Ineed on this guys, you.

1. add or subtract. show your work for each problem by using boxes, circles, colored underlines, or grouping
to identify the like terms before you simplify.
4 points each (1 point for correct answer, 3 points for showing all work.)
a. (−2x
^2 −4x+ 13)+ (12x
^2 + 2x −25) b. (7x
^2 + 4x − 26)− (−7x^
2 − 3x + 15)

2. multiply. show all your work including boxes, circles, colored underlines, distributing, or grouping to identify
the like terms before you simplify.
6 points (1 point for correct answer, 5 points for showing all work)
(5x − 1)(6x
^2 + 3x + 7)
3. find the roots. show your work. list your steps correctly.
6 points (2 points for correct answer, 2 points for showing all work, 2 points for writing the steps of the
problem)

(n) = n
^2 − 6n − 16

The solutions to your three problem question are:

1.

       a.    10x^2 −2x -12

       b.    14x^2 + 7x -41

2.   30x^3 + 9x^2 + 32x  - 7

3.

     n1 = 8

     n2 = -2

Step-by-step explanation:

1. First problem

We need to Add or subtract the expressions to find the equivalent terms

a) (−2x^2 −4x + 13)+ (12x^2 + 2x −25)

We add together the terms with the same exponent

= (−2x^2 + 12x^2 ) +  (−4x + 2x) + (13 - 25)

= (10x^2 ) +  (−2x) + (-12)

=  10x^2 −2x -12

b) (7x^2 + 4x − 26)− (−7x^2 − 3x + 15)

= (7x^2 + 4x − 26) +  (7x^2 + 3x - 15)

We add together the terms with the same exponent

= (7x^2 + 7x^2 ) +  (4x + 3x) + (- 26 -15)

= (14x^2 ) +  (7x) + (-41)

=  14x^2 + 7x -41

2. Second problem

(5x − 1)(6x^2 + 3x + 7)

We need to multiply to find the equivalent expression\

(5x − 1)(6x^2 + 3x + 7) = (5x)*(6x^2 + 3x + 7) + (-1)*(6x^2 + 3x + 7)

= [(5x)*(6x^2 + 3x + 7)]  + [-6x^2 - 3x - 7]

=  [(5x*6x^2) + (5x*3x) + (5x*7)]  +  [-6x^2 - 3x - 7]

= [(30x^3) + (15x^2) + (35x)]  +  [-6x^2 - 3x - 7]

We add together the remaining terms

= [(30x^3) + (15x^2 - 6x^2) + (35x - 3x)  - 7]

= (30x^3) + (9x^2) + (32x)  - 7

= 30x^3 + 9x^2 + 32x  - 7

3. Third problem

f(n) = n^2 − 6n − 16

We need to find the roots for the polynomial f(n)

That is, the values of n for which f(n) = 0

We can find an analysis of the function in the images below.

Lets use the quadratic formula

Let   y = ax2 + bx + c

a = 1

b = -6

c = -16

x = -b/(2*a) ± sqrt(b^2 -4ac)/(2*a)

x = 3 ± 10/2  = 3 ± 5

roots

n1 = 8

n2 = -2

the answer is a) y= 2 csc [0.5 (x+pi/2)]-1

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)