Peter bought an 18-ounce box of cereal for $4.50. What was the cost per ounce?

Solve the system by using a matrix equation

Sergeu [11.5K]

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as $\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]$

A= $\left[\begin{array}{cc}6&-9\\3&4\end{array}\right]$

X= $\left[\begin{array}{c}x\\y\end{array}\right]$

B= $\left[\begin{array}{c}3\\7\end{array}\right]$

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

= (-24)-(-27)

= (-24) + 27 = 3

so, |A| = 3

Adj A= $\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]$

A⁻¹ = $\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]$ /3

A⁻¹ = $\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]$

X= A⁻¹ B

X= $\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]$

X= $\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]$

X= $\left[\begin{array}{c}-4+21\\-3+14\end{array}\right]$

X= $\left[\begin{array}{c}17\\11\end{array}\right]$

x= 17, y= 11

solution set= (17,11).

6 0

3 years ago

Read 2 more answers

What is the length of a 50-inch TV that has a width of 27 inches?

drek231 [11]

Answer:

42.08inches

Step-by-step explanation:

Given data

SIze of TV= 50 inch

Width= 27inches

Length= ??

Applying Pythagoras theorem

z^2= x^2+y^2

50^2= x^2+27^2

square root both sides

50^2= x^2+27^2

2500= x^2+ 729

2500-729=x^2

1771=x^2

x= √1771

x= 42.08

Hence the lenght is 42.08inches

7 0

2 years ago

What is the MAD of 0 0 0 1 3 and 8

IgorLugansk [536]

The Mean Absolute Deviation is - 0 +0+0+1+3+8 = 24/ 6 which would = 4 that's the answer to your question .

Hope that it helps .

7 0

3 years ago

Sugar was traditionally produced and sold as sugarloaves, which are cones of sugar wrapped in paper. Find the total surface area

Zolol [24]

Answer:

A = 326,73 cm²

Step-by-step explanation:

The area of a circular cone is area of the base (A₁ ) plus area lateral ( area of a circular sector of radius the slant height )

Then we proceed to calculate the area of the base A₁

diameter of circular base is 8 cm then the radius is 4 cm and the area is:

A₁ = π*r² = 3,14* (4)²

A₁ = 3,1416*16 = 50,2656 cm²

Now Lateral area of the cone (A₂) is equal to the area of a circular sector with radius the slant height. We will calculate it, taken into account that this circular sector is part of a circle of radius the slant height.

Between the area of circular sector with radius the slant height and the area of the circle with the same radius there is a linear relation. That is we can calculate area of a circular sector by rule of three as follows:

The length of the circular sector is the length of the circle of the base of the cone, that is:

L = 2*π*(4)

L = 2*3,1416*4

L = 25,1328 cm

Then we have a circular sector of length 25,1328 cm

The area of the circle of radius 22 cm is:

A(c) = π*(22)² ⇒ A(c) = 1520,5344 cm²

And the length of this circle is:

L(c) = 2*π*(22) ⇒ 138,2304 cm

Then we apply a rule of three

For a length of 138,2304 cm ⇒⇒⇒ (area) 1520,5344 cm²

Then for a length of 25,1328 cm ⇒⇒⇒(area) A₂ (??)

Therefore:

A₂ = (25,1328)*1520,5344)/ 138,2304

A₂ = 276,4608 cm²

Then total area of the cone is:

A = A₁ + A₂

A = 50,2656 +276,4608

A = 326,7264 cm²

Round answer A = 326,73 cm²

8 0

3 years ago

Read 2 more answers

Can someone please help me with this question

bezimeni [28]

Answer:

21x^2-2x+1

Step-by-step explanation:

The area of shaded region= The area of the floor - area of the identical islands

The area of shaded region=(5x+1)^2-2*(2x)(x+3)=25x^2+1+10x-4x^2-12x=21x^2-2x+1

6 0

2 years ago