Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
<h3>
Answer: 9</h3>
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Work Shown:
a = unknown = leg #1
b = 12 = leg #2
c = 15 = hypotenuse
Plug those values into the pythagorean theorem and solve for 'a'
a^2 + b^2 = c^2
a^2 + (12)^2 = (15)^2 .... substitution
a^2 + 144 = 225
a^2 = 225 - 144 ... subtracting 144 from both sides
a^2 = 81
a = sqrt(81) .... applying square root to both sides
a = 9
Answer:
B
Step-by-step explanation:
let X represent the smaller paintings and Y represent the larger paintings
since she bought 8 paintings
X+Y=8
She bought all the eight paintings for $230 and X is worth 25 while Y is worth 40
25×X+40×Y=230
25X+40Y=230
They have sold ten full cases
but have sold 10 and a half cases in total
