x ≤ 12
x ≤ –12
x ≤ 22
x ≤ –22
19. 2z > –28 (1 point)
z > –56
z > –14
z < –14
z < 14
20. –0.6n ≤ 9.6 (1 point)
n ≥ –16
n ≥ 16
n ≤ –16
n ≤ 16
21. Your class collected more than 380 cans of food for the annual food drive. In the first week, 145 cans were collected. How many cans c of food were collected in the second week? Write and solve an inequality. (1 point)
145 + c < 380; c < 235
c + 145 > 380; c > 525
c – 145 ≥ 380; c ≥ 525
145 + c > 380; c > 235
Solve the inequality. Graph the solution.
22. x – 1 ≤ 6 (1 point)
A solution is shown graphed on a number line. A number line has numbers ranging between negative 10 and 10. A closed circle is shown on the number line at 7. The number line is shaded to the left of this closed circle.
A solution is shown graphed on a number line. A number line has numbers ranging between negative 10 and 10. A closed circle is shown on the number line at 5. The number line is shaded to the left of this closed circle.
A solution is shown graphed on a number line. A number line has numbers ranging between negative 10 and 10. A closed circle is shown on the number line at 7. The number line is shaded to the right of this closed circle.
A solution is shown graphed on a number line. A number line has numbers ranging between negative 10 and 10. An open circle is shown on the number line at 7. The number line is shaded to the left of this open circle.
Short Answer
Note: Your teacher will grade your response to question 23 to ensure you receive proper credit for your answer.
23. Leslie decides to join a gym. She must pay a monthly fee plus a one-time fee to open a membership. This situation can be modeled by the expression 55x + 80. Explain how each number and letter in the expression relates to the problem. (3 points)
24. Your friend thinks that the equation k – 3.5 = 21 is a true statement. Is your friend correct? Explain. (2 points)
why did no one try to solve this
start fraction lower d plus lower g over lower h end fraction for d = 29, g = 16, and h = 9
A. 8
B. 2.375
C. 5.375
D. 5
what is the answer to number 20
1. To find the value of 3(y + 1) for y = 2, we substitute the value of y into the expression and evaluate it.
3(y + 1) = 3(2 + 1) = 3(3) = 9.
Therefore, the answer is 9.
2. To find the value of start fraction lower d plus lower g over lower h end fraction for d = 45, g = 18, and h = 9, we substitute the values of d, g, and h into the expression and evaluate it.
start fraction lower d plus lower g over lower h end fraction = start fraction 45 plus 18 over 9 end fraction = start fraction 63 over 9 end fraction = 7.
Therefore, the answer is 7.
3. To find the cost for 44 people, we substitute n = 44 into the equation 59 + 13n and evaluate it.
Cost = 59 + 13(44) = 59 + 572 = 631.
Therefore, the cost for 44 people is $631.
4. The word phrase for p ÷ 3 is "the quotient of a number and 3."
5. The algebraic expression to show how many pieces of gum the player might chew in n games is 17n.
6. To solve the equation x - 14 = 13, we isolate the variable x by adding 14 to both sides of the equation.
x - 14 + 14 = 13 + 14
x = 27.
Therefore, the value of x is 27.
7. Jamie owns 42 books, which is about 3 times as many books as Carly. We can write an equation to estimate the number n of books Carly owns by dividing Jamie's number of books by 3.
3n = 42
n = 42 ÷ 3 = 14.
Therefore, Carly owns about 14 books.
8. To solve the equation -13x = -78, we isolate the variable x by dividing both sides of the equation by -13.
-13x ÷ -13 = -78 ÷ -13
x = 6.
Therefore, the value of x is 6.
9. To solve the equation start fraction r over 8 end fraction = -6, we isolate the variable r by multiplying both sides of the equation by 8.
8 * start fraction r over 8 end fraction = 8 * -6
r = -48.
Therefore, the value of r is -48.
10. To solve the equation 12.4x + 7.7 = 82.1, we isolate the variable x by subtracting 7.7 from both sides of the equation, and then dividing by 12.4.
12.4x + 7.7 - 7.7 = 82.1 - 7.7
12.4x = 74.4
x = 74.4 ÷ 12.4
x = 6.
Therefore, the value of x is 6.
11. To find the number of CDs Gabriella had originally, we can write the equation c - 64 = 147, where c represents the number of CDs. Solving this equation, we get:
c - 64 = 147
c = 147 + 64
c = 211.
Therefore, Gabriella originally had 211 CDs.
12. The correct graph for the equation b - 5 = -8 is A number line with numbers ranging from negative 5 to 5 is shown. A closed circle is on 3.
13. To solve the equation 5x + 10 = 15, we isolate the variable x by subtracting 10 from both sides of the equation.
5x + 10 - 10 = 15 - 10
5x = 5
x = 5 ÷ 5
x = 1.
Therefore, the value of x is 1.
14. To find how long it will take to reach the destination, we subtract the number of miles driven from the total distance and divide it by the driving speed.
Time = (Total distance - Distance already driven) / Average speed
Time = (295 - 20) / 55 = 275 / 55 = 5.
Therefore, it will take 5 hours to reach the destination.
15. The solution to the inequality x > 7 is x > 7, meaning that x is any number greater than 7.
16. The correct inequality for the given graph is x > 3, which means x is any number greater than 3.
17. The inequality that models the situation "The number n of people who applied for the job was at least 6" is n ≥ 6, which means n is greater than or equal to 6.
18. To solve the inequality x + 17 ≤ -5, we isolate the variable x by subtracting 17 from both sides of the inequality.
x + 17 - 17 ≤ -5 - 17
x ≤ -22.
Therefore, the solution to the inequality is x ≤ -22.
19. To solve the inequality 2z > -28, we isolate the variable z by dividing both sides of the inequality by 2.
2z ÷ 2 > -28 ÷ 2
z > -14.
Therefore, the solution to the inequality is z > -14.
20. To solve the inequality -0.6n ≤ 9.6, we isolate the variable n by dividing both sides of the inequality by -0.6. Note that when dividing by a negative number, the direction of the inequality sign is reversed.
(-0.6n) ÷ (-0.6) ≥ 9.6 ÷ (-0.6)
n ≥ -16.
Therefore, the solution to the inequality is n ≥ -16.
21. To find the number of cans c collected in the second week, we write the inequality 145 + c < 380, where c represents the number of cans collected in the second week. Solving this inequality, we get:
c < 380 - 145
c < 235.
Therefore, c is less than 235.
22. The correct graph for the inequality x - 1 ≤ 6 is A solution is shown graphed on a number line. A number line has numbers ranging between negative 10 and 10. A closed circle is shown on the number line at 7. The number line is shaded to the right of this closed circle.
23. In the expression 55x + 80, the letter x represents the number of months Leslie wants to be a member of the gym. The number 55 represents the monthly fee she has to pay, and the number 80 represents the one-time fee she has to pay to open a membership. So, for each month that Leslie wants to be a member, she pays 55 dollars, and in addition, she has to pay a one-time fee of 80 dollars to open the membership.
24. Your friend is incorrect in thinking that the equation k - 3.5 = 21 is true. To check, we can solve the equation:
k - 3.5 = 21
k = 21 + 3.5
k = 24.5.
Therefore, the correct statement is k - 3.5 = 21 is false. The value of k is 24.5.
So where are your attempts to solve these?
By the way three times three is nine.