The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr
<h3>What is speed?</h3>
Speed is a scalar quantity that refers to "how fast an object is moving".
Given that, two buses leave a station at the same time and travel in opposite directions, one bus travels 15 km/h faster than the other, the two buses are 1004 kilometres apart after 4 hours,
Speed = distance/ time
Let the speed of the slower bus be v and the faster bus be (v+15)
According to the question,
vt + (v+15)t = 1004
vt + vt + 15t = 1004
t = 4
4v + 4v + 60 = 1004
8v = 944
v = 118
Hence, The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr
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It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.
<h3>What is perpendicular bisector?</h3>
A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.
Now, consider an example;
When you wish to build a perpendicular line on a line segment, like line AB, you do the following;
- Set the compass on a radius more than half the length of the line AB.
- Using A as your center, draw an arc above and below line AB.
- With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.
- Join the two arc intersections to cut line AB at M.
A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.
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Dilation is the process in which the dimensions of a given shape is increased or decreased by a scale factor. Therefore the answers to the questions are:
A. Since the dilation of triangle XYZ do not affect the measure of its internal angles, then the trigonometric ratios of respective internal angles are the same.
B. segment CB = 10
ii. segment AB = 11.18
From the given information in the question, triangle XYZ is an image of triangle ACB. In triangle XYZ, given that Sin X = ; it implies that its hypotenuse is 5.59, and the opposite side as 5. So that;
Sin X =
X = 0.8945
X =
Thus,
<X + <Y + <Z =
+ + <Z =
<Z = -
=
<Z =
So then, the third side can be determined by applying the Pythagoras theorem.
= +
= +
= -
= 6.2481
x =
= 2.49962
x = 2.5
Thus,
Cos X =
=
Cos X =
Tan X =
=
Tan X =
Therefore:
A. Considering triangles XYZ and ACB, the measure of their respective internal angles are the same.
i.e <X ≅ <A
<B ≅ <Z
<C ≅ <Y
So that the trigonometric ratios of respective internal angles are the same.
B. Given that triangle XYZ was dilated by a scale factor of 2, then the respective length of each sides of triangle ACB is twice that of XYZ.
Then,
i. segment CB = 2 x segment YZ
= 2 x 5
segment CB = 10
ii. segment AB = 2 x segment XZ
= 2 x 5.59
segment AB = 11.18
Answer:
Jim got 24£
Step-by-step explanation:
We consider 8£ as the plus 1 part that gavin took. Since the money were shared in equal parts in the ratio 4:3.
From there we can consider:
3 × 8 £= 24£
Answer:
d. (1, 3) and (-3, -1)
Step-by-step explanation:
Equating the expressions for y, we have ...
... x² +3x -1 = y = x +2
Subtracting x+2 gives ...
... x² +2x -3 = 0
... (x +3)(x -1) = 0 . . . . . factored form
... x = -3, 1 . . . . . . . . . . .values that make the factors zero
The second equation tells us, y = x+2, so
... For x = -3, y = -3 +2 = -1. The solution is (-3, -1)
... For x = 1, y = 1 +2 = 3. The solution is (1, 3)
