1. The graph represents a mechanic’s labor costs for a given number of hours of car repair.
A graph titled Car Repairs. The horizontal axis shows Labor Time (hours) numbered 0.25 to 2.5, and the vertical axis shows Labor Costs (dollars), numbered 25 to 250. The line remains constant at $50 dollars over 1 hour, then increases sharply. The line remains at 50 dollars from 0 to 1 hour, then move upward to end at 175 dollars at 2.5 hours.
Which statement describes the relationship between labor cost and time for a car repair?
All repairs requiring 1 hour or less have the same labor cost.
Labor costs the same no matter how many hours are used for a repair.
Labor costs for a repair are less expensive as the number of hours increases.
There is no cost of labor for a repair requiring less than 1 hour.
2. What is the value of x in the equation 7x+2y=48 , when y = 3?
x = 6
x = 7
x = 8
x = 9
3. The solution to an inequality is represented by the number line.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
How can this same solution be written using set-builder notation?
{x | x >__}
The graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.
A graph titled Lunch Cost. The x-axis shows the number of slices purchased, numbered 1 to 8, and the y-axis shows the cost in dollars, numbered 5 to 40. Blue diamonds appear at points (0, 7.5), (1, 10), (2, 12.5), (3, 15), (4, 17.5), (5, 20), (6, 22.5), (7, 25), (8, 27.5).
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
$1.50
$2.00
$2.50
$3.00
5. Mr. Valenzuela’s new bottle of shampoo contains 60 ounces of shampoo. He uses One-fourth ounce of shampoo each time he washes his hair. Which equation can be used to find x, the number of washes after which 24 ounces will remain in the bottle?
One-fourth x minus 60 equals 24
60 minus one-fourth x equals 24
One-fourth x minus 24 equals 60
24 minus one-fourth x equals 60
6. A hot air balloon can hold up to 300 pounds of weight. The balloon's pilot weighs 140 pounds. How many 20-pound bags of sand (b) can also be carried by the hot air balloon? Select three options.
–2
0
5
8
10
7. Rami is solving the equation for x .
–6x – 1 = 5
–6x – 1 Empty square 1 = (5 Empty square 1)
–6x = 6
–6x Empty circle – 6 = 6 Empty circle –6
x = –1
Which operation symbols should Rami write in the Empty squareand the Empty circle?
Empty circle should contain +; Empty square should contain ×
should contain +; should contain ÷
Empty circle should contain –; Empty square should contain ×
Empty circle should contain –; Empty square should contain ÷
8. Solve.
one-thirds – 6 < 24
{s | s < 6}
{s | s < 10}
{s | s < 54}
{s | s < 90}
9. Which values are solutions to StartFraction k minus 3 Over 4 EndFraction >–2? Select two options.
k = –10
k = –7
k = –5
k = –1
k = 0
10. A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the number of calories, numbered 3 to 27. A straight line with a positive slope begins at point (0, 0) and ends at point (6.8, 27).
The graph shows the relationship between the number of strawberries eaten and the approximate number of calories consumed. Which statement is true?
Each strawberry contains 4 calories.
Each strawberry contains 3 calories.
Twenty-four strawberries contain 6 calories.
Four strawberries contain 15 calories.
7 answers
Let's go through each question in order:
The graph represents labor costs: Answer: All repairs requiring 1 hour or less have the same labor cost.
Explanation: The graph indicates that the labor cost remains constant at $50 for any repair that takes 1 hour or less.
Solving the equation 7x + 2y = 48 for y = 3:
Substitute y = 3:
7x + 2(3) = 48
7x + 6 = 48
7x = 42
x = 6. Answer: x = 6.
Set-builder notation of the inequality shown:
The number line indicates that x is greater than 3. Answer: {x | x > 3}.
Cost increase per slice of pizza:
The total cost for 1 slice appears to be $10 and for 2 slices is $12.50. The increase from 1 to 2 slices:
$12.50 - $10 = $2.50. Answer: $2.50.
Finding the equation for shampoo washes:
You want to find out how many washes will leave 24 ounces remaining:
60 - (1/4)x = 24.
Rearranged, this gives us the most suitable equation: Answer: 60 - one-fourth x equals 24.
