Please answer any of those 2 or the 2 of them together (PLEASE show steps)
One of the questions says "Angle 1 = X^2 and angle 3 = 10x -24" angle 1 = angle 3. Find angle 2
the angles look like this: http://bookbuilder.cast.org/bookresource…
The other question is Find the measure of the angle formed by the hands of a clock at 3:30.
Thank you so much :)
One of the questions says "Angle 1 = X^2 and angle 3 = 10x -24" angle 1 = angle 3. Find angle 2
the angles look like this: http://bookbuilder.cast.org/bookresource…
The other question is Find the measure of the angle formed by the hands of a clock at 3:30.
Thank you so much :)
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Angle 1 = Angle 3 because they are vertical angles (a.k.a. opposite angles)
x² = 10x - 24
Subtract 10x - 24 from both sides
x² - 10x + 24 = 0
Factor
(x - 4)(x - 6) = 0
x = 4 or 6
Now angle 2 it supplementary to both angle 1 and 3.
1st case, x = 4
m<2 = 180 - (4)² = 180 - 16 = 164°
2nd case, x = 6
m<2 = 180 - (6)² = 180 - 36 = 144°
.: Angle 2 has a measurement of either 164° or 144°.
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There are 360° to a circle
There are 12 hours
Therefore the hour hand moves 360/12 or 30° / hour.
For every n minute, the hour hand, moves n / 60 • 30° or n / 1800 °
At 3:30, the minute hand points to 6, while the hour hand is right in between 3 and 4
There's 2 whole hours from 4 to 6, 2 x 30(degrees / hr) = 60°
Since 30 minutes passed, 30 / 60 • 30 = 15°
60° (from 4 to 6) + 15° (from 3 1/2 to 4) = 75°
Thus, the formed angle is 75°.
x² = 10x - 24
Subtract 10x - 24 from both sides
x² - 10x + 24 = 0
Factor
(x - 4)(x - 6) = 0
x = 4 or 6
Now angle 2 it supplementary to both angle 1 and 3.
1st case, x = 4
m<2 = 180 - (4)² = 180 - 16 = 164°
2nd case, x = 6
m<2 = 180 - (6)² = 180 - 36 = 144°
.: Angle 2 has a measurement of either 164° or 144°.
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There are 360° to a circle
There are 12 hours
Therefore the hour hand moves 360/12 or 30° / hour.
For every n minute, the hour hand, moves n / 60 • 30° or n / 1800 °
At 3:30, the minute hand points to 6, while the hour hand is right in between 3 and 4
There's 2 whole hours from 4 to 6, 2 x 30(degrees / hr) = 60°
Since 30 minutes passed, 30 / 60 • 30 = 15°
60° (from 4 to 6) + 15° (from 3 1/2 to 4) = 75°
Thus, the formed angle is 75°.
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angle 1 and 3 are equal, so x^2 = 10x - 24.
You can rewrite the equation as x^2 - 10x + 24 = 0
This can simplify to (x-6)(x-4) = 0 so x = 4, 6
Angle 1 and 3 both = 36 degrees (for a total of 72 degrees).
Since the total degrees must add up to 360 and angles 2 and 4 are also equal, 360 - 72 = 2*angle2
Angle 2 = 144 degrees
For the 2nd question, note that the total degrees of a clock is 360. Therefore each hour segment contains 30 degrees. At 3:30, the hour hand is halfway between the 3 and 4, and the minute hand is directly on the 6. From 6 to 4 is 60 degrees. From 4 to 3 1/2 is 15 degrees.
Therefore the answer is 75 degrees.
You can rewrite the equation as x^2 - 10x + 24 = 0
This can simplify to (x-6)(x-4) = 0 so x = 4, 6
Angle 1 and 3 both = 36 degrees (for a total of 72 degrees).
Since the total degrees must add up to 360 and angles 2 and 4 are also equal, 360 - 72 = 2*angle2
Angle 2 = 144 degrees
For the 2nd question, note that the total degrees of a clock is 360. Therefore each hour segment contains 30 degrees. At 3:30, the hour hand is halfway between the 3 and 4, and the minute hand is directly on the 6. From 6 to 4 is 60 degrees. From 4 to 3 1/2 is 15 degrees.
Therefore the answer is 75 degrees.
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First question: x² = 10x - 24
x² - 10x + 24 = 0
(x-6)(x-4) - 0
x = 6, 4
angle 2 = 180 - angle1
angle 2 = 180 - x²
angle 2's value depends on which value of x you choose to use.
For the second:
3:30 is looks very similar to 3:00, but it's off by a few degrees.
3:00 makes a 90 degree angle, and 3:30 makes a smaller angle than that.
There are 3 hour intervals, so we break up 90 degrees into three sections. At 3:30, the hour hand is halfway between 3 and 4, so that's half of a third of 90.
So, x = 30 + 30 + 1/2(30) = 60 + 15 = 75 degrees.
x² - 10x + 24 = 0
(x-6)(x-4) - 0
x = 6, 4
angle 2 = 180 - angle1
angle 2 = 180 - x²
angle 2's value depends on which value of x you choose to use.
For the second:
3:30 is looks very similar to 3:00, but it's off by a few degrees.
3:00 makes a 90 degree angle, and 3:30 makes a smaller angle than that.
There are 3 hour intervals, so we break up 90 degrees into three sections. At 3:30, the hour hand is halfway between 3 and 4, so that's half of a third of 90.
So, x = 30 + 30 + 1/2(30) = 60 + 15 = 75 degrees.