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STatiana [176]
3 years ago
8

When the function f(x) = 2x^n + ax^2 - 6 is divided by (x - 1), the remainder is -7 and when divided by (x + 3), the remainder i

s 129.
Calculate the value of "a" and "n" and hence write the polynomial function completely.
Mathematics
2 answers:
hodyreva [135]3 years ago
5 0

Answer:

Step-by-step explanation:

From the fact that the remainder is -7 after we divide by x -1 , then we know that f(1) = -7. But f(1) = 2 + a - 6.

So 2 + a - 6 = -7

a - 4 = -7

a = 4 - 7

a = -3.

Also we know that when divided by x + 3 the remainder is 129. Hence f( -3) = 129

129 = f(-3) = 2 (-3)^ n + (-3)(-3)^2 -6

129 = 2 (-3)^n -27 - 6

129 = 2 (-3)^n -33

129 + 33 = 2(-3)^n

162 = 2 (-3)^n

81 = (-3)^n

Hence n =4 and therefore f(x) = 2x^4 -3x^2 - 6.

zhannawk [14.2K]3 years ago
3 0

Answer:

Step-by-step explanation:

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3 0
3 years ago
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Shobos mother present age is six times shobos present age. Shobos age five from now will be one third of his mother's present ag
r-ruslan [8.4K]

Answer:

Step-by-step explanation:

From the problem statement, we can setup the following equations:

M = 6S

S + 5 = \frac{1}{3}M

where S is the current age of Shobos and M is the current age of his mother.

Substituting the first equation into the second will allow us to solve for S:

S + 5 = \frac{1}{3}M

S + 5 = \frac{1}{3}(6S)

S + 5 = 2S

S = 5

Substituting this value into the first equation gives us the age of the mother:

M = 6S

M = 6(5)

M = 30

5 0
3 years ago
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Matthew is going to drive from Salt Lake City, Utah, to Las Vegas, Nevada. His car travels a consistent
Eddi Din [679]

Answer: 14 gallons of gasoline.

Step-by-step explanation:

given data:

25(x + 3) = 424

where x is the number of gallon of gasoline needed to purchase.

Solution.

25(x + 3) = 424

first we open the bracket

25x + 75 = 424

collect like terms

25x = 424 – 75

25x = 349

divide both sides by 25

25x/25 = 349/25

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mathew needs to get 14 gallons of gasoline.

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3 years ago
Pleaseee help meee struggling currently
lisabon 2012 [21]

Answer: 2908.92435 inches.

Step-by-step explanation for shape 1: A = 2(wl + hl + hw) = 2 · (30 · 13 + 13 · 13 + 13 · 30) = 1,898 inches.

Step-by-step explanation for shape 2:

Using the formulas:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving for A:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=9·30+13·30+9·30+1

2·﹣94+2·(9·13)2+2·(9·9)2﹣134+2·(13·9)2﹣94≈1010.92435

Step-by-step explanation for total volume: 2908.92435 inches.

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3 years ago
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