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3 years ago

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Consider the two different numbers 327b (327 is base b) and 327b 1 (327 in base b 1), where b is a positive integer 8 or greater

. If the difference between these two numbers is 89, what is the value of b

1 answer:

Nata [24]3 years ago

5 0

Answer:

Value of b = 14

Step-by-step explanation:

The detailed calculations with steps is shown in the attachment.

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In Problems 23–30, use the given zero to find the remaining zeros of each function

Talja [164]

Answer:

x = 2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

$f(x) = x^3 - 4x^2+ 4x - 16$

One of the zeroes of the above polynomial is 2i, that is :

$f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0$

Thus, we can write

$(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Now, we check if -2i is a root of the given polynomial:

$f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0$

Thus, we can write

$(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Therefore,

$(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Dividing the given polynomial:

$\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4$

Thus,

$(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

X = 4 is a root of the given polynomial.

$f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0$

Thus, 2i, -2i and 4 are the roots of given polynomial.

4 0

3 years ago

Find the area of a trapezium whose parallel sides are 25 cm ,13 cm and other sides are 15 cm and 15 cm

cupoosta [38]

The answer is area= 285 cm

8 0

3 years ago

Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount i

ella [17]

I believe the answer would be $79.50.

7 0

3 years ago

Brandon buys a radio for $43.89 in a state where the sales tax is 7percent

kkurt [141]

Answer:

$3.07 in taxes

Step-by-step explanation:

You multiply 43.89 by .07 and the number you get is 3.07 and that represents the taxes. The total would be 46.96

6 0

3 years ago

Read 2 more answers

A color printer prints 7 pages in 3 minutes.

mojhsa [17]

Answer:

2 pages per minute

Step-by-step explanation:

when you divide 7 by 3, your answer would be 2.3333333333 and so on.

however, you can say

iT pRiNtS 2 aNd A tHiRd pAgEs PeR MiNuTe.

you should say it prints 2 whole pages a minute.

i hope this helps!

stay safe!

:)

4 0

3 years ago