(x - a)^2 + (y - b)^2 = (y - d)^2
<span>x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2dy + d^2 </span>
<span>Subtract y^2 from both sides... </span>
<span>x^2 - 2ax + a^2 - 2by + b^2 = -2dy + d^2 </span>
<span>Now I would just substitute in the the values (a = -4, b = 17/8, d = 15/8)... </span>
<span>x^2 - 2(-4)x + (-4)^2 - 2(17/8)y + (17/8)^2 = -2(15/8)y + (15/8)^2 </span>
<span>Simplify... </span>
<span>x^2 + 8x + 16 - (17/4)y + 289/64 = -(15/4)y + 225/64 </span>
<span>Add (17/4)y to both sides... </span>
<span>x^2 + 8x + 16 + 289/64 = (2/4)y + 225/64 </span>
<span>x^2 + 8x + 16 + 289/64 = (1/2)y + 225/64 </span>
<span>Subtract 225/64 from both sides... </span>
<span>x^2 + 8x + 16 + 1 = (1/2)y </span>
<span>x^2 + 8x + 17 = (1/2)y </span>
<span>Multiply both sides by 2... </span>
<span>2x^2 + 16x + 34 = y </span>
<span>...which is equal to equation D.</span>
Answer:
C. 
Step-by-step explanation:
We have been given a triangle. We are asked to find the measure of angle Z using Law of cosines.
Law of cosines: 
, where, a, b and c are sides opposite to angles A, B and C respectively.
Upon substituting our given values in law of cosines, we will get:
Now, we will use inverse cosine or arc-cos to solve for angle Z as:
Therefore, the measure of angle Z is approximately 51 degrees.
Answer:
77 bowls of soup
Step-by-step explanation:
if you divide 33 bowls by 3 days, you find that they sell 11 bowls of soup per day. multiply 11 by the 7 days to find that they sell 77 bowls of soup.
Answer:
- 150π ft²
- 10π ft.
Step-by-step explanation:
Area of the sector :
Finding the area given r = 30 ft. and θ = 60° :
⇒ Area = π × (30)² × 60/360
⇒ Area = π × 900/6
⇒ Area = 150π ft²
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Length of the arc :
Finding the arc length given r = 30 ft. and θ = 60° :
⇒ Arc Length = 2 × π × 30 × 60/360
⇒ Arc Length = 60/6 × π
⇒ Arc Length = 10π ft.
Answer:
Number of plain cookie boxes sold = 785 boxes
Step-by-step explanation:
Given: Cost of a chocolate chip cookie box = $1.25
Cost of a plain cookie box = $0.75
Total number of boxes sold = 1585
Total cost of the sold boxes = $1588.75
Let, number of plain cookie boxes sold = x
Number of chocolate chip cookie boxes sold = 1585 - x
So,
Total cost = total cost of the sold plain cookie boxes + total cost of the sold chocolate chip cookie boxes
$1588.75 = x ($0.75) + (1585 - x) ($1.25)
1588.75 = 0.75 x + 1981.25 - 1.25 x
0.5 x = 392.5
Therefore,
<u>Number of plain cookie boxes sold: x = 392.5 ÷ 0.5 = 785 boxes</u>
