To solve this question, you need to find how long jump is. For 2m high with <span>1.67 m/s2 it would be:
h= 1/2 gt^2
2= 1/2 * (1.67) t^2
t^2= 1.67
t= 1.29
If the speed is 20 mph and the jump is 2 second, the distance traveled would be:
20 miles/ hour * 1.29 second * (1 hour/3600second)= 0.007179 miles
If you need to convert it to meter then: </span>0.007179 mile * 1609.34meter/ mile= 11.55 meter
Short answer
For 6: 72 ft^2
For 7: 650 m^2
Six
The base is a square. It's measurement is s = 4
Base = 4^2
Base = 16 ft^2
One triangle
A = 1/2 * b * h
A = 1/2 * 4 * 7
A = 14 tt^2
Four triangles
A = 4 * 14
A = 56 ft^2
Total Area = 56 + 16 = 72 ft^2
Answer 72 square feet
Seven
Triangles
Area of 1 triangle = 1/2 * 10 * 13
Area of 1 triangle = 65
Area of 6 triangles
Area of 6 triangles = 6 * area of 1 triangle
Area of 6 triangles = 390
Base
As near as I can tell, the base is a hexagon. It's using a rather out of the way method of drawing it. I will assume it is a regular hexagon. The area of a regular hexagon is 3 sqrt(3)/2 * S^2 where s is the side of the hexagon.
Area = 3sqrt(3)/2 s^2
s = 10
Area = 3sqrt(3)/2 10^2
Area = 5.1962 * 100 /2
Area = 259.81
Total area
Total area = area of the base + area of the triangles
Total area = 259.81 + 390
Total area (rounded ) = 650
Answer C <<<< answer
I'll do one more in this batch and then you'll need to repost again.
Eight
If you draw two diagonals on the base of the figure, the intersection point will meet the base of the height. Read that a couple of times.
Join the intersection to the midpoint of the length of the square bottom. You should get 3.5
x is found by using the pythagorean theorem.
h = 6
s = 3.5
x = ????
x^2 = 6^2 + 3.5^2
x^2 = 36 + 12.25
x^2 = 48.25
x = sqrt(48.25)
x = 6.95
C <<<< answer
Answer:
x=23°; θ=87°
Step-by-step explanation:
These two angles create what is known as supplementary angles, or 2 angles that add up to 180°. We know this because all horizontal lines are 180° on either side. Since we know the total value of these two angles should equate to 180°, we can set up a simple equation:
Now, using algebra, we can solve for x:
Plugging x back into the equation, we get:
Therefore, the total angle is equal to 87° and x is equal to 23°.
Hope this helps!
<span>1,
During a 1-hr television program, there were 22 commercials, Some
commercials were 15 sec and some were 30 sec long. Find the number of
15- sec commercials and the number of 30 sec commercial if the total
playing time for commercial was 9.5 minutes.
</span>a) <span>show how to formulate your system of equations for your problem,
Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language
b) state the two equations:
- translate the word statement into algebraic equations:
</span><span>* there were 22 commercials => x + y = 22
* the total playing
time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>
Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y = 570
c) state which method you will use to solve either addition or substitution
Answer:
adition: multiply the first equation times - 15 and add the two equations.
d) solve your system showing and explaining each step of the process
Answer:
- muliply eq (1) times - 15
-15x - 15y = - 330
- add that to the eq (2):
-15x + 15x - 15y + 30y = -330 + 570
- add like terms: 15y = 240
- divide both members by 15: 15y/15 = 240 / 15 => y = 16
- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6
Solution: x = 6, y = 16
e) Be sure to check your solution!
x + y = 22
6 + 16 = 22
22 = 22 --> check
15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check
f) Once a solution is found explain what this solution means in the context
of the problem, write the answer to the word problem in words</span><span>
The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.
2, How many quarts of water should be mixed with a 30% vinegar solution
to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>
a) variables:
- state the variables
x: number of quarters of water
y: number of quarters of vinegar
- translate the words into mathematical language
12 qt 25% vinegar solution
=> total number of quarts = 12 = x + y
balance in vinegar:
vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution
0 + 0.3y = 0.25 (x + y)
c) Equations
Eq (1) x + y = 12
Eq (2): 0.3y = 0.25x + 0.25y
=> 0.25x - 0.05y = 0
d) solve
- multiply eq (1) times 0.05 and add to eq (2)
0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6
x = 0.6 / 0.3 = 2
x + y = 12 => y = 12 - y = 12 - 2 = 10
Solution: x = 2, y = 10
e) check:
x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check
vinegar:
10*0.3 = 12*0.25
3 = 3 -> check
f) Explanation of the solution
The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.
