Answer:
Equation: 1.5s + 20 = 200
How long it will take for Samantha to finish a 200 meter race: 120 seconds
Step-by-step explanation:
The problem says Samantha walks at a rate of 1.5 meters per second. If we let "s" represent seconds, then we can write this as 1.5s. Since she gets a 20 meter head start, you can then write the equation as 1.5s + 20. Finally, its says use this equation to find how long it would take to finish a 200 meter race. So you set the previous equation equal to 200. Or 1.5s + 20 = 200.
To solve for "s" and find how long it would take to finish a 200 meter race, you first subtract 20 from each side. You should be left with 1.5s = 180. Then divide by 1.5. 180/1.5 equals 120. So it will take Samantha 120 seconds to finish the 200 meter race.
Hi there!
We'll use the image below as a reference diagram. As you can see, the hexagon is divided into 6 triangles. And, one red line (center to point on the hexagon) would be the radius. Since we know that all of the triangles are equilateral triangles, and the hexagon is a regular hexagon, we know that one side of the hexagon is equal to
77m.
(If the circle actually has a diameter (all the way across the circle), the answer would be 38.5m)
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
1. The problem statement tells you to find "the area of the hexagonal face".
2. If we assume the intent is to find the shaded area of the face only, it differs from the area of a regular hexagon in that there is a hole in the middle.
3. You must find the area of the regular hexagon, and subtract the area of the circular hole in the middle.
4. The formula for the area of a circle in terms of its radius is
... A = πr²
5. The formula for the area of a regular hexagon in terms of the radius of the circumcircle is
... A = (3√3)/2·r²
6. The radius of the circumcircle of the regular hexagon is given. No additional information is needed.
7. You can use the trig functions of the angles of an equilateral triangle to find the apothem, but there is no need for that when you use the formula of 5.
8. All this is unnecessary. The apothem is (8 mm)·(√3)/2 = 4√3 mm ≈ 6.9282 mm, the shorter leg is (8 mm)·(1/2) = 4 mm. The perimeter is 6·8 mm = 48 mm.
9. The area of the hexagon is
... A = 3√3/2·(8 mm)² = 96√3 mm² ≈ 166.277 mm²
10. The area of the circle is
... A = π·(4 mm)² = 16π mm² ≈ 50.265 mm²
11. The area of the hexagonal face is approximately ...
... 166.277 mm² - 50.265 mm² = 116.01 mm²
Answer:
Addition: -1 + -3 = -4
Subtraction: (-4) - 5 = -10
Step-by-step explanation:
Since adding a positive makes a negative number stay negative, it equals -4.
Then by subtracting a negative with a positive (5), the number stays negative once again, which then equals -10.
