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What are the answers to the following questions: 12. m9 / m2=?, 13. Find the gradient of the line passing through points (0,2) and (1,5). 14. If Q = [50, 30, 60]^T and P = [60, 20, 70]^T, what is Q+P?
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Step-by-step solution
12 steps- Step 1: Apply the rule of exponents for division, .
Simplify the exponent.
The simplified expression is .
- Step 1: Identify the coordinates of the two points. Point B: Point D:
Use the formula for the gradient (slope) of a line
.
Calculate the gradient.
The gradient of the line is .
- Step 1: Identify the given matrices P and Q.
To determine , add the corresponding elements of the matrices.
Perform the addition.
The result of is .
- Step 1: State the given map distance and actual distance. Map distance = Actual distance =
Express the scale as a ratio of map distance to actual distance.
Scale =
Simplify the ratio so that the map distance is .
Divide both sides by 16.
The scale of the map in statement form is .
- Step 1: State the given map distance and actual distance. Map distance = Actual distance =
Convert the actual distance to centimeters to have consistent units for the ratio.
So, .
Actual distance = .Express the scale as a ratio of map distance to actual distance.
Scale =
Simplify the ratio so that the map distance is .
Divide both sides by 4.
The scale of the map is .
- Step 1: State the given map scale and map distance. Scale = (This means on the map represents in actual distance). Map distance =
Calculate the actual distance in centimeters.
Actual distance = Map distance Scale factor
Actual distance =
Actual distance =Convert the actual distance from centimeters to kilometers.
Actual distance in km =
Actual distance =
The actual length of the road is .
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