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.
An example of a negative mixed fraction: -5 1/2. Because slash is both signs for ... fractional exponents: 16 ^ 1/2 • adding fractions and mixed numbers: 8/5 + 6 2/7
Answer:
0.40 foot
Step-by-step explanation:
In the first case, a 50 - foot building casts a- foot shadow (1-foot). Let the angle of elevation of the sun from the shadow be represented by θ.
Then:
Tan θ = ![\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Tan θ = ![\frac{50}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B50%7D%7B1%7D)
Tan θ = 50
⇒ θ =
50
= 88.8542
= ![88.85^{o}](https://tex.z-dn.net/?f=88.85%5E%7Bo%7D)
The angle of elevation is approximately
.
For a 20-foot pole,
Tan θ = ![\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Tan
= ![\frac{20}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7Bx%7D)
x = ![\frac{20}{Tan 88.85^{o} }](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7BTan%2088.85%5E%7Bo%7D%20%7D)
= 0.4015
= 0.40 foot
The length of the shadow of the pole is 0.40 foot.
Answer: Nine Hundred Fifty Nine
Step-by-step explanation: