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3 years ago

Which polynomial identity will prove that 49 − 4 = 45?

1 answer:

3 0

49 is a square of 7 and 4 is a square of 2. To get 45 you need to subtract 7² and 2². Therefore, its the difference of squares.

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Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

RSB [31]

Answer:

$f(x)=2x^{3}+24x^{2}+82x+60$

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

$f(x)=a(x+6)(x+5)(x+1)$

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

$60=a(0+6)(0+5)(0+1)$

$60=a(6)(5)(1)$

$60=30a$

$a=2$

$f(x)=2(x+6)(x+5)(x+1)$

Applying the distributive property

Convert to expanded form

$f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60$

3 0

4 years ago

The hypotenuse of a right triangle measures 13cm and one of its legs

hoa [83]

Answer:

6.9

Step-by-step explanation:

Use the Pythagorean theorem :

a^2 + b^2 = c^2

so,

11^2 + b^2 = 13^2

121 + b^2 = 169

b^2= 48

b = 6.928

Round to the tenth : 6.9

8 0

3 years ago

Renee is a sales associate at a store. She earns $80 a week plus a 15% commission on her sales. Last week, she sold $200 worth o

Y_Kistochka [10]

She earned $30 on commission and the total would be $110. Hope this helps

6 0

3 years ago

Read 2 more answers

(PLEASE HELP)(THIS IS MIDDLE SCHOOL LEVEL EASY!) What is the surface area of the box

artcher [175]

Answer:

C) 42 square cm

Step-by-step explanation:

each rectangle 2x3 = 6

each square 3x3 =9

4 rectangles 4x6 = 24

2 squares 2x9=18

24+18 = 42

7 0

2 years ago

Which of the following would be an acceptable first step in simplifying the expression:

Aleks04 [339]

The correct answer is tanx(1-secx)/(1+secx)(1-secx)

6 0

3 years ago