Hello!
5x + 2y = 9
4x - 3y = 44
We can eliminate y by multiplying both expressions in order to have the y coefficients equal.
The LCM (least common multiple) of 2 and 3 is 6, so we can multiply each accordingly:
3(5x + 2y = 9)
2(4x - 3y = 44)
Distribute:
15x + 6y = 27
8x - 6y = 88
Cancel using addition:
15x + 6y = 27
8x - 6y = 88
------------------
23x = 115
Divide:
x = 5.
Plug in this value of x into an equation to solve for y:
5(5) + 2y = 9
25 + 2y = 9
2y = -16
y = -8
The solution of the system is:
(5, -8).
We assume that the prism being referred in this item may be any prism. For our case, we take both prisms to be rectangular prism so that the volume is equal to,
V = L x W x H
The dimensions of the prisms,
(1) 10 cm x 10 cm x 24 cm
(2) 5 cm x 20 cm x 24 cm
On the presumption that it is a cubic die, on average you will not gain nor lose any money. Out of the six faces, 1/3 of them are a 5 or a 2. So 1/3 of the time, you will gain 3$, but will lose 1$ from the initial payment. 1/3 of 3$ is 1$, so on average, you will gain 1$, while losing 1$.
Another way of looking at it is to take the possible out comes, and add the gains/loses, and you will come up with 0$.
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Related Questions (More Answers Below)
Answer:
see below
Step-by-step explanation:
x⁵ - 8x⁴ + 22x³ - 26x² + 21x - 18 = 0
x = 2, x = ± i, x=3 with multiplicity 2
-----------------------------------------------------
x⁴ - 5x³ + 7x² - 5x + 6 = 0
x = 2, x=3, x = ± i
--------------------------------------------------------
<u>-1 + 4i</u> = 4 + i
i
--------------------------------------------------------
x³ - 26x² + 21x - 18 = 0
x = ± 2i, x = 3/2
--------------------------------------------------------
(1 + i) (-3 - 4i)
= 1 - 7i
--------------------------------------------------------
6.
(-5 + 2i) + (3 - 6i)
= -2 -4i
--------------------------------------------------------
7.
x⁴ + 5x² + 4 = 0
x = ± i , x = ± 2i
--------------------------------------------------------
8.
(7 - i) - (-5 + 6i)
= 12 - 7i
--------------------------------------------------------
9.
(4 - i) (4 + i)
= 17
--------------------------------------------------------
10.
(3 + 8i) (4 - 3i)
= 36 + 23i
