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vladimir2022 [97]
2 years ago
8

How can these models be used to find the sum 1.8 + 1.56?

Mathematics
1 answer:
enyata [817]2 years ago
3 0

Answer:

The sum of  1.8 and 1.56 is 3.36 according to the model

Sum of decimals

Given the expression  1.8 + 1.56

Using the partial sum method

1.8 + 1.56 = (1.0 + 0.8) + (1.0+0.56)

Regroup as whole and decimal number

1.8 + 1.56 = (1.0 + 1.0) + (0.8 +0.56)

1.8 + 1.56 = 2.0 + 1.36

1.8 + 1.56 = 3.36

Hence the sum of  1.8 and 1.56 is 3.36 according to the model

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The length of a model car is 1/20 of the length of the actual car. If the model. is 8.7 inch long, how long is the actual car? E
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Simplify (4x^2+2)÷(2x^2-9x-5)​
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Answer:

4.1     Pull out like factors :

   4x2 + 2  =   2 • (2x2 + 1) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 2x2 + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2  and the Trailing Constant is  1.

 The factor(s) are:

of the Leading Coefficient :  1,2

 of the Trailing Constant :  1

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      3.00        -1     2      -0.50      1.50        1     1      1.00      3.00        1     2      0.50      1.50   

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

 4.3     Factoring  2x2 - 9x - 5 

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -5 = -10 

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   -9 .

     -10   +   1   =   -9   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  1 

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Step-4 : Add up the first 2 terms, pulling out like factors :

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              Add up the last 2 terms, pulling out common factors :

                     1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                    (2x+1)  •  (x-5)

             Which is the desired factorization

Final result :

2 • (2x2 + 1) —————————————————— (x - 5) • (2x + 1)

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