MATHEMATICS HIGH SCHOOL

Based on the information below, what are the values of x and y of the solution to the system of equations used to create the information? [A]=[4 -6 8 -2][Ax]=[38 -6 26 -2][Ay]=[4 38 8 26]x = -5, y = 2
x = -0.2, y = 0.5
x = 0.5, y = -0.2
x = 2, y = -5

Answers

Answer 1

Answer:

The correct option is D. x = 2, y = -5. The values of x and y of the solution to the system of equations are 2, -5.

When solving a set of equations in mathematics, a matrix is a collection of integers or expressions.

The matrix A is

[A]=[4 -6 8 -2]

The matrix Ax is

[Ax]=[38 -6 26 -2]

The matrix Ay is

[Ay]=[4 38 8 26]

All of the matrices' determinant is

|A| = 40

|Ax| = 80

|Ay| = -200

The value of x is (|Ax|) /(|A|) = 80/(40) = 2

The value of y is ( |Ay|)/(|A|) = -200/(40) = -5

Therefore, the value of x and y is 2, -5. The correct option is D

Learn more about system of equations here

brainly.com/question/25869125

#SPJ1

Related Questions

A student heats 100 g of aluminum to 60°C. He places it in 100 g of water at 20°C. Over time, what will most likely happen?a. The water's temperature will increase slightly, and the metal's temperature will decrease a lot. b. The water's temperature will increase a lot, and the metal's temperature will decrease slightly. c. The water's temperature will decrease slightly, and the metal's temperature will increase a lot. d. The water's temperature will increase by about the same amount as the metal's temperature decreases.
Jen wants to tile the floor of her kitchen . The floor is recrangular and measures 12 feet by 8 feet. If it costs $2.50 per square foot for the materials, what is the total cost of the materials, what is the total cost of the materials for tiling the kitchen floor?
Given the 2 functions find (f+g)(X)
If it costs $3 per hour to park in a parking lot, with a maximum cost of $12 Explain why the amount of time a car is parked is not a function of the parking cost
Solve for "z" 6=z/5.9

In Andrew’s Furniture Shop, he assembles both bookcases and TV stands. Each type of furniture takes him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.

Answers

Answer:

6 bookcases
12 TV stands

Step-by-step explanation:

Given Andrew has $600 for materials and can make 18 pieces of furniture, you want to know the number of each kind that maximizes profit if each bookcase costs $20 and gives $60 profit, while each TV stand costs $40 and gives $100 profit.

Setup

If x and y represent the numbers of bookcases and TV stands Andrew builds, respectively, then he wants to ...

maximize 60x +100y

subject to ...

x + y ≤ 18
20x +40y ≤ 600

Solution

The attached graph shows the solution space for these constraints. The profit is maximized at the vertex of the space where the profit function line is farthest from the origin. Andrew maximizes his profit by building ...

6 bookcases
12 TV stands

Final answer:

Andrew needs to solve a linear programming problem to find how many bookcases and TV stands he should manufacture for optimal profit. This is done by setting up and solving inequalities representing Andrew's time and material cost constraints, graphing the feasible region, and finding the point(s) in this region that yield the highest profit.

Explanation:

This question deals with the topics of linear programming and profit maximisation. Here, Andrew has to decide how much of each type of furniture, bookcases or TV stands, he should produce to maximise profit while considering time and material cost constraints.

From the given conditions, we get two inequalities. The first related to time says that the total number of bookcases and TV stands is less than or equal to 18: let bookcases be x, TV stands be y, thus we have x + y <= 18. The second involving the cost of material says that the total cost spent on materials for both products does not exceed $600: thus, we also have 20x + 40y <= 600.

You can graph these inequalities on the x-y plane to get a visual representation of the possibilities.

Finally, to find the optimal solution (i.e., the highest profit), you calculate the profit function P = 60x + 100y for each point in the feasible region and select the point that provides the highest profit.

Learn more about Linear Programming here:

brainly.com/question/34674455

#SPJ3

Is LNM =(~) OQP? If so, name the postulate that applies.

Answers

Answer:

The postulate that applied if $\triangle L N M \cong \triangle O Q P$ is an option (b) Congruent -ASA.

Step-by-step explanation:

What is Congruent -ASA?

By the Congruent -ASA rule, two angles in one triangle are congruent with two angles in a second triangle, and if the sides included in both triangles are also congruent, then the triangles are congruent.

Determine the postulate if $\triangle L N M \cong \triangle O Q P$ :

Given:

$&\overline{\mathrm{LM}} \cong \overline{\mathrm{OP}} \n$

$&\overline{\mathrm{MN}} \cong \overline{\mathrm{PQ}} \n$

$&\angle \mathrm{M} \cong \angle \mathrm{P}$

Here, the answer is obvious from the question,

$\angle \mathrm{M}$ is LM and MN's Angle.

$\angle P$ is PQ and PO's Angle.

Hence, it is ASA.

So, if the angle $\triangle L N M \cong \triangle O Q P$ , then the postulate that is applied is Congruent -ASA.

To learn more about Congruent -ASA here:

brainly.com/question/10349343

Yes; LNM ~ OQP because of the SAS~ postulate

If 3 cats catch 3 rats in 3 minutes, how many cats will catch 100 rats in 100 minutes?

Answers

3 cats can catch 3 rats in 3 minutes ==> 1 rat per minute.

It takes 3 cats to catch 1 rat per minute.

100 rats in 100 minutes ==> 1 rat per minute

The same 3 cats can do it, if they don't wear out and take naps.

A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solve an equation to find the price of each shrub.A. 9p + 11.5p = $94.75; p = $4.62

B. 9(p + $11.50) = $94.75; p = $5.00

C. 9p + $11.50 = $94.75; p = $11.75

D. 9p + $11.50 = $94.75; p = $9.25

Answers

Based on the data provided if the customer went to the shop and bought the potting soil and shrubs with the total bill of $94.75 and the potting soil alone is for $11.50. We can determine the price of the shrubs in total by deducting the 2 values. $94.75 - $11.50 = $83.25. Now that we have the total amount of the shrubs to get the amount of each shrub we then divide the total amount versus the number of shrubs which is 9, ergo $83.25/9 = 9.25 per shrub.

So the answer to this question is:

D. 9p + $11.50 = $94.75 p=$9.25

In Chemistry class, Andrew has earned scores of 64, 69, and 73 on three tests. He must maintain an average of 70 to pass the course. What score must Andrew earn on the final exam to pass the course?