In 1997, how many more liters of paint did home paint jobs use than commercial paint jobs? I really did not understand it.

Find a polynomial function of degree 3 with 2, i, -i as zeros.

sergiy2304 [10]

Answer:

$p(x)= x^3-2x^2+x-2$

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if $\alpha , \ \beta \ \& \ \gamma$ are the zeros of the cubic polynomial , then ,

$\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)$

Here in place of the Greek letters , substitute 2,i and -i , we get ,

$\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)$

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

$\sf \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}$

Simplify using i = √-1 ,

$\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )$

Multiply by distribution ,

$\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)$

Simplify by opening the brackets ,

$\sf\longrightarrow p(x)= x^3+x-2x^2-2$

Rearrange ,

$\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}$

4 0

2 years ago

The center of a circle is at (−3, 1) and its radius is 9.

pickupchik [31]

Answer:

Sorry but the correct answer is (x+3)2+(y−1)2=81

Step-by-step explanation:

Because the radius squared is the answer of the equation

4 0

3 years ago

The product of 263 and v is equal to the quotient of 215 and r

sveticcg [70]

Answer:

263 · v = 215 ÷ r

Step-by-step explanation:

I hope this helps!

3 0

3 years ago

Vincent’s Hotel currently pays a $2.20 common stock dividend. Dividends have been recently growing at a 3% annual rate and are e

Lerok [7]

Answer:

<u>The current value of Vincent's Hotel common stock is US$ 12.95, that fulfills the requirement of an investor of 17% of rate of return annually.</u>

Step-by-step explanation:

1. Let's review the information given for answering correctly the question:

Currently common stock dividend = US$ 2.20

Annual growth of the dividend for the next 2 years = 3%

Annual growth of the dividend after the next 2 years = 0%

2. What is the current value of Vincent’s Hotel common stock to an investor requiring 17% rate of return?

17% = 0.17

Current value of Vincent's Hotel common stock = 2.20/0.17

<u>Current value of Vincent's Hotel common stock = US$ 12.95</u>

8 0

3 years ago

Read 2 more answers

Laura placed a bucket of water in her garden. Over the course of a week, she watched the water evaporate and recorded the volume

nikdorinn [45]

Answer:

1. 0.5 L; 2. 5.00 L

Step-by-step explanation:

V = 5.00 - 0.5n

If you include units, the equation becomes

V(in litres) = 5.00 L - (0.5 L/day) × (n days)

1. Rate of evaporation

When you include the units, it becomes easier to see that the water is evaporating at a rate of 0.5 L/day.

That is, 0.5 L of water evaporates each day.

The negative sign shows that the volume of water is decreasing.

2. Volume at the beginning

At the beginning of the experiment, n = 0. Then

V = 5.00 -0.5×0 = 5.00 - 0 = 5.00 L

The bucket originally contained 5.00 L of water.

4 0

3 years ago