What is another name for the addition method to solve a system of equations in two variables?

The process of converting a quadratic function to vertex form.

In math quadratic function is defined as a polynomial where the highest degree of any variable is 2.

Here we have to write the steps to convert the a quadratic function to vertex form.

Here we have to convert quadratic equation from standard form to vertex form

Let us consider that the given quadratic equation is given as,

=> y = ax² + bx + c { a, b, c € R, a ≠ 0}.

Here from the above equation we have to take a as common from the terms containing x.

then the equation is rewritten as,

=> y = a(x² + bx/a) + c

In order to Complete the square inside the bracket by adding and subtracting (b/2a)², then we get,

[tex]y=a[x^2+\frac{bx}{a} +(\frac{b}{2a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]

When we factorize it, then we get,

[tex]y=a[(x+\frac{bx}{a})^2 - (\frac{b}{2a})^2 ]+ c[/tex]

Rewrite it as follows:

[tex]y=a[x+\frac{bx}{a}]^2 - (\frac{b}{2a})^2+ c[/tex]

Let us consider that the value of

=> h = -b/2a and k = c - b²/4a

Then we get the vertex form of the expression as,

=> y = a(x - h)² + k.

To know more about expression here.

https://brainly.com/question/14083225

#SPJ4

Answer:

d) 0.1a

e) -5.2m^2 + 7.8m + 4.5k

f)[tex]4g^{2}[/tex]

g)-3t^2 +4.29t+9

h)4n

i)2.6g^2 -5.4g

Step-by-step explanation:

Hope this helps!

The surface area of a square pyramid with base length of 3 ft. and height of 6 ft. is 45 square ft. (option A)

The formula for the surface area of a square pyramid is given by:

A = a² + a  √(a² + 4h²)

Where:

A = surface area

a = base length

h = height of the pyramid

In the given problem, the side length of the base = W = L = 3 ft.

Hence,

a = 3 ft.

h = 6 ft.

Plug these parameters into the formula:

A = 3² + 3 x √(3² + 4x6²)

A = 9 + 3 x √153

A = 45 ft². (option (A)

Learn more about pyramid here:

https://brainly.com/question/27523686

#SPJ4

Answer:

C. Functional

Step-by-step explanation:

I hope I helped you,

Alex Martin :)

There are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The number of non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the number of solutions to the equation x1 + x2 + x3 + x4 = 6, which is the number of ways to place 6 distinguishable balls into 4 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the equation x1 + x2 + (x3/2) + (x4/2) = 6. The variables x1, x2, x3 and x4 are non-negative integers, thus (x3/2) and (x4/2) are also non-negative integers.

The number of solutions to x1 + x2 + (x3/2) + (x4/2) = 6 is equivalent to the number of ways to place 6 distinguishable balls into 3 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20.

Because each of x1 and x2 are integers and (x3/2) and (x4/2) are integers, it ensures x1, x2, x3, and x4 are also integers. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

Learn more about Non Negative Integer here:

https://brainly.com/question/16155009

#SPJ4

To plot the graph of the given quadratic function y = 2x², evaluation the value of the function for several values of x  at the left and right side of the origin, then plot the data.

The standard form of a quadratic function is:

y = f(x) = ax² + bc + c

Steps to plot the graph of a quadratic function includes:

However, in the given function y = 2x²,  x-intercept, y-intercept, and the extreme point are all (0,0) or the origin. Hence, we need to use auxiliary points.

Evaluate the value of y for several values of x in the left and right of the extreme value, (0,0). The results are given in the following table.

x  y

-5  50

-4  32

-3  18

-2  8

-1  2

0  0

1  2

2  8

3  18

4  32

5  50

Plot the data and we get the graph of y = 2x² ( as in the attached picture)

Learn more about graph here:

https://brainly.com/question/29175470

#SPJ4

Inconsistent Pair of Linear Equations is the type of system of linear equation which has no solution notice that the two lines are parallel and will never intersect.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

Learn more about linear equation

brainly.com/question/1189779

#SPJ4

Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

Answer:

For f(1), it's -14. For determining x, x = -1.

Step-by-step explanation:

For f(1), just plug in 1 to x. -6(1) is -6, + -8 is -14.

For determining x, if you plug in -1, you get -6(-1), which is +6. +6 -8 is -2.

Answer:

c)   (0,6) and (-5,-9)

Step-by-step explanation:

if you graph the system you will get a line and a parabola

the two points at which they intersect will be (0,6) and (-5,-9)

Answer:

6.3

Step-by-step explanation:

70+7x=114.1

7x=44.1

x=6.3

mark brainliest

The original price of the shiny key chain that Zachary wants to buy, can be found to be $ 1.33

The question notes that there is a sale going on where the items on sale are being discounted by 25 %. This means that the current sale price of the shiny key chain as $ 1, is actually 25 % less than the original price.

The original price of the shiny key chain can then be found by the formula :

= Sale price / ( 1 - sales discount percentage )

= 1 / ( 1 - 25 %)

= 1 / 0. 75

= $ 1.33

Find out more on original price at https://brainly.com/question/811730

#SPJ1

The full question is:
A sale says that all items are 25% off. Zachary wants to buy a shiny key chain. The sale price is $1. What was the original price?

We can see from the graph that the temperature decreases with increasing time. As a result, the two quantities temperature and time are inversely proportional to one another. The necessary relationship between these quantities is  x ∝ 1/y or x = k(1/y)

The two are said to be inversely proportional when one quantity's value increases relative to another's decline or vice versa. It suggests that in nature, the two quantities behave in opposite ways. Taking time and speed as an example, they are inversely related. Speed increases result in a shorter amount of time.

Other names for this type of proportion that are also used in this context are reciprocal proportion, inverse proportion, varying inversely, inverse variation, and inverse variation. Let's use the example of x and y to illustrate the relationship between the two variables.

x ∝ 1/y or  x ∝ y⁻¹

Learn more about inversely proportional

https://brainly.com/question/29597811

#SPJ1

Answer:7

Step-by-step explanation: 21/3 = 7

Answer:

1/7 km/min

Step-by-step explanation:

Divide/simplify the two values, 3/21 = 1/7

The values of x that are solutions to the equation 10x²-64 36+6x² are x = 5, x = