Here are the answers to each question based on the information provided:
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What is another way to represent this solution set?
The solid circle indicates that 4.5 is included (because it's shaded towards negative infinity). Therefore, the correct representation is:
{x | x ≤ 4.5} -
Solve. 5x – 10 ≤ 20
Adding 10 to both sides gives us:
5x ≤ 30
Dividing by 5 results in:
x ≤ 6
So the correct solution is:
(–∞, 6] -
What is the first step in solving the inequality 2x + 3 ≥ 17?
The first step is to isolate the term involving x. Therefore, you would:
Subtract 3 from both sides. -
Which statement best describes a possible number of people she can take in her car?
Since p < 5, the possible number of people must be less than 5:
Mrs. Valdez can take 2 people because 2 < 5. -
Which inequality best shows how many more pages (p) Devin needs?
She needs at least 1,000 signatures, and she currently has 380. She needs another 1,000 - 380 = 620 signatures. Since each page holds 80 signatures, the inequality is:
\( p \geq 620/80 \) which simplifies to \( p \geq 7.75 \) (implying that she needs at least 8 pages). Hence:
8 ≤ p -
What is the greatest number of side dishes they can buy?
Total money available for side dishes = $35 - $18 = $17. Each side dish costs $3. Therefore, the maximum number of side dishes is:
17 / 3 = 5.67, so the greatest number of side dishes they can buy is:
5 -
Which are correct representations of this solution?
From the solution n > 3, correct representations are:
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.
and
(3, ∞) -
Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month?
Total gas budget is $150. Already spent is $60, hence:
\( 30n + 60 ≤ 150 \) or
\( 30n < 90 \) where \( n \) is the number of fill-ups. Therefore, the correct inequality is:
30n + 60 < 150 -
Which statement best describes a possible solution to Cate’s problem?
Since c < 28, we need a number that is less than 28:
The shelter can house 17 cats because 17 < 28. -
What is the maximum number of 8-hour days Xavier can work for the rest of the week?
He can work a maximum of 40 hours. He has already worked 24 hours, so he can work:
40 - 24 = 16 hours remaining. Each day is 8 hours, so:
16 / 8 = 2 days. Hence, the maximum number of 8-hour days he can work is:
2
If you have any further questions or need additional clarification, feel free to ask!