So here we need to use the formula: Distance = Rate * Time
So for Kate, 5 = r10, so rate = 1/2
Saying that Josh travels at the same speed, means he's traveling at the same rate
So for Josh, 2 = 1/2t, so time = 4 minutes
4 minutes
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Answer:
The discount would be 25%
Step-by-step explanation:
24 and 18 are both divisible by 6
24 is just 4×6
18 is just 3×6
This means that 18/24 is the same as 3/4
We calculate the discount by subtracting the percentage of the sale price from the original price.
3/4 is the same as 75% of 100% meaning the discount percentage is 100-75, which gives us 25%
1
The first one is correct.
2
A hexagon has the weird property of having the radius and the side being of exactly the same length
The formula is A = 3 * sqrt(3) * a^2 / 2
where a = the side or radius
A = 3 * sqrt(3) * 5^2 / 2
A = 3 * sqrt(3) * 25 / 2
A = 1.5 * sqrt(3) * 25
A = 64.95
A <<<< Answer (the first one is the answer.)
C
This one seems so much more entailed. Do you know what the cos law is? That's what I will use to find c.
c^2 = a^2 + b^2 - 2*ab* cos(C)
C = 33 degrees
a = 2.75 miles
b = 1.32 miles
c^2 = 2.75^2 + 1.32^2 - 2 * 2.75 * 1.32 * cos(33)
c^2 = 9.3049 - 6.0887
c^2 = 3.2162
c = sqrt(3.2162) = 1.7934
Now you have to use this result to get the area. You have to use Heron's formula.
A = sqrt(s * (s - a) * (s - b) * (s - c) )
s = 1/2 the perimeter
s = 1/2 (2.75 + 1.32 + 1.7934)
s = 1/2(5.8634)
s = 2.9317
I'll finish this in the comments. I have to leave for a bit.
An appropriate order for drawing a hexagon is ...
- Use the circle's radius to set the width of the compass.
- Draw a circle using the compass.
- Add a point on the circle.
- Place the point of the compass on the point most recently drawn on the circle.
- Create an arc with the compass that intersects the circle.
- Mark the intersection with a point.
- Repeat the previous step 4 times. [meaning steps 4–6]
- Connect consecutive points with the straightedge.
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<em>Comment on this construction</em>
A lot of math is much more understandable if you have real-life experience with physical objects. In geometry, there is really no substitute for actually doing these steps using a compass and straightedge.
One of the things you learn by doing is that you need to be very precise when you're following the process. Otherwise, your hexagon comes out somewhat irregular.
You also find there are other methods (perhaps more accurate and requiring less work), involving symmetry and the center of the circle.
