Answer:
she can fill 42 6-ounce glasses with the punch mixture
Step-by-step explanation:
1 cup = 8 ounces
15 cups = 120 ounces
132+120 = 252 ounces of punch mixture
252/6 = 42
42 glasses (each glass 6 ounces)
Answer:Let the base of the 15ft long ladder be placed x ft away from the wall so that it exactly reaches the top of a 12- foot tall wall.
By Pythagorean theorem
12
2
+
x
2
=
15
2
⇒
x
2
=
15
2
−
12
2
=
81
⇒
x
=
√
81
=
9
ft
Step-by-step explanation:
Answer:
28 miles
Step-by-step explanation:
Let w stand for the number of miles Derrick runs each week. Then after 4 weeks of training, he wants the total mileage to be 100 miles.
16 + 3w = 100
3w = 84 . . . . . . . subtract 16
w = 28 . . . . . . . . divide by 3
Derrick will run 28 miles each week to achieve his training goal.
6a3-5b2+2c2-3a2bc if a=5 b=2c=-1
Answer:
132 feet
Step-by-step explanation:
Given that Alejandro is standing at a distance of 140 feet from the base of the tree and his eyes are 6 feet above the ground.
Let AB is the height of the tree and point E is the location of his eyes which is 6 feet above from C on the ground as shown in the figure.
The distance between points A and C, AC=140 feet.
Drawing a horizontal line from point E which meets AB at point D as shown.
As ACED forms a rectangle, so
AC=DE=140 feet ...(i)
CE=AD= 6 feet ...(ii)
The height of the tree, AB=AD+DB
By using equation (ii), AB=6+DB ...(iii)
Now, given that the on watching the top of the tree, the reading on the clinometer is 42 degrees.
So,![\angle DEB = 42^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20DEB%20%3D%2042%5E%7B%5Ccirc%7D)
In triangle DEB,
![\tan 42^{\circ} = \frac {DB}{DE} \\\\\Rightarrow DB = DE \times \tan 42^{\circ} \\\\](https://tex.z-dn.net/?f=%5Ctan%2042%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%20%7BDB%7D%7BDE%7D%20%5C%5C%5C%5C%5CRightarrow%20DB%20%3D%20DE%20%5Ctimes%20%5Ctan%2042%5E%7B%5Ccirc%7D%20%5C%5C%5C%5C)
[from (i)]
feet
From equation (iii) the height of the tree is
AB=6+126=132 feet.
Hence, the height of the tree is 132 feet.