Answer:
240
Step-by-step explanation:
you do 3x10 which is 30 then multiply that by 8 and you have your answer.
Answer: ![(15+2w)(13+2w)-195\leq 80](https://tex.z-dn.net/?f=%2815%2B2w%29%2813%2B2w%29-195%5Cleq%2080)
Step-by-step explanation:
The area of a rectangle can be calculated multiplying its dimensions.
Observe the figure attached, where "w" is the constant width of the gravel pathway around the rectangular garden.
You can notice that the length of the rectangular garden is 15 meters and the width is 13 meters. Then, its area is:
![A_g=(15\ m)(13\ m)\\\\A_g=195\ m^2](https://tex.z-dn.net/?f=A_g%3D%2815%5C%20m%29%2813%5C%20m%29%5C%5C%5C%5CA_g%3D195%5C%20m%5E2)
Based on the figure, you can determine that the dimensions of the pathway around the garden are:
![length=(15+2w)\\\\width=(13+2w)](https://tex.z-dn.net/?f=length%3D%2815%2B2w%29%5C%5C%5C%5Cwidth%3D%2813%2B2w%29)
Therefore, the area of that gravel pathway would be:
![(15+2w)(13+2w)-195=A_p](https://tex.z-dn.net/?f=%2815%2B2w%29%2813%2B2w%29-195%3DA_p)
Its area must be less than or equal to 80 square meters, then you can write the following inequality that represents all the posible width, in meters, of the pathway:
![(15+2w)(13+2w)-195\leq 80](https://tex.z-dn.net/?f=%2815%2B2w%29%2813%2B2w%29-195%5Cleq%2080)
Answer:
9). 15 miles
10). 12880.8 in²
Step-by-step explanation:
9). Total distance to be covered by Kelly = Perimeter of the given triangle
= Sum of three sides of the triangle
To know the length of Laurel drive (Hypotenuse of the triangle), we will apply Pythagoras theorem in the given triangle,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
= (2.5)²+ 6²
= 6.25 + 36
Hypotenuse = ![\sqrt{42.25}](https://tex.z-dn.net/?f=%5Csqrt%7B42.25%7D)
= 6.5 mi.
Therefore, total distance covered by Kelly = 6.5 + 2.5 + 6
= 15 mi.
10). Amount of paper required to cover one desk of the class
= Area of the trapezoid shown in the figure
= ![\frac{1}{2}(b_1+b_2)h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28b_1%2Bb_2%29h)
Here,
and
are the parallel sides of the trapezoid
And 'h' is the distance between the parallel sides.
By applying Pythagoras theorem in ΔPRT,
PR² = RT² + PT²
PT = ![\sqrt{PR^2-RT^2}](https://tex.z-dn.net/?f=%5Csqrt%7BPR%5E2-RT%5E2%7D)
PT = ![\sqrt{(18)^2-2^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%2818%29%5E2-2%5E2%7D)
= ![\sqrt{324-4}](https://tex.z-dn.net/?f=%5Csqrt%7B324-4%7D)
= ![\sqrt{320}](https://tex.z-dn.net/?f=%5Csqrt%7B320%7D)
= 17.89 in.
Area of the trapezoid PQRS = ![\frac{1}{2}(PQ+RS)(PT)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28PQ%2BRS%29%28PT%29)
= ![\frac{1}{2}(22+26)(17.89)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2822%2B26%29%2817.89%29)
= 429.36 in²
Therefore, paper required to cover 30 desks = 30 × 429.36
= 12880.8 in²
Answer:
5
Step-by-step explanation:
Use the rule:
![({a}^{b} )^{c} = {a}^{b \times c}](https://tex.z-dn.net/?f=%28%7Ba%7D%5E%7Bb%7D%20%29%5E%7Bc%7D%20%20%3D%20%20%7Ba%7D%5E%7Bb%20%5Ctimes%20c%7D%20)
So:
![{ ({5}^{ \frac{1}{3} } )}^{3} = {5}^{ \frac{1}{3} \times 3 } = {5}^{1} = 5](https://tex.z-dn.net/?f=%20%7B%20%28%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%29%7D%5E%7B3%7D%20%20%3D%20%20%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%203%20%7D%20%20%3D%20%20%7B5%7D%5E%7B1%7D%20%20%3D%205)