Calculating how many bags of sand can be carried:
The total weight capacity of the balloon is 300 pounds. The pilot weighs 140 pounds, leaving:
300 - 140 = 160 pounds available for bags of sand. Each bag is 20 pounds:
160 / 20 = 8 bags. Answer: 8.
Finding operations for Rami's equation:
Rami has the equation -6x - 1 = 5. To isolate x, he would first add 1 to both sides and then divide by -6:
This gives:
-6x = 6 (adding 1)
x = -1 (dividing by -6).
Thus, the operations are: Answer: Empty circle should contain +; Empty square should contain ÷.
Solving the inequality one-third s - 6 < 24:
Add 6 to both sides:
one-third s < 30
Multiply by 3:
s < 90. Answer: {s | s < 90}.
Finding solutions for the inequality (k - 3)/4 > -2:
Multiply both sides by 4:
k - 3 > -8.
Add 3:
k > -5.
Solutions must be greater than -5. So, the two options from given choices that work are: Answer: k = -1 and k = 0.
Analyzing the strawberry calorie graph:
The line suggests that the graph starts at (0,0) and has a positive slope. If the point (6.8, 27) is taken, calculations show that:
Calories per strawberry = 27 calories / 6.8 strawberries = approximately 4. Therefore, no option fits this exactly in the multiple-choice options provided. However, simplified: Answer: Each strawberry contains 4 calories (based on slope from the graph). Actual calorie content aligns more closely but isn't an option given.
Based on the answers we discussed, they are as follows:
All repairs requiring 1 hour or less have the same labor cost.
x = 6.
{x | x > 3}.
$2.50.
60 - one-fourth x equals 24.
Empty circle should contain +; Empty square should contain ÷.
{s | s < 90}.
k = -1 and k = 0.
Each strawberry contains 4 calories.
Eli left his house one afternoon to study at the library. The graph shows his distance, in miles, away from his house as a function of time, in minutes.
A graph titled Eli's Trip to the Library. The horizontal axis shows Time (minutes), numbered 0 to 135, and the vertical axis shows Distance from Home (miles) numbered 0 to 5. The line begins at 0, goes up to 4 miles from 30 to 120 minutes, then goes down to 0 miles in 133 minutes.
What could explain what happened when the time was equal to 120 minutes?
Eli arrived at the library.
Eli rode his bicycle home from the library.
Eli rode his bicycle to the store, getting farther away from his house.
Eli continued to study at the library for 13 more minutes.
12. Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of granola that costs $2.00 per pound. The walnuts cost $6 per pound. He uses the equation to represent the total cost, where x represents the number of pounds of granola and y represents the number of pounds of walnuts. He solves the equation for y, the number of pounds of walnuts he can buy.
2x+6y=12
2(3)+6y=12
6+6y+6=12+6
y=3
Which is the first error that Tomas made?
Tomas substituted the 3 for x when he should have substituted 6 for x.
Tomas added 6 to both sides of the equation instead of subtracting 6.
Tomas should have written the equation as 3x+6y=12 .
Tomas substituted 3 for x when he should have substituted 3 for y.
13. Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lb. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?
14. The graph shows the relationship between the total amount of money that Carly will have left, y, if she buys x packs of baseball cards.
A graph titled Money Left after Purchase. The x-axis shows packs of cards bought, numbered 1 to 9, and the y-axis shows the money left (in dollars), numbered 2 to 18. Blue diamonds appear at points (1, 16), (2, 12), (3, 8), (4, 4), (5, 0).
How much money will she have if she doesn't buy any packs of baseball cards?
$16
$18
$19
$20
15. The equation |p| = 2 represents the total number of points that can be earned or lost during one turn of a game. Which best describes how many points can be earned or lost during one turn?
–2
2
0 or 2
–2 or 2
Let's address each question in order:
Eli's Trip to the Library:
At the 120 minute mark, Eli was at 4 miles from home. The graph shows that after this point, he begins to decrease back to 0 miles, meaning he is returning home. The most logical conclusion for what happened at 120 minutes is:
Answer: Eli rode his bicycle home from the library.
Tomas making trail mix:
Tomas starts with the equation \(2x + 6y = 12\). He substitutes \(3\) for \(x\) correctly as he is buying \(3\) pounds of granola. However, the mistake occurs during his manipulation of the equation. When he writes \(6 + 6y + 6 = 12 + 6\), it incorrectly involves adding \(6\) to both sides which is not correct. The correct operation after substituting would involve correctly isolating \(y\):
Answer: Tomas added 6 to both sides of the equation instead of subtracting 6.
