Answer:
k = 11/3
Step-by-step explanation:
If the line is tangent to the curve, then Δ = 0.
______________
Remembering:
Δ>0 two different points of intersection x' 
x''
Δ=0 one point of intersection x' = x''
Δ<0 two different points of intersection in the complex plan x' and -x'
______________
As the line and the curve have one point of intersection, which is (x, y), we can make a equality between them:
2x + k = 3x² + 4
0 = 3x² - 2x + (4 - k)
Now we can use the Δ=0 (Δ= b² - 4ac)
Δ = 0 = (-2)² - 4.3.(4-k)
0 = 4 - 48 + 12k
12k = 44
k = 44/12 = 2 . 22 /3. 2.2 = 22/3.2 = 11/3
k = 11/3
34. x - 3 = 8x + 4
-3 - 4 = 8x - x
-7 = 7x
-7/7 = x
-1 = x
y = x - 3
y = -1 - 3
y = -4
solution is (-1,-4)
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35. -6 = -x - 2y
x = -2y + 6
2 + 5x = -2y
2 + 5(-2y + 6) = -2y
2 - 10y + 30 = -2y
32 = -2y + 10y
32 = 8y
32/8 = y
4 = y
2 + 5x = -2y
2 + 5x = -2(4)
2 + 5x = -8
5x = -8 - 2
5x = -10
x = -10/5
x = -2
solution is (-2,4)
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36. 4x + 6y = 2000
x + y = 410
==================
37. 4x + 6y = 2000
x + y = 410......multiply by -6
----------------------
4x + 6y = 2000
-6x - 6y = - 2460 (result of multiplying by -6)
--------------------add
-2x = - 460
x = -460/-2
x = 230 <=== tickets in advance
Answer:
$82.16
Step-by-step explanation:
78.25 * .20 = 15.65 as a tip,
78.25 *.15 = 11.74 as the discount, subtract from initial value:
78.25 - 11.74 = 66.51
then add the tip: 15.65 + 66.51 = $82.16
Answer:
4x-12
Step-by-step explanation:
use distributive property and distribute the 4 through
