Select the correct augmented matrices. Liam wants to buy a car and pay for it in three installments. The total cost of the car is $29,000. Two times the first installment is $1,000 more than the sum of the third installment and three times the second installment. Liam must pay 15% interest on the second and the third installments: the interest will amount to $2,100. If x, y, and z represent the first, second, and third installments, respectively, identify the augmented matrices that model Liam's situation.

Step-by-step explanation:

Given:

The total cost of the car is 29,000 dollars.  Which is paid in three installments . x , y and z are the installments.

To Find:

The value of x, y and z.

Solving:

It is said that 2 times the 1 installment is $1,000 ore than the sum of the 3 rd installment and 3 times the second installment.

= 2x =  1000 + z + 3y

Transposing:

= z = 2x - 3y  - 1000

x + y  + z  = 29000 + 2100

= x + y  + z = 31100

= x + y  + 2x - 3y  - 1000 = 31100

= 3x - 2y = 32100

First installment at start paid = x (We have assumed)

Remaining Installment which is left to pay  = 29,000 - x

(29,000 - x) * 15 /100  =  Interest for First

= (29000 - x) * 3/20  

=> 4350 - 0.15x  

Installment Paid Second = y

(29000 - x)   +  4350 - 0.15x    -  y ) * 15/100 =  Interest  Second

(29000 - x)  + 4350 - 0.15x    -  y  ) * 3/20

= 5002.5 - 0.1725x - 0.15y

Interest of 1st installment +  Interest of 2nd  installment  = 2100

Using this principle solving:

=  4,350 - 0.15x  + 5,002.5 - 0.1725x - 0.15y  = 2,100

=  0.3225x  +  0.15y =  7,252.5

= 6.45x  + 3y  = 1,45,050

= 12.9x  + 6y = 2,90,100

= 4.3x + 2y = 96,700

= 4.3x + 2y = 96700

= 3x - 2y = 32,100

= 7.3x = 1,28,800

= x ≈ 17644     ( 17,643.8356)

3x - 2y = 32,100

= y ≈ 10416     (10,415.7534 )

 x + y + z = 31100

= z ≈ 3040   ( 3,040.4110 )

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

answer: h

step-by-step explanation: