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givi [52]
3 years ago
14

Find a polynomial with a degree of 3 and zeros -3,3,5

Mathematics
1 answer:
Aliun [14]3 years ago
6 0

Answer:

f(x) = x³ - 5x² - 9x + 45

Step-by-step explanation:

Given x = a, x = b are the zeros of a polynomial, then

(x - a), (x - b) are the factors and f(x) is the product of the factors.

Here the zeros are x = - 3, x = 3 and x = 5, thus

(x + 3), (x - 3) and (x - 5) are the factors and

f(x) = (x + 3)(x - 3)(x - 5) ← expand the first pair of factors using FOIL

     = (x² - 9)(x - 5) ← distribute

    = x³ - 5x² - 9x + 45

   

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I need answers asap... please
aleksandrvk [35]

Answer:

see explanation

Step-by-step explanation:

(4)

consider the left side

factor the numerator

cosx - cos³x = cosx(1 - cos²x)

\frac{cosx(1-cos^2x)}{sinx}[/tex = [tex]\frac{cosxsin^2x}{sinx}

cancel sinx on numerator/denominator

= cosxsinx =right side ⇒ verified

(5)

Consider the left side

expand the factors

(1 + cotΘ)² + (1 - cotΘ)²

= 1 + 2cotΘ + cot²Θ + 1 - 2cotΘ + cot²Θ

= 2 + 2cot²Θ

= 2(1 + cot²Θ) ← 1 + cot²Θ = cosec²Θ

= 2cosec²Θ = right side ⇒ verified

(6)

Consider the left side

the denominator simplifies to

cosxtanx = cosx × \frac{sinx}{cosx} = sinx

\frac{sin^2x(secx+cosecx)}{sinx}

= sinx( \frac{1}{cosx} + \frac{1}{sinx})

= \frac{sinx}{cosx} + \frac{sinx}{sinx}

= tanx + 1 = right side ⇒ verified











3 0
3 years ago
A store charges 7% sales tax. Which expression can be used to find the total cost of an item with a price of p? 0.07p
Elan Coil [88]

Answer:

a. o.o7p

Step-by-step explanation:

3 1
3 years ago
Please help me asap​
Elenna [48]

Answer:

Not sure what number sense is, but 3 is the answer.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the area of the poster board that she has left
steposvetlana [31]
Find the area of the parallelogram, find the area of the triangle, then subtract the triangle's area from the area of the parallelogram.

Area of Parallelogram:
A= base * height
A= 20 in * 10 in
A= 200 in^2

Area of Triangle:
A= 1/2 base * height
A= 1/2 (10 in)(9 in)
A= 1/2 (90)
A= 45 in ^2

Area of Poster Left:
subtract the difference
A= Parallelogram Area - Triangle Area
A= 200 in^2 - 45 in^2
A= 155 in^2

ANSWER: 155 in^2 is the area of the poster board she has left.

Hope this helps! :)
5 0
3 years ago
The distance between 5,3 and 1,3
mel-nik [20]

Answer:

(4,0)

Step-by-step explanation:

(5,3) (1,3)

You need to subtract from the x axis on both coordinates and the y axis in both coordinates.

(5-1) (3-3)

(4,0)

I also checked on a graph as well, so it's correct.

4 0
3 years ago
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