Bob's weights:
Bob's total weight equation can be represented with \(x\) as the number of 3 lb weights and \(y\) as the number of 10 lb weights. The total weight would be \(3x + 10y = 50\). Thus:
Answer: 3x + 10y = 50.
Money left after purchasing baseball cards:
The points on the graph show how much money Carly has left as she buys packs of cards. The point (1, 16) indicates after buying 1 pack she has $16 left. The point (0, ?) indicates how much she has before buying any packs. Since the data shows a consistent decrease of $4 for each pack, the point when \(x = 0\) would logically be $16 technically. The answer is:
Answer: $16.
Points earned or lost in a game:
The equation \(|p| = 2\) indicates that the value \(p\) can either be \(2\) or \(-2\) (the absolute value could represent earning or losing). Therefore, the best description would be:
Answer: -2 or 2.
To summarize:
11. Eli rode his bicycle home from the library.
12. Tomas added 6 to both sides of the equation instead of subtracting 6.
13. 3x + 10y = 50.
14. $16.
15. -2 or 2.
70 D; 6 is yes its 8 BUT they wanted 3 answers so its 8 5 and 0
9 is k=-1 yay! but the other answer was k=0
13 is 3x = 50 – 10y
14 is $20
It seems there were some misunderstandings regarding your previous questions and responses, particularly with the additional details or specific answers you provided. Let's clarify each question based on your feedback:
Eli's Trip to the Library:
Original answer remains the same: Eli rode his bicycle home from the library.
Tomas making trail mix:
Original analysis remains: Tomas made an error in adding, which was correctly pointed out in the previous response. However, if the final calculation is aiming for what he can afford, it seems a level of interpretation was necessary. The correct resolution might yield different parameters.
Bob's weights:
The correct interpretation of the options initially asked was misconstrued. The equivalent equation: 3x + 10y = 50 was the first equation. If you indicate the correct final statement as 3x = 50 - 10y, that is a valid rearrangement of the total weight equation.
Money left after purchasing baseball cards:
I apologize for the confusion in my initial response. If the graph shows Carly having $0 left after buying 5 packs, then she would have had $20 initially. Therefore, $20 is correct.
Now revising your responses:
For the equation solutions for the weights, saying 3x - 10y = 50 is not the direction to the total weight from all types for summed equality. Therefore, the correctly conveyed relationships must maintain the integrity of the options awarded.
You stated the other answers correctly were for inequalities and weighed within, signifying different approaches through all statements should enhance clarity in making connections clear.
If combined with your conclusions, the responses would be:
Eli rode his bicycle home from the library.
Tomas added 6 instead of subtracting for accurate solving.
The correct amount Carly had initially: $20 is reaffirmed.
Additionally, you've noted solutions for the inequalities with respect to other values indicating k = -1 and k = 0 with inclusion proposed.
If you need further refinement or need other issues clarified in subsequent equations or context, please provide the structure or values again, and I'll ensure precise clarity and context for the parameters suitably addressed.
One day, you ride your bike to a local bookstore. You purchase a few of your favorite comic books, put them in your backpack, and ride home. Once you get home, you sit in a rocking chair and read your comic books.
Which resource in this scenario is nonrenewable?
the steel frame used to make the bike
the paper used to make the comic books
the cotton used to make the backpack
the wood used to make the rocking chair
In this scenario, the nonrenewable resource is:
the steel frame used to make the bike.
Explanation:
Steel: The steel used to create the frame of the bike is a nonrenewable resource. While steel itself can be recycled, the raw materials (such as iron ore) used to produce steel are finite and can take a long time to replenish naturally.
Paper: The paper used to make comic books is typically considered a renewable resource because it comes from trees, which can be replanted and regrown.
Cotton: The cotton used to make the backpack is also a renewable resource, as cotton plants can be cultivated repeatedly.
Wood: The wood used to make the rocking chair is likewise generally considered renewable, provided it comes from sustainably managed forests.
Conclusion:
The only option that fits the definition of a nonrenewable resource in this context is the steel frame used to make the bike.
4 answers