Answer:
r = - 7, r = - 5
Step-by-step explanation:
Given
r² = - 12r - 35 ( add 12r to both sides )
r² + 12r = - 35
To complete the square
add ( half the coefficient of the r- term )² to both sides
r² + 2(6)r + 36 = - 35 + 36
(r + 6)² = 1 ← take the square root of both sides )
r + 6 = ± 1 ( subtract 6 from both sides )
r = - 6 ± 1, thus
r = - 6 - 1 = - 7 or r = - 6 + 1 = - 5
the scale factor used in Emily scale drawing is K = 1.63 mm/m
<h3>
What scale did Emily use?</h3>
We know that Emily drew a scale drawing of a house and its lot.
In the scale drawing, the back patio is 42 millimeters long, and we know that the actual patio is 27 meters long.
Then the scale relates the measures 44mm and 27 meters, such that if the scale is K, we can write:
K*27m = 44mm
Solving for K, we can write:
K = (44/27) mm/m = 1.63 mm/m
So the scale factor used in Emily's scale drawing is K = 1.63 mm/m
If you want to learn more about scale factors:
brainly.com/question/25722260
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Answer:
Wonka bars=3 and Everlasting Gobstoppers=24
Step-by-step explanation:
let the wonka bars be X
and everlasting gobstoppers be Y
the objective is to
maximize 1.3x+3.2y=P
subject to constraints
natural sugar
4x+2y=60------1
sucrose
x+3y=75---------2
x>0, y>0
solving 1 and 2 simultaneously we have
4x+2y=60----1
x+3y=75------2
multiply equation 2 by 4 and equation 1 by 1 to eliminate x we have
4x+2y=60
4x+12y=300
-0-10y=-240
10y=240
y=240/10
y=24
put y=24 in equation 2 we have'
x+3y=75
x+3(24)=75
x+72=75
x=75-72
x=3
put x=3 and y=24 in the objective function we have
maximize 1.3x+3.2y=P
1.3(3)+3.2(24)=P
3.9+76.8=P
80.7=P
P=$80.9
So the total is 120. You want 1/6 of those.
So do (1/6)*120
You get 20.
YAY
