If a+ar =b+r the value of an item of b and r can be expressed as

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

5 0

$a+ar=b+r\\
a(1+r)=b+r\\
a=\dfrac{b+r}{1+r}$

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Find a polynomial function of lowest degree with real coefficients having zeroes of 2 and -Si (Show all work to earn credit.)

antoniya [11.8K]

Answer: The required polynomial of lowest degree is $p(x)=x^3-2x^2+25x-50$

Step-by-step explanation: We are given to find a polynomial function of lowest degree with real coefficients having zeroes of 2 and -5i.

We know that

if x = a is a zero of a real polynomial function p(x), then (x - a) is a factor of the polynomial p(x).

So, according to the given information, (x - 2) and ( x + 5i) are the factors of the given polynomial.

Also, we know that complex zeroes occur in conjugate pairs, so 5i will also be a zero of the given polynomial.

This implies that (x - 5i) is also a factor of the given polynomial.

Therefore, the polynomial of lowest degree (three) with real coefficients having zeroes of 2 and -5i is given by

$p(x)=(x-2)(x+5i)(x-5i)\\\\\Rightarrow p(x)=(x-2)(x^2-25i^2)\\\\\Rightarrow p(x)=(x-2)(x^2+25)\\\\\Rightarrow p(x)=x^3-2x^2+25x-50$

Thus, the required polynomial of lowest degree is $p(x)=x^3-2x^2+25x-50$

4 0

4 years ago

Clarissa works in sales for a software company. Her pay each month varies, because each month she receives a base pay of $2,400.

Natasha_Volkova [10]

If Clarissa had $18,000 in sales during the month of November, and she earns an 8% commission on the dollar value of her sales, then we first need to find out how much she made on commissions alone for the month of November. We can do that by multiplying the percentage by the amount of money she made off of sales.

To do this, we first must convert the percentage into a decimal. We can do this by either dividing the percent by 100, or (my personal shortcut) just shifting the decimal point over 2 places to the left.

8% = 0.08

Now, we multiply the decimal by the amount she made

0.08 * 18000 = 1440

So Clarissa made $1,440 off of commissions. But that's not what the question is asking. It wants to know what percentage of Clarissa's income for the month of November was from commissions. We can do this by adding her base pay to the amount she made from commissions, and then dividing the amount she got from commissions by the total amount she made for the month of November.

2400 + 1440 = 3840

1440 / 2840 = 0.375

We can convert this decimal back to a fraction by multiplying by 100

0.375 = 37.5%

37.5% of Clarissa's pay for the month of November was from commissions.
Hope that helped =)

5 0

3 years ago

What is the solution to the following system?<br> x+y+z=6 <br> x-y+z=8 <br> x+y-z=0

Ghella [55]

I don't really know if this is correct but I think it is x+y+z=14

4 0

3 years ago

Read 2 more answers

I need help with this

Svet_ta [14]

you cant do that because they are not like terms

5 0