What type of solutions do the methods for solving systems of equations find and how does this relate to setting the equations equal to each other?

Answers

Answer 1

Answer: A system of equations is a set of two or more equations that share two or more unknowns. The solutions to a system of equations are all the values that make all of the equations true, or the points where the graphs of the equations intersect. We can solve a system of linear equations through graphing, substitution and linear combination. Systems of nonlinear functions, such as quadratic or exponential equations, can be handled with the same techniques.

Answer 2

Answer:

Final answer:

Methods to solve systems of equations typically find the values of variables that satisfy all equations in the system, relating this to setting equations equal to each other. Common methods include substitution, elimination, and graphing for linear equations, and factoring, using the quadratic formula, or completing the square for quadratic functions.

Explanation:

Methods for solving systems of equations often result in finding the values of variables that satisfy all equations in the system simultaneously. This is directly related to setting the equations equal to each other because when we equate two or more equations, we are essentially looking for their common solutions or intersection points. For instance, consider two equations y = b + mx and y = ax^2 + bx + c, linear and quadratic respectively. In order to ascertain their intersection points or common solutions, you would have to set them equal to each other, thus leading to a new equation, ax^2 + bx + c = b + mx.

The process of solving systems of equations underlies various natural phenomena and engineering processes; knowing the methods to handle these equations is crucial. For linear equations, common methods include substitution, elimination, and graphing. For quadratic functions, solutions can often be found using factoring, using the quadratic formula, or, if necessary, completing the square.

In the context of real-world applications, understanding how systems of equations function can play a part in everything from kinematic problem-solving to interpreting rates of change in scientific or technological processes. Such knowledge, then, is indispensable to anyone seeking to manage these processes effectively.

Learn more about Systems of Equations here:

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Do you mind helping me :)

Answers

Answer:

B: 1 1/2

Step-by-step explanation:

just do 5.75 - 4.25 and that gives you 1.5 which is the same as 1 1/2

Answer:

1 1/2. That's Answer B

Step-by-step explanation:

The scale divisors are 1/4 unit apart. Thus, the length of the red segment is 6 units, or 6/4, or 1.5, or 3/2. That's also 1 1/2. That's Answer B.

Write the equation For a Line that intersects points(1,3) And (2,5) which one is a.y=x+2 B.y=2x+1. C.y=3x-3. D.Y=-x+3 For me is letter B.please help

Answers

$(1,3) ,\ \ (2,5) \n \n \n First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \n \n m= (y_(2)-y_(1))/(x_(2)-x_(1) ) \n \nm=(5-3)/(2-1) = (2)/(1)=2 \n \nNow \ use \ y = mx + b \ with \ either \ point \ to \ find \ b, \ the \ y-intercept \ : \n \n y=mx+b \n \n3=2 \cdot 1+b\n \n3= 2 +b \n \nb=3-2=1 \n \n y=2x+1 \ is \ the \ answer \ B$

$3=a\cdot1+b\n 5=a\cdot2+b\n\n b=3-a\n 2a+b=5\n\n 2a+3-a=5\n a=2\n\n b=3-2\n b=1\n\n y=2x+1 \Rightarrow B$

If the midpoint between (18, y) and (20, -15) is (19, -5), find the value of y.

Answers

$(18, y) \ and \ (20, -15) \ is \ (19, -5) \n \n(x _(m),y _(m)) =[ (x_(1) +x _(2))/(2) , (y _(1)+y _(2))/(2)] \n \n (19,-5)= [(20+19)/(2),(y-15)/(2)] \n \n(19,- 5)= [19,(y-15)/(2)] \n \n -5= (y-15)/(2) \ \ / *2\n \n-10 = y-15\ \ | +15\n \ny=-10 + 15 \n \n y = 5\n \n(19,- 5)= [19,(5-15)/(2)] \n \n(19,- 5)= ( 19,-5) \n \n \n Aswer : y = 5$

What’s 222,702 to the nearest ten thousand

Answers

220,000 is the answer! have a good day

Add and subtract functions

Answers

Answer: $3x^2+5x+3$

Step-by-step explanation:

For this exercise you need to remember the multiplication of signs:

$(+)(+)=+\n(-)(-)=+\n(-)(+)=-\n(+)(-)=-$

You know that the function f(x) is:

$f(x)=5x+3$

And the function g(x) is:

$g(x)=3x^2$

Then to find $(f+g)(x)$ you need to add the function f(x) and the function g(x) by adding (or combining) the like terms, you get that the sum is the following:

$(f+g)(x)=(5x+3)+(3x^2)$

$(f+g)(x)=5x+3+3x^2\n\n(f+g)(x)=3x^2+5x+3$

As you can notice, when you add the functions given in the exercise, you get a Quadratic function, which is a function whose highest exponent is 2 and has this form:

$f(x) = ax^2 + bx + c$

Where "a", "b", and "c" are numbers ( $a\neq 0$ )

A circle has a radius of 12 cm. If the radius of the circle is increased by a factor of 7, how many times larger will the circle's circumference be?

Answers

Considering it's own equation, the circumference of the circle will be increased by a factor of 7.

What is the circumference of a circle?

The circumference of a circle of radius r is:

$C = 2\pi r$

Since the radius is elevated to power 1, if it is multiplied by a factor of 7, the circumference of the circle will also be increased by a factor of 7.

More can be learned about the circumference of a circle at brainly.com/question/20489969

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