Answer:
9. 6k + 5 and 2k - 1.
10. 5√2 .
Step-by-step explanation:
9. Area = 12k^2 + 4k - 5
Factoring:
12k^2 - 6k + 10k - 5
= 6k(2k - 1) + 5(2k - 1)
= (6k + 5)(2k - 1)
So the required lengths are 6k + 5 and 2k - 1.
10. The ratio of a leg to the hypotenuse is 1: √2 so if the hypotenus = 10 the length of a leg is 10 / √2
= 10 √2 / 2
= 5√2 .
<span>The dot product here is 10(9) + 6(5)=120
so the vectors are not orthogonal
</span><span>u.v = |u| x |v| cos (theta) ; theta is the angle between them
we know from above that u.v = 120
|u| = sqrt[10^2+6^2]=11.66
|v| = sqrt[9^2+5^2]=10.29
so we know:
theta =cos^-1 120/(11.66x10.29)
so theta = 25 degrees</span><span>
</span>
Answer:
638 in.²
Step-by-step explanation:
Assuming you need to cover just the surface area of the box with no overlaps, and the shape is a rectangular prism, then you need to find the surface area of a rectangular prism.
SA = PH + 2LW
where
P = perimeter of base = 2(L + W),
H = height of prism
L = length of base
W = width of base
SA = 2(16 + 7)(9) + 2(16)(7)
SA = 638
Calculate area of the triangle:
Height x Lenght of base x 1/2
4cm x 6cm x 1/2 = 12 square cm
Now multiply the are with the length of the prism:
12 square cm x 10 cm = 120 cubic cm
112/15= 7.46 or 7.5
the school would need 7 and a half classes.
