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77julia77 [94]
3 years ago
13

Factorize 2a^2+7a-15​

Mathematics
2 answers:
tresset_1 [31]3 years ago
8 0

Answer:

2a^2+10a-3a-15

2a(a+5)-3(a+5)

(2a-3) (a+5)

loris [4]3 years ago
5 0

\huge\bf  \pink {\underline{Solution :-}}

2 {a}^{2}  + 7a - 15

= 2 {a}^{2}  + 10a - 3a - 15

= 2a(a + 5) - 3(a + 5)

= (a + 5)(2a - 3)

\sf \red{Hence, Answer \:  is  \: (a + 5)(2a - 3).}

\\

\bf \purple{ \underline{ Important  \: Formulas  \: for  \: Factorization :-}}

• \:  {a}^{2}  + 2ab + {b}^{2} =  {(a + b)}^{2}

• \: (a + b)(a - b) =  {a}^{2}  -  {b}^{2}

• \:  {a}^{2} - 2 ab  +  {b}^{2}  =  {(a - b)}^{2}

• \:  {a}^{3}  + 3 {a}^{2} b + 3a {b}^{2}  +  {b}^{3} =  {(a + b)}^{3}

• \:  {a}^{3}   -  3 {a}^{2} b + 3a {b}^{2}   -  {b}^{3} =  {(a  - b)}^{3}

•  \:  {(a + b)}^{2}  +  {(a - b)}^{2}  = 2( {a}^{2}  +  {b}^{2} )

• \: {(a + b)}^{2}   -   {(a - b)}^{2}  = 4ab

• \: (a + b)( {a}^{2}   -ab   +  {b}^{2}  ) =  {a}^{3}  +  {b}^{3}

• \: (a  -  b)( {a}^{2}    + ab   +  {b}^{2}  ) =  {a}^{3}   -  {b}^{3}

• \:   {( \frac{a + b}{2} )}^{2}  - ( {\frac{a - b}{2} } )^{2}  = ab

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THE ARNOLD'S :

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Question 1
Alexxx [7]

Answer:

Water needed for pool = 486 cubic feet

Plastic liner required for the pool = 298.3 feet

Step-by-step explanation:

Top view of the pool is a composite figure, having one rectangle and a trapezoid.

1). Water needed for the pool = volume of the pool

Volume of the pool = Area of the base × Depth

                               = (Area of the rectangle + Area of the trapezoid)× depth  

Area of the trapezoid = \frac{1}{2}(b_{1}+b_{2})\times h

                                    = \frac{1}{2}(11+9)\times (12-1.5)

                                    = 105 ft²

Area of the rectangle = Length × width

                                    = 11 × 1.5

                                    = 16.5 ft²

Now, volume of the pool = (105 + 16.5) × 4

                                          = 121.5 × 4

                                          = 486 cubic feet

b). Liner required = surface area of the pool excluding top

                             = Surface area of the walls + Area of the pool base

                             = (Perimeter of the pool) × depth + area of the base

                             = (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5

                             = 176.8 + 121.5

                             = 298.3 square feet

Therefore, amount of water required = 486 cubic feet

liner needed = 298.3 square feet                                  

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