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Igoryamba
3 years ago
15

Simplify the following polynomial expression. 3x( 4x+5) -4 (-x-3) (2x -5)

Mathematics
1 answer:
Vikki [24]3 years ago
5 0

Answer:

20x^2 +19x - 60

Step-by-step explanation:

3x( 4x+5) -4 (-x-3) (2x -5)

Distribute

12x^2 +15x - 4 (-x-3) (2x -5)

FOIL

12x^2 +15x - 4( -2x^2 -6x +5x +15)

12x^2 +15x - 4( -2x^2 -x +15)

Distribute

12x^2 +15x +8x^2 +4x -60

Combine like terms

20x^2 +19x - 60

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Rob and Amy each improved their yards by planting rose bushes and shrubs. They bought their supplies from the same store. Rob sp
Dmitriy789 [7]

Answer:

The cost of one rose bushes be $10 and the cost of shrubs $4.

Step-by-step explanation

Let us assume that the cost of rose bushes be x .

Let us assume that the cost of shrubs be y .

As given

Rob and Amy each improved their yards by planting rose bushes and shrubs.

They bought their supplies from the same store.

Rob spent $100 on 8 rose bushes and 5 shrubs.

Than the equation

8x + 5y = 100

Amy spent $112 on 8 rose bushes and 8 shrubs.

8x + 8y = 112

Than the two equation

8x + 5y = 100 and  8x + 8y = 112

Subtracting 8x + 5y = 100 from 8x + 8y = 112

8x - 8x + 8y - 5y = 112 - 100

3y = 12

y = \frac{12}{3}

y = $4

Put in the equation 8x + 5y = 100 .

8x + 5 × 4 = 100

8x + 20 = 100

8x = 100 - 20

8x = 80

x = \frac{80}{8}

x = $10

Therefore the cost of one rose bushes be $10 and the cost of shrubs $4.


7 0
4 years ago
Each paper clip is 3/4 of an inch long and cost 0.02. Exactly enough paper clips I laid into him to have a total length of 36 in
Artist 52 [7]

Answer:

0.96

Step-by-step explanation:

price of 0.75 inch paper clip = 0.02$

To get price of 36 inches

0.75 --------0.02

36. --------. X

X = (36*0.02)/0.75 = 0.96$

6 0
3 years ago
Help me please thank you :)
Radda [10]
I have no idea but good luck
4 0
3 years ago
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side
lorasvet [3.4K]

Answer:

Step-by-step explanation:

1.

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

       =cot x (sec²x)²

       =cot x (1+tan²x)²     [ ∵ sec²x=1+tan²x]

       =  cot x(1+ 2 tan²x +tan⁴x)

       =cot x+ 2 cot x tan²x+cot x tan⁴x

        =cot x +2 tan x + tan³x        [ ∵cot x tan x =\frac{ \textrm{tan x }}{\textrm{tan x}} =1]

       =R.H.S

2.

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

 L.H.S =(sin x)(tan x cos x - cot x cos x)

          = sin x tan x cos x - sin x cot x cos x

           =\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}

           = sin²x -cos²x

           =1-cos²x-cos²x

           =1-2 cos²x

           =R.H.S

         

3.

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

         =1+\frac{{sin^2x}}{cos^2x}                       [\textrm{sec x}=\frac{1}{\textrm{cos x}}]

         =1+tan²x                        [\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]

         =sec²x

        =R.H.S

4.

\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}

L.H.S=\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}

       =\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}

      =\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}

     =\frac{\textrm{2sin x}}{sin^2 x}

      = 2 csc x

    = R.H.S

5.

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

        = sec²x-tan²x

        =\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}

        =\frac{1- sin^2x}{cos^2x}

        =\frac{cos^2x}{cos^2x}

        =1

     

       

8 0
4 years ago
9 * 6 * 10 / the power of 3
andreyandreev [35.5K]

Answer:

54,000

Step-by-step explanation:

10^3=1000

1000*6=6000

6000*9=54000

4 0
3 years ago
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