Answer:
(3, -9)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
- Solving systems of equations by graphing
Step-by-step explanation:
<u>Step 1: Define systems</u>
-5x - 3y = 12
y = x - 12
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: -5x - 3(x - 12) = 12
- Distribute -3: -5x - 3x + 36 = 12
- Combine like terms: -8x + 36 = 12
- Isolate <em>x</em> term: -8x = -24
- Isolate <em>x</em>: x = 3
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: y = x - 12
- Substitute in <em>x</em>: y = 3 - 12
- Subtract: y = -9
<u>Step 4: Graph systems</u>
<em>Check the solution set.</em>
Answer:
-1/3
Step-by-step explanation:
Use the formula, (y2 - y1)/(x2 - x1). In this case, there is a negative slope.
Start from point, (1, 9) and go to point (4, 8).
Use the formula:
(y2 - y1)/(x2 - x1)
Y2 = 8
Y1 = 4
X2 = 9
X1 = 1
(8 - 9)/(4 - 1) = -1/3
Therefore, the slope is -1/3
Answer:
x = 5,-1
Step-by-step explanation:
(x-5)(x+1)
Answer:
28.27 cm/s
Step-by-step explanation:
Though Process:
- The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
- the radius
- Punch is being poured into the bowl
- The height at which the punch is increasing in the bowl is
- the exposed area is a circle, (since the bowl is a hemisphere)
- the radius of this circle can be written as
- what is being asked is the rate of change of the exposed area when the height
- the rate of change of exposed area can be written as
. - since the exposed area is changing with respect to the height of punch. We can use the chain rule:
- and since
the chain rule above can simplified to 
-- we can call this Eq(1)
Solution:
the area of the exposed circle is
the rate of change of this area can be, (using chain rule)
we can call this Eq(2)
what we are really concerned about is how 
changes as the punch is being poured into the bowl i.e 
So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:
and rearrage the formula so that a is the subject:
now we can derivate a with respect to h to get
simplify
we can put this in Eq(1) in place of
and since we know
and now we use substitute this 
. in Eq(2)
simplify,
This is the rate of change of area, this is being asked in the quesiton!
Finally, we can put our known values:
from the question
Nine times d = 9*d = 9d
47 decreased by 9d = 47 - 9d
= 47 - 9d.
