Solve the system of linear equations by graphing.2x + 3y = 16.9
5x = y + 7.4
What is the solution to the system of linear equations? Round to the nearest tenth as needed.
Answers
2x + 3y = 16.9
3y = -2x + 16.9
y = (-2/3)x + 16.9/3
5x = y + 7.4
5x - 7.4 = y
So in the graphing calculator,
Y1 = (-2/3)x + 16.9/3
Y2 = 5x - 7.4
Then find the point of intersection and the x value of that would be the solution.
You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1
Taking into account the definition of a system of linear equations, the solution to the system of linear equations is x=2.3 and y=4.1
System of linear equations
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
This case
In this case, the system of equations to be solved is
There are several methods to solve a system of equations, and it is decided to solve it using the graphical method, which consists of representing the equations on a graph, in the same coordinate system. The intersection of the lines representing the equations is the solution of the system.
In this case, the graph is observed in the attached figure, where it can be seen that the intersection of both lines is the point (x,y)= (2.3,4.1).
Finally, the solution to the system of linear equations is x=2.3 and y=4.1
Learn more about system of equations:
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Answers
If the ladder is 15 feet long, then what is the angle at which the ladder is leaning?
Answers
The angle at which the ladder is leaning is 62.18°.
What is trigonometry?
Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.
For the given situation,
The length of the ladder = 15 feet
The distance between the house and the ladder base = 7 feet
The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.
we know that, θ =
The figure below shows the relationship between the sides.
⇒ θ =
⇒ θ =
⇒ θ =
Hence we can conclude that the angle at which the ladder is leaning is 62.18°.
Learn more about trigonometry here
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Answer:
62.182°
Step-by-step explanation:
Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.
Answers
5(x - 8) - 7 = 40
B)
5(8 - x) - 7 = 40
C)
7(x - 8) - 5 = 40
D)
7(8 - x) - 5 = 40
Answers
Answer : D 7(8-x)-5 = 40
The product of eight minus a number and seven equals forty when decreased by five
Let the unknown number be x
eight minus a number means 8 -x
For product we multiply
The product of eight minus a number and seven
It means the product of 8-x and 7
So expression becomes 7(8-x)
The product of eight minus a number and seven equals forty when decreased by five
To decrease by 5 we subtract 5
7 (8-x) -5 and this equals 40
So equation becomes 7(8-x)-5 = 40
let X = unknown number
eigth minus a number is 8 - x. since the product is seven and eight minus a number then 7 * [8-x] or 7(8-5).
40 is its equivalent when the product is decreased by 5; therefore, 7(8-x) - 5= 40.
Answers
Let's say that the two points we are given is
Another thing to keep in mind:
When you have 0 in the numerator, and a number in the denominator, that means that the slope is 0.
When you have 0 in the denominator, and a number in the numerator, that means that there is no slope, or that the slope is undefined.