The race is 111.6 m long.
8 hurdles spaced 12.3 m apart means 7 spaces that are 12.3 m in length; 7*12.3 = 86.1
Add to this the distance to the first hurdle and the distance from the last hurdle:
86.1+15+10.5 = 111.6 m
a) To find the missing side length on triangle A, we can use the Pythagorean theorem.
a^2 + 12^2 = 13^2
a^2 + 144 = 169
a^2 = 25
a = 5 cm
5 and 12 = 5 and 12
b) The two triangles are congruent because they have two side lengths in common. If at least two side lengths are the same on two triangles, then they are congruent. In addition, these triangles have one angle in common as well.
Hope this helps!! :)
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Answer:
q = 40
Step-by-step explanation:
When the quadratic has roots p and r, it can be factored as ...
(x -p)(x -r) = x² -(p+r)x +pr
So, the sum of the roots is 14, and their difference is 6. This lets us find the roots from ...
p + r = 14
p - r = 6
2p = 20 . . . add the two equations
p = 10
r = 14 -p = 4
The value of interest is then ...
q = pr = (10)(4)
q = 40
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The graph shows the roots to be 4 and 10, as we found.
Answer:
8.9 meters
Step-by-step explanation:
this seems like a problem where you can use the pythagorean theorem:
you know one of the two legs (6m) and the hypotenuse (9m), you must find the other leg
a^2 + 6^2 = 9^2
a^2 + 36 = 81
a^2 = 45
a = 
or 
· 
which simplifies to be 3 or approx. 8.9 meters
Answer:
2 or -2
Step-by-step explanation:
If x² - 8x = -12
Step 1
We find x by solving
x² - 8x = -12
We equate to zero
x² - 8x + 12 = 0
We factorise
x² - 6x - 2x + 12 = 0
x(x - 6) -2(x - 6) = 0
(x - 6) (x - 2) = 0
x - 6 = 0, x = 6
x - 2 = 0, x = 2
x = 6 or 2
Step 2
What is x - 4?
When x = 6
= 6 - 4 = 2
When x = 2
= 2 - 4 = -2
Therefore, x - 4 = 2 or -2
