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Alexeev081 [22]
3 years ago
5

Quotient of 8 decreased by 2 times t and 3

Mathematics
1 answer:
Paraphin [41]3 years ago
4 0

Answer:

Quotient = \frac{8 - 2t}{3}

Step-by-step explanation:

Quotient, in maths, is what you get when two number or expressions together. That is, dividend over the divisor.

Thus, from what we're given:

dividend is 8 decreased by 2 times t, which can be expressed as 8 - 2*t = 8 - 2t.

The divisor is 3.

Quotient = \frac{8 - 2t}{3}

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0.08 can be written as 8%

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Select another name for angle 2 in the figure below.
Anna [14]

Answer:

Angle CAB

Step-by-step explanation:

Find the points that correspond to angle 2 and name them in order.

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With bases V1, V2 , V3 andw1, w2 , W3, suppose T(v1) = w2 and T(v2) = T(v3) = w1 + w3 . T is a linear transformation. Find the m
Roman55 [17]

Answer:

See picture and explanation below.

Step-by-step explanation:

With this information, the matrix A that you can find is the transformation matrix of T. The matrix A is useful because T(x)=Av for all v in the domain of T.

A is defined as T=([T(v_1)] [T(v_2] [T(v_3)])\text{ where }[T(v_i)] denotes the vector of coordinates of T(v_i) respect to the basis (we can apply this definition because forms a basis for the domain of T).

The vector of coordinates can be computed in the following way: if T(v_i)=a_1w_1+a_2w_2+a_3w_3 then [T(v_i)]=(a_1,a_2,a_3)^t.

Note that we have all the required information: T(v_1)=0w_1+1\cdot w_2+0w_3 then [T(v_1)]=(0,1,0)^t

T(v_2)=T(v_3)=1\cdot w_1+0w_2+0w_3 hence [T(v_2)]=[T(v_3)]=(1,0,0)^t

The matrix A is on the picture attached, with the multiplication A(1,1,1).

Finally, to obtain the output required at the end, use the properties of a linear transformation and the outputs given:

T(v_1+v_2+v_3)=T(v_1)+T(v_2)+T(v_3)=w_2+w_1+w_1=w_2+2w_1  

In this last case, we can either use the linearity of T or multiply by A.

4 0
3 years ago
(6y + 3) minus (3y + 6) when y=7
never [62]

Answer:

y

Step-by-step explanation:

((((2•3y3) -  22y2) -  3y) -  —) -  2

                               y    

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  y  as the denominator :

                      6y3 - 4y2 - 3y     (6y3 - 4y2 - 3y) • y

    6y3 - 4y2 - 3y =  ——————————————  =  ————————————————————

                            1                     y          

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

5

:

Pulling out like terms

5.1     Pull out like factors :

  6y3 - 4y2 - 3y  =   y • (6y2 - 4y - 3)

Trying to factor by splitting the middle term

5.2     Factoring  6y2 - 4y - 3

The first term is,  6y2  its coefficient is  6 .

The middle term is,  -4y  its coefficient is  -4 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   6 • -3 = -18

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -4 .

     -18    +    1    =    -17

     -9    +    2    =    -7

     -6    +    3    =    -3

     -3    +    6    =    3

     -2    +    9    =    7

     -1    +    18    =    17

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

y • (6y2-4y-3) • y - (6)     6y4 - 4y3 - 3y2 - 6

————————————————————————  =  ———————————————————

           y                          y        

Equation at the end of step

5

:

 (6y4 - 4y3 - 3y2 - 6)    

 ————————————————————— -  2

           y              

STEP

6

:

Rewriting the whole as an Equivalent Fraction :

6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  y  as the denominator :

        2     2 • y

   2 =  —  =  —————

        1       y  

Checking for a perfect cube :

6.2    6y4 - 4y3 - 3y2 - 6  is not a perfect cube

Trying to factor by pulling out :

6.3      Factoring:  6y4 - 4y3 - 3y2 - 6

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -3y2 - 6

Group 2:  6y4 - 4y3

Pull out from each group separately :

Group 1:   (y2 + 2) • (-3)

Group 2:   (3y - 2) • (2y3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

6.4    Find roots (zeroes) of :       F(y) = 6y4 - 4y3 - 3y2 - 6

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

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  y  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  6  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,6

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        1.00    

     -1       2        -0.50        -5.88    

     -1       3        -0.33        -6.11    

     -1       6        -0.17        -6.06    

     -2       1        -2.00        110.00    

Note - For tidiness, printing of 13 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

6.5       Adding up the two equivalent fractions

(6y4-4y3-3y2-6) - (2 • y)      6y4 - 4y3 - 3y2 - 2y - 6

—————————————————————————  =  ————————————————————————

            y                            y            

Polynomial Roots Calculator :

6.6    Find roots (zeroes) of :       F(y) = 6y4 - 4y3 - 3y2 - 2y - 6

    See theory in step 6.4

In this case, the Leading Coefficient is  6  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,6

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        3.00    

     -1       2        -0.50        -4.88    

     -1       3        -0.33        -5.44    

     -1       6        -0.17        -5.73    

     -2       1        -2.00        114.00    

Note - For tidiness, printing of 13 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

 6y4 - 4y3 - 3y2 - 2y - 6

 ————————————————————————

            y            

4 0
2 years ago
Read 2 more answers
Find the image of triangle GHJ under the translation of (X,Y) ——> ( x-1, y-8)
MAVERICK [17]

Answer:

triangle KLM

Step-by-step explanation:

Take one point on the initial triangle and move it according to the given translation to locate the image. I used point G. Its coordinate plot is at

(2,3). I perform the operation of the given translation to this. (X1-X2, y1-y2).

So, (2-1, 3-8). The new coordinates will be (1,-5) and the only triangle with these coordinates is triangle KLM.

8 0
3 years ago
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