Here are the answers to your questions:
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Which inequality can be used to represent the lengths of the glass that will fit in the frame?
- Answer: \( 12 < x \leq 12.2 \)
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Which are possible values for x from the inequality \( x < 9 \) or \( x \geq 14 \)?
- Possible values: $8, $14
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Solve the equation \( -x + 8 + 3x = x - 6 \).
- Solution: \[ -x + 8 + 3x = x - 6 \] \[ 2x + 8 = x - 6 \] \[ 2x - x = -6 - 8 \] \[ x = -14 \]
- Answer: \( x = -14 \)
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What is the equivalent equation solved for \( h \)?
- Answer: \( \frac{P}{mg} = h \)
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What interval includes all possible values of \( x \) for the inequality \( -3(6 - 2x) \geq 4x + 12 \)?
- Solution: Simplifying the inequality \( -3(6 - 2x) \geq 4x + 12 \): \[ -18 + 6x \geq 4x + 12 \] \[ 2x \geq 30 \] \[ x \geq 15 \]
- Answer: \( [15, \infty) \)
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Which number line represents the solution set for the inequality \( 3x < -9 \)?
- Solution:
\[ x < -3 \]
- An open circle at -3 with a line extending to the left.
- Solution:
\[ x < -3 \]
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What expression represents Nikita’s distance for the second part of the race?
- Solution: Let \( t \) be the time spent in the first part of the race. The second part lasts \( 0.65 - t \) hours. So, the distance for the second part of the race is: \[ \text{Distance} = \text{Rate} \times \text{Time} = 6(0.65 - t) \]
- Answer: \( 6(0.65 - t) \)
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Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.
- Using the formula: \[ A = \frac{1}{2} b h \] \[ 30 = \frac{1}{2} \times 12 \times h \] \[ 30 = 6h \] \[ h = 5 \]
- Answer: \( 5 \) units
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Solve the equation \( 2x − 3 + 4x = 21 \).
- Equation: \[ 6x - 3 = 21 \] \[ 6x = 24 \] \[ x = 4 \]
- Answer: \( x = 4 \)
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Using the sum of the interior angles formula, how many sides does a polygon have if the sum of the interior angles is \( 1,260^\circ \)?
- Equation: \[ 180(n - 2) = 1260 \] \[ n - 2 = 7 \] \[ n = 9 \]
- Answer: \( 9 \text{ sides} \)
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What is the last line of the justification for n = -2?
- Answer: \( 0.8 = 0.8 \)
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What is the value of p in the linear equation?
- Answer: Cannot be answered without the specific linear equation.
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What is the solution to \( -4(8 - 3x) \geq 6x - 8 \)?
- Solve the inequality: \[ -32 + 12x \geq 6x - 8 \implies 6x \geq 24 \implies x \geq 4 \]
- Answer: \( x \geq 4 \)
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What value of x is in the solution set of the inequality \( -2(3x + 2) > -8x + 6 \)?
- Solve it: \[ -6x - 4 > -8x + 6 \implies 2x > 10 \implies x > 5 \]
- Possible values: \( -6, -5, 5, 6 \) with 6 satisfying \( x > 5 \).
- Answer: \( 6 \)
- What is the value of r, Hector’s rate of work in part per hour?
- Shawn's rate: \[ \frac{1}{9} \text{ part/hour} \]
- Together rate: \[ \frac{1}{6} \text{ part/hour} \]
- Rate calculation: \[ \frac{1}{6} = \frac{1}{9} + r \implies r = \frac{1}{6} - \frac{1}{9} = \frac{3-2}{18} = \frac{1}{18} \]
- Answer: \( \frac{1}{18} \) part/hour
Feel free to ask if you need further assistance or clarification regarding the answers!