Solve the following math problems: 1. One morning, Marcia works from 08:20 to 11:15. Find how long she works for. Give your answer in hours and minutes. 2. Expand: 7(x-8) 3. Here... Solve the following math problems: 1. One morning, Marcia works from 08:20 to 11:15. Find how long she works for. Give your answer in hours and minutes. 2. Expand: 7(x-8) 3. Here is a sequence: a, 13, 9, 3, -5, -15, b, ... Find the value of a and the value of b. 4. Complete these statements: (a) When w= ..., 10w = 70. (b) When 5x = 15, 12x = ... 5. Given the numbers 22, 17, 25, 41, 39, 4, work out the difference between the two prime numbers in the list above.
Understand the Problem
The user has provided an image of a math worksheet consisting of 5 problems. The problems cover topics such as calculating the duration between two times, expanding algebraic expressions, identifying patterns in sequences, solving simple equations, and identifying prime numbers.
Answer
1. 2 h 55 min 2. $7x - 56$ 3. $a = 15$, $b = -27$ 4. a) $w = 7$ b) $12x = 36$ 5. 24
Answer for screen readers
- 2 h 55 min
- $7x - 56$
- $a = 15$, $b = -27$
- a) $w = 7$ b) $12x = 36$
- 24
Steps to Solve
- Calculate the duration between 08:20 and 11:15
To find the duration, subtract the start time from the end time.
Hours: $11 - 8 = 3$ hours Minutes: $15 - 20 = -5$ minutes
Since we have negative minutes, we need to borrow an hour from the 3 hours, converting it into minutes.
1 hour = 60 minutes, so we now have 2 hours and $60 - 5 = 55$ minutes.
- Expand the expression $7(x - 8)$
Distribute the 7 to both terms inside the parentheses: $7 * x - 7 * 8 = 7x - 56$
- Find the values of a and b in the sequence
The sequence is: $a, 13, 9, 3, -5, -15, b$
The difference between consecutive terms is: $13 - 9 = 4$ $9 - 3 = 6$ $3 - (-5) = 8$ $-5 - (-15) = 10$
The differences are increasing by 2 each time (4, 6, 8, 10). So, the next difference should be 12.
To find $b$, subtract 12 from -15: $b = -15 - 12 = -27$
To find $a$, we need to go backwards in the sequence. The difference before the '4' must have been 2. Thus $a - 13 = 2$, so $a = 13 + 2 = 15$.
- Complete the statements
(a) $10w = 70$ Divide both sides by 10 to find $w$. $w = 70 / 10 = 7$
(b) $5x = 15$ First, solve for $x$: $x = 15 / 5 = 3$ Now, substitute $x = 3$ into $12x$: $12x = 12 * 3 = 36$
- Find the difference between the two prime numbers
The list of numbers is: 22, 17, 25, 41, 39, 4 Prime numbers are numbers that have only two distinct factors: 1 and themselves. The prime numbers in the list are 17 and 41.
The difference between 41 and 17 is: $41 - 17 = 24$
- 2 h 55 min
- $7x - 56$
- $a = 15$, $b = -27$
- a) $w = 7$ b) $12x = 36$
- 24
More Information
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.
Tips
- When calculating time durations, forgetting to borrow an hour (60 minutes) if the minutes subtraction results in a negative value is a common mistake.
- For the sequence, not recognizing the pattern in the differences between the terms can lead to an incorrect calculation of a and b.
- Forgetting to solve for $x$ before substituting it into $12x$ in question 4 (b).
- Confusing composite and prime numbers
- When expanding, forgetting to multiply both terms in parenthesis
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