Answer:

Step-by-step explanation:
P(gold) =
=
= 
Answer:
7
Step-by-step explanation:
The area for a parallelogram is given by the following formula:

Where b is the base and h is the height.
We already know the area is 28 and the height is 4. So, substitute:

Divide both sides by 4:

So, the base length is 7.
Our answer is 7 :)
Answer: A. A relation that is a function.
Step-by-step explanation:
A relation is said to be a function if each input value is associated with one unique output value.
Here, Number of miles run by car is directly proportional to the quantity of gasoline.
Independent variable - quantity of gasoline.
Dependent variable - Number of miles
On assuming the condition of car as good, the number of miles a car can run highly depends on the gallons of gasoline in the tank .
As quantity of gasoline increases number of miles driven would also increases.
i.e. Number of miles driven is a function with respect to quantity of gasoline.
Hence, the given line best describe as : A relation that is afunction.
Answer:
y + 1 = 3(x - 5) Answer
Step-by-step explanation:
<u><em>Find the slope of the perpendicular line.</em></u>
m1 * m2 = - 1
m1 = - 1/3
m2 is the slope of the perpendicular
(-1/3) * m2 = - 1 Multiply both sides by -3
-(3)(-1/3) * m2 = -1 * -3
m2 = 3
The slope of the perpendicular line is 3
<em><u>Find the equation of the line.</u></em>
m = (y - y1)/(x -x1)
y - y1 = m(x - x1) is the equation of the line.
y1 =5
x1 = - 1
(y - - 1) = 3(x - 5)
y + 1 = 3(x - 5) Answer
The given <span>polynomial is ⇒⇒⇒ </span><span>f(x) = x³ - 3x² + 81x - 243
</span>
by factoring the absolute term (243) to find one of the factors of the the polynomial
∴ 243 = (1 * 243) or (3 * 81) or (9 * 27)
check which of the numbers {1 , 3 , 9 , 27 , 81 , 243} make f(x)<span>= 0
</span>
i have checked 3 and it makes <span>polynomial = 0
</span>
i.e: f(3) = 0 ⇒⇒ (x - 3) is one of the factors of f(x)
By using the reminder theorem ⇒⇒ see the attache figure
∴

And ⇒⇒ (x² + 81) is a sum of two squares which can be factored using the complex numbers as following
x² + 81 = ( x + 9i ) ( x - 9i )
∴ f(x) = <span>
x³ - 3x² + 81x - 243 = (x - 3)(x + 9i)(x - 9i)</span>