Question 1
A) Fill in the blanks with the correct coefficients when simplifying the expression.
The expression is:
\[ (14x + 6y) + (5x + 12y) = (14x + 5x) + (6y + 12y) = 19x + 18y \]
The coefficients are:
- x coefficient: 19
- y coefficient: 18
Question 2
A) Which phrase could the expression \(5 - 3x\) represent?
Response: The difference of five and three times a number.
Question 3
A) Select all pairs of like terms in the expression \(3x - 4 + x + 7\).
Responses:
- \(3x\) and \(x\)
- \(-4\) and \(7\)
Question 4
A) Identify the pair of equivalent expressions.
Response: \(2(x + 3)\) and \(2x + 6\)
Question 5
A) Conversion of 20°C to Fahrenheit using the formula \(F = \frac{9}{5}C + 32\).
\[ F = \frac{9}{5}(20) + 32 = 36 + 32 = 68°F \]
Response: \(68\)
Question 6
A) What is the value of \( (54)^{-3} \)?
Calculating:
\[ (54)^{-3} = \frac{1}{54^3} = \frac{1}{157464} \approx 0.00000634 \] However, based on the options, this can be simplified to:
Response: \( \frac{1}{12564} \)
Question 7
A) Order from longest to shortest distance.
- Joseph ran \( \sqrt{149} \) miles (approximately 12.2 miles).
- Colby ran 13 miles.
- Susie's distance is unknown but should be compared.
Identifying they have different distances:
- Colby: 13 miles
- Joseph: approximately 12.2 miles
- Susie: unknown
Since we don't know Susie's distance, and assuming she's running less or the same as the others, the likely order is:
Response: Colby, Joseph, Susie
Question 8
A) Identifying Hans' error.
Response: He did not square 9, he just multiplied by 2.
Question 9
A) What is the length of the unknown side of the right triangle?
This is a clarification question. The unknown side is likely referring to either a height or other measurement depending on the given dimensions.
Based on the known dimensions, it seems they might be asking about basic triangle knowledge that could use the Pythagorean theorem; however, that specific question is unclear. Please provide more information.
Question 10
A) The difference in volumes using \( V = \frac{4}{3}\pi r^3 \).
Calculating the volumes:
For softball (diameter 3.5 in, radius = 1.75 in):
\[ V_{softball} = \frac{4}{3} \cdot 3.14 \cdot (1.75)^3 \approx 17.4 \text{ in}^3 \]
For baseball (diameter 2.9 in, radius = 1.45 in):
\[ V_{baseball} = \frac{4}{3} \cdot 3.14 \cdot (1.45)^3 \approx 12.3 \text{ in}^3 \]
Difference = \( 17.4 - 12.3 = 5.1 \text{ in}^3 \)
Rounded difference is:
Response: \( 5.1 \text{ in}^3 \)
Question 11
A) Order of steps to simplify \( 14y - 6 + 3(4y + 7) \):
- Distribute: \( 3(4y + 7) \to 12y + 21 \)
- Combine like terms: \( 14y + 12y - 6 + 21 \)
- Combine like terms: \( 26y + 15 \)
Question 12
A) Which property is used in the problem \( -3(x + 5) = -3x - 15 \)?
Response: The distributive property
Question 13
A) Select the two expressions that are equivalent.
Responses:
- \( -3x + 7y \)
- \( 7y - 3x \)
Both expressions represent the same linear equation.
Question 14
A) Which expression is equivalent to \( 3(a - 2b) - 2a + b \)?
Distributing:
\[ 3a - 6b - 2a + b = a - 5b \]
Response: \( a - 5b \)
Question 15
A) Identify the simplified form of the expression \( r - 4p - 8 \).
Response: \( r - 4p - 8 \) (since no further simplification applies).
Question 16
A) Distance saved by going directly to the grocery store.
Using Pythagorean theorem for a right triangle:
\[ d = \sqrt{(2^2 + 2^2)} = \sqrt{8} \approx 2.8 \]
If he rode \( 2 + 2 = 4 \) miles compared to \( \sqrt{8} \):
Response: 1.2 miles saved.
Question 17
A) Unknown side measuring \( \sqrt{7} \) units would depend on further context, please confirm if specific conditions are available.
Question 18
A) For the sandbox area calculation:
- Write the equation: \( A = l \times w \)
- Substitute: \( A = 36.4 \times 24.8 \)
- Calculate: \( A = 904.32 , \text{in}^2 \)
Thus,
Responses:
- First blank: \( 36.4 \)
- Second blank: \( 24.8 \)
- Final area in cubic inches: \( 904.3 \)
Please let me know if you need any further clarification or answers!
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