What is the determinant of the coefficient matrix of this system?
4x-3y=-8
8x-3y=12

Answers

Answer 1

Answer:

The coefficient matrix is build with its rows representing each equation, and its columns representing each variable.

So, you may write the matrix as

$\left[\begin{array}{cc}\text{x-coefficient, 1st equation}&\text{y-coefficient, 1st equation}\n\text{x-coefficient, 2nd equation}&\text{y-coefficient, 2nd equation} \end{array}\right]$

which means

$\left[\begin{array}{cc}4&-3\n8&-3\end{array}\right]$

The determinant is computed subtracting diagonals:

$\left | \left[ \begin{array}{cc}a&b\nc&d\end{array}\right]\right | = ad-bc$

So, we have

$\left | \left[\begin{array}{cc}4&-3\n8&-3\end{array}\right] \right | = 4(-3) - 8(-3) = -4(-3) = 12$

Related Questions

A tree is 118 inches tall. How tall is it in feet and inches? prodft in
A square acre of land is 4,840 square yards. The length of one side of the square is between which of the following?A 14 yd and 48 yd B 69 yd and 70 yd C 98 yd and 100 yd D 124 yd and 139 yd
The y-intercept of the line whose equation is 2x + 5y = 8 is 8 4 8/5
WILL MARK BRAINLIESTtwo sides of a triangle have lengths 6 and 17 which inequalities represent the possible lengths for the third side, x?
Write a proof for the conjecture using the contrapositive. If 5x + 7 = -13, then x = -4.

a movie theater charges $6 for a ticket to a matinee and $10 for a ticket to an evening show. last week on tuesday a total of 130 tickets were sold, with the total income amounting to $1120. how many tickets to a matinee were sold?

Answers

Answer:

45 tickets for the matinee were sold

Step-by-step explanation:

let m represent the number of matinee tickets sold and

let e represent the number of evening tickets sold.

Create a system of equations and solve for m

m + e = 130 → (1) ( total ticket sales )

6m + 10e = 1120 → (2) ( income from tickets sold )

multiplying (1) by - 10 and adding the result to (2) will eliminate e

- 10m - 10e = - 1300 → (3)

add (2) and (3) term by term to eliminate e

(6m - 10m) + (10e - 10e) = 1120 - 1300

- 4m + 0 = - 180

- 4m = - 180 ( divide both sides by - 4 )

m = 45

the number of matinee tickets sold was 45

10. Madison is 7 less than four times as old as Paige.

Answers

madison is 13 & paige is 5

What does 5/6 equal as a decimal?

Answers

The decimal of 5/6 is 0.8333

Hi there! To turn a fraction into a decimal we divide the numerator by the denominator. So, we have the fraction 5/6 where 5 is the numerator and 6 is the denominator. 5÷6=0.8333 repeating. Therefore, 5/6 as a decimal is 0.8333

Margaret drove to a business appointment at 60 mph. Her average speed on the return trip was 50 mph. The return trip took one fifth 1 5 hr longer because of heavy traffic. How far did she travel to the appointment?

Answers

She traveled 60 miles to the appointment place.

Step-by-step explanation:

Let the distance to appoint be s and time for appointment trip be t.

The return trip took one fifth hr longer because of heavy traffic.

Time for return trip = t + one fifth hour = (t + 0.2) hr

Speed of appointment trip = 60 mph

Speed of return trip = 50 mph

We have

s = 60 t and

s = 50 (t + 0.2)

s = 50 t + 10

60t = 50 t + 10

10 t = 10

t = 1 hour

Distance to appointment = 60 t = 60 x 1 = 60 miles

She traveled 60 miles to the appointment place.

Which measures would be the side lengths of a right triangle?A. 2 cm, 5 cm, 7 cm
B. 9 cm, 14 cm, 17 cm
C. 7 cm, 17 cm, 24 cm
D. 5 cm, 12 cm, 13 cm

Answers

Conditions for side lenghts for triangle:
a<b+c and
b<c+a and
c<a+b
so we check all posibilities:
A) 2+5=7 we can see that one condition is not fulfilled so they can't be side lenghts of triangle
B) 9<14+17
14<9+17
17<14+19
All conditions are fulfilled so they can be side lenghts of triangle
C)7<17+24
17<7+24
24<17+7
All conditions are fulfilled so they can be side lenghts of triangle
D)5<12+13
12<5+13
13<5+12
All conditions are fulfilled so they can be side lenghts of triangle

The height of water shooting from a fountain is modeled by the function f(x) = -4x2 + 24x - 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. -4(x - 3)2 - 29; The maximum height of the water is 3 feet.
-4(x - 3)2 - 29; The maximum height of the water is 29feet.
-4(x - 3)2 + 7; The maximum height of the water is 7 feet.
-4(x - 3)2 + 7; The maximum height of the water is 3 feet.

Answers

yo don't need max height
yo use 'find vertex' equestion

since leading term is negative, this equation has a max

the vertex is the max
in the form
y=ax^2+bx+c
vertex=-b/2a

-4x^2+24x-29
a=-4
b=24

vertex=-24/(2*-4)=-24/-8=3

max height is 3 feet
dunno wat the compete square is

I can do that fo ou though
move -29 off to side and undistriute -4
-4(x^2-6x)-29
complete the square, take 1/2 of -6 an square it andadd 0
-4(x^2-6x+9-9)-29
complete square
-4((x-3)^2-9)-29
move the 9 out by distributing the -9 to the -4
36
-4(x-3)^2+36-29
-4(x-3)^2+7

answer is 3rd option

Answer: The correct answer for this question is option...

(C) −4(x − 3)2 + 7; The maximum height of the water is 7 feet.

Hope this helps :)

Have a great day!!

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