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snow_tiger [21]
3 years ago
10

When multiplying 1,729 times 308, does Clayton got a product of 53,253. Without calculating, does his product seem reasonable? E

xplain your thinking

Mathematics
2 answers:
Harrizon [31]3 years ago
7 0

It is not reasonable, because if we estimate by rounding each factor and multiplying the result. It would be higher than 53,253

<h3>Further explanation</h3>

When we estimate a calculation we can rounding each factor. In this case would be:

1,729 rounding to 2000

308 rounding to 300

2000 x 300 = 600,000

which is higher than 53,253. So if we multipy the exact number the result would be higher.

to get the precise result, we can use the area model

=\boxed {1729 \times308\ }\\ =\boxed{(1000+7000+20+9) \times(300+8)\ }

=\boxed{\(300000+210000+6000+2700+8000+5600+160+72)\ }\\ =\boxed {532532\ }

<h3>Learn more</h3>

Standard algorithm model brainly.com/question/1150215

Total money collected brainly.com/question/2298497

Alfalfa eaten by horses in a number of days brainly.com/question/848633

Keywords: multiplication, standard algorithm, area model, three digits multiplication, additional, estimate, rounding number

ExtremeBDS [4]3 years ago
3 0
Nope if you round the first number to 2000 and the second to 300 you should expect around 600000 which is not the case.
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4x2-28x+49  

Final result :

 (2x - 7)2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22x2 -  28x) +  49

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4x2-28x+49  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -28x  its coefficient is  -28 .

The last term, "the constant", is  +49  

Step-1 : Multiply the coefficient of the first term by the constant   4 • 49 = 196  

Step-2 : Find two factors of  196  whose sum equals the coefficient of the middle term, which is   -28 .

     -196    +    -1    =    -197  

     -98    +    -2    =    -100  

     -49    +    -4    =    -53  

     -28    +    -7    =    -35  

     -14    +    -14    =    -28    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  -14  

                    4x2 - 14x - 14x - 49

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

                   2x • (2x-7)

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

                   7 • (2x-7)

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

                   (2x-7)  •  (2x-7)

            Which is the desired factorization

Multiplying Exponential Expressions :

2.2    Multiply  (2x-7)  by  (2x-7)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (2x-7)  and the exponents are :

         1 , as  (2x-7)  is the same number as  (2x-7)1  

and   1 , as  (2x-7)  is the same number as  (2x-7)1  

The product is therefore,  (2x-7)(1+1) = (2x-7)2  

Final result :

 (2x - 7)2

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