a+c\ The linear transformation T:P₂→R³ is defined by T(a+bt+ct²) = b Verify the rank nullity theorem for T. Find matrix associated to T with respect to the standard basis of P, as {1,t,t²} and the standard basis of R³ as 2

Q: Part A and Part B for Max`s car together cost $1,693 dollars, Part A cost $58 dollars more than…

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Q: The product of two consecutive even whole numbers is 120. The two integers are and

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Q: There are two numbers whose sum is 72. One number (x) is twice the other (y). What are the numbers?…

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Q: A number multiplied by 8 divided by 4 gives 7 more than the number

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Q: A two digit number is four times the sum and three times the product of its digits .Find the number

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Q: How many gallons of a 30% acid solution should be mixed with a 50 gallons of 80% acid solution to…

A: Let x gallons of a 30% acid solution should be mixed with a 50 gallons of 80% acid solution to yield…

Q: Find the number whose absolute value is 54 more than the number itself.

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Q: if a burger plus 2 portions of fries cost $17.00 and 3 Burgers  and 4 portions of fries   cost…

A: let burger cost is x and one portion of fries cost is f. given that cost of 1 burger and 2 portions…

Q: The sum of the two-digit number is 9. The tens digit is three less than three times the units digit.…

A: Lets the ten's digit be x ,and let unit's digit be y Then the number formed is 10x+y As the sum of…

Q: The sum of the two-digit number is 8. The unit digit is four less than five times the tens digit.…

A: Let  'ab' denotes a two digit number where 'b' is unit digit and 'a' denotes tens digit. Given that…

Q: When a whole number, x is subtracted from 20, the result is less than 15.

A: x is subtracted from 20 means 20-x This is less then 15 means 20 - x < 15 20 - 15 < x Then  5…

Q: Ten subtracted from a number yields the sum of twice a number and fifteen

A: let  x= number  then  x-10=2x+15 x-2x=15+10 -x=25 x=-25

Q: why can’t the sum of two numbers never be zero?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.