Answer:
C is correct
Step-by-step explanation:
I just know this from having previously learned it, I'm not sure how to explain it but hope the answer helps!
I think the answer is 3.52 for 64 ounces because 3.52 / 64 = 0.055 which rounds 0.06 which is not exactly 0.06 then 2.88 / 48 = exactly 0.06
Part
A:
<span>In
the expression given, 65 + 15w + 25m: 65 =
constant; 15 and 25 = coefficients; w and m = variables.</span>
Thus,
to define:
Constant
is a number which the value is already fixed.
Variable
is the unknown value in the algebraic expression.
Coefficient
is a number which is placed before a variable that indicates how many times the
variable is to be multiplied.
65 + 15w + 25m
65 = 15 (1) + 25 (2)
Part
B:
Let
x be the savings account balance
W
= # of weeks
M
= frequency of mowing the lawn
First,
let’s use the expression given above: 15w + 25m.
Since we are solving for a
constant, only the variables and coefficient of the expression given are to be
used.
Then,
we substitute the variables’ corresponding values.
X
= 15 (20) + 25 (3)
Therefore,
the savings deposits will amount to:
X
= 300 + 75
X
= $375
Part
C:
$75
+ w + 3m
Constant
will be $75.
Variables:
w = no weekly deposit, m = 3
Coefficients:
w = 1, m = remains at 25
This is because we need to adjust the variables and coefficients to solve for the constant.
Answer: B. 5/13
This is the same as writing ![\frac{5}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B13%7D)
==========================================================
Reason:
We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.
a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse
![a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%20%3D%20c%5E2%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B5%5E2%2B12%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B25%2B144%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B169%7D%5C%5C%5C%5Cc%20%3D%2013%5C%5C%5C%5C)
The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.
Now we can compute sine of theta
![\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\](https://tex.z-dn.net/?f=%5Csin%28%5Ctext%7Bangle%7D%29%20%3D%20%5Cfrac%7B%5Ctext%7Bopposite%7D%7D%7B%5Ctext%7Bhypotenuse%7D%7D%5C%5C%5C%5C%5Csin%28%5Ctheta%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%5C%5C%5C%5C)
This points us to choice B as the final answer.
----------------
Extra Info (optional)
- 5/12 is the value of tan(theta) since it's opposite/adjacent
- 12/5 is the value of cot(theta), the reciprocal of tangent
- 12/13 is the value of cos(theta), because cos = adjacent/hypotenuse