Answer:
The rule '' A rule for a translation right and up (x + __, y + __) '' describes this transformation.
Step-by-step explanation:
To Determine:
Which rule describes this transformation?
Fetching Information and Solution Steps:
As Quadrilateral PQRS was
- translated 5 units to the right and
to create quadrilateral P′Q′R′S′.
In order to determine the rule of this transformation, we need to understand some knowledge about the translation.
- In geometry, translation is a term that is used to describe a function that moves any figure a certain distance.
- In translation, every point of the figure or object must be moved for the same distance and in the same direction.
There are some rules when translation is made on the Coordinate Plane. These rules are as follows:
- If the object is moved left and down, the rule would be (x - __, y - __). Here the blanks are the distances moved along each axis.
- A rule for a translation right and up (x + __, y + __)
- A rule for a translation right and down (x + __, y - __)
- A rule for a translation left and up: (x - __, y + __)
As Quadrilateral PQRS was translated 5 units to the right and 3 units up to create quadrilateral P′Q′R′S′.
Therefore, we can conclude that the rule '' A rule for a translation right and up (x + __, y + __) '' describes this transformation.
Keywords: transformation rule, translation
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Answer:
29.7 m²
Step-by-step explanation:
The relevant area formula is ...
A = 1/2ab·sin(C)
A = 1/2(12.6 m)(8.9 m)sin(32°) . . . . use given values
A = (1/2)(12.6)(8.9)(0.52992) m² ≈ 29.7 m²
Answer: x = 5
y = 2
z = 2
Step-by-step explanation:
-3x+4y+2z=-3 - ,- - - - - - 1
2x-4y-z=0 - - - - - - - - - - 2
y=3x-13 - - - - - - - - - - 3
We will use the method of substitution.
Substituting y = 3x -13 into equation 1 and equation 2, it becomes
-3x+4(3x-13)+2z=-3
-3x + 12x - 52 + 2z=-3+52
9x+2z = 49 - - - - - - -4
2x - 4(3x-13)-z= 0
2x - 12x + 52 - z = 0
-10x- z = -52 - - - - - - --5
Using elimination method to solve equation 4 and equation 5
Multiply equation 5 by 2 and equation 4 by 1
-20x - 2z = -104
9x+2z = 49
Adding both equations,
-11x = -55
x = -55/-11
x = 5
Substituting x = 5 into equation 3
y = 3x - 13
y = 3×5 -13 = 15-13
y = 2
Substituting x = 5 and y = 2 into equation 1,
-3x+4y+2z=-3
-3×5 + 4×2 +2z = -3
-15+8+2z = -3
-7+2z = -3
2z = -3+7
2z = 4
z = 4/2 = 2
Answer:
7
Step-by-step explanation:
Answer: 10:55
Step-by-step explanation:
Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.
The time the buses will be back at the depot simultaneously will be when:
N(a) * 25mins = N(b) * 35mins
Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.
Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc
Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc
This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.
So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is
at 08:00 + 2:55 = 10:55
