Answer:
- Emma made a mistake. The slope should be -40.
Step-by-step explanation:
<u>Pair of points (x, y):</u>
- (165, 900) and (180, 300)
<u>Slope formula:</u>
<u>Calculate the slope:</u>
- Slope = (300 - 900)/(180 - 165) = -600/15 = -40
Answer:
a = 5 and b = 12
Step-by-step explanation:
<u>Step 1: Find angle B</u>
<em>Angle C = 90°</em>
<em>Angle A = 22.6°</em>
<em>Angle B = B</em>
<em>All angles in a triangle are equal to 180°.</em>
Angle A + Angle B + Angle C = 180°
22.6 + 90 + B = 180°
B = 180 - 112.6
B = 67.4°
<u>Step 2: Find the value of side AC 'b'</u>
<em>Hypotenuse = 13</em>
<em>Adjacent = b</em>
<em>Angle A = 22.6°</em>
Cos (Angle) = Adjacent/Hypotenuse
Cos (22.6) = b/13
b = 12
<u>Step 3: Find the value of side CB 'a'</u>
<em>Hypotenuse = 13</em>
<em>Opposite = a</em>
<em>Angle A = 22.6°</em>
Sin (angle) = Opposite/Hypotenuse
Sin (22.6°) = a/13
a = 4.99 rounded off to 5
Therefore, the value of a=5 and b=12.
!!
Answer:
It will cost $427.04 to paint deck and it will cost 958.485 to add fencing around deck
Step-by-step explanation:
Diameter of swimming pool = 27 feet
Radius of pool r=
Surrounding the pool is a deck that extends 5 feet from the edges of the pool
Outer radius R = 13.5+5=18.5
Area of deck = Outer area - Inner area
Area of deck =
Area of deck = 
Area of deck = 
Cost of painting 1 sq.feet = $0.85
Cost of painting 502.4 sq.feet = 
Perimeter of deck = 
Cost of fencing 1 foot = $8.25
Cost of fencing 116.18 foot = 
Hence it will cost $427.04 to paint deck and it will cost 958.485 to add fencing around deck
In order to solve this, you have to set up a systems of linear equations.
Let's say that children = c and adults = a
30a + 12c = 19,080
a + c = 960
I'm going to show you how to solve this system of linear equations by substitution, the easiest way to solve in my opinion.
a + c = 960
- c - c
---------------------- ⇒ Step 1: Solve for either a or c in either equation.
a = 960 - c
20(960 - c)+ 12c = 19,080
19,200 - 20c + 12c = 19,080
19,200 - 8c = 19,080
- 19,200 - 19,200
---------------------------------- ⇒ Step 2: Substitute in the value you got for a or c
8c = -120 into the opposite equation.
------ ---------
8 8
c = -15
30a + 12(-15) = 19,080
30a - 180 = 19,080
+ 180 + 180
-------------------------------
30a = 19,260
------- -----------
30 30
a = 642
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I just realized that there can't be a negative amount of children, so I'm sorry if these results are all wrong.
Answer:
A. Sam, Joe, Lynn, Kori
B. Kori, Lynn, Sam, Joe
Step-by-step explanation:
We need Kori and Lynn together and Kori and Sam at least a seat apart.
A. Sam, Joe, Lynn, Kori
B. Kori, Lynn, Sam, Joe
C. Lynn, Kori, Sam, Joe
D. Responses A and C
It seems both A. Sam, Joe, Lynn, Kori and B. Kori, Lynn, Sam, Joe both work. There is no choice for both of them so I'll just put both of them as my answer.