Alright.. so the operations would be multiplication and addition.
The reason for this is you're finding the amount the school got --24*8-- and the amount the homeroom got --24*3-- then add those to get the total he got.
Let's use the variable 't' to represent the total he collected.
We know that the school gets 8 for every book and he sold 24, so this can be represented with 8*24.
We also know that the homeroom gets 3 for every book, so 3*24. Both of these added will give you the total amount of money he earned, 't'.
So the sentence can be written as
t=8(24)+3(24).
t=192+72.
t=264.
So, we can see that the total he earned was $264.
If you look back at the equation, we know that the 8*24 represents the amount the school earned, which means that school earned $192.
The same goes with the amount the homeroom earned; we know that this is represented by 3*24, and thus the homeroom earned $72.
And that's it!!! (:
Answer:
1. B
2. B
Step-by-step explanation:
** Attached picture of the situation
The bird caught the fish at point A, flew until B (which is 100 yds away, dropped the fish at C (which is horizontally 50 yards from A).
1.
We want the angle that the bird creates with the water (horizontal). It is angle BAC. With respect to the right triangle, we can say that we know "hypotenuse" and "adjacent" side to angle BAC. cosine relates hypotenuse and adjacent, thus we can write:
correct answer is B
2.
Here, we want to find the distance (length) of segment BC. With respect to the angle BAC (we found to be 60), we can say BC is "opposite". We know hypotenuse to be 100. So let's use sine, since sine is ratio of opposite to hypotenuse. Thus, we can write:
correct answer is B
Answer:
15
Step-by-step explanation:
3/4 times 20 is equal to 15
X = amount of 50% solution
y = total amount after mixing
Note that the amount of alcohol in the 20% solution is 80 (0.2) = 16 oz.
We have 2 unknowns, so we need 2 equations:
first, we can write the equation for the total volume:
y = x + 80
next, apply the percentages to get an equation for the amount of alcohol:
0.4 y = 0.5 x + 16
Finally, solve the pair of equations (in this case, by substitution of the 1st into the second:
0.4 (x + 80) = 0.5x + 16
0.4 x + 32 = 0.5X + 16
rearrange and combine like terms:
0.1x = 16
x = 160
from the 1st equation:
y = 160 + 80 = 240
1. The area of the full rectangle is 21 * 28 = 588. We will need this later.
Like you drew, there is an imaginary triangle missing. We can find the dimensions of it by subtracting from the given information. The shorter leg of it is 21 - 12 = 9, the longer leg is 28 - 14 = 14.
Now we find the area of the triangle. Area of a triangle is 1/2 * base * height. So 1/2 * 9 * 14 = 1/2 * 126 = 63.
Now we do the full area of 588 minus the area of the missing triangle piece.
588 - 63 = 525 ft²
2. Do the area of the rectangle and then this time add on the area of the triangle. 7 * 15 = 105. Area of the triangle = 1/2 * 2 * 7 = 1/2 * 14 = 7.
105 + 7 = 112 in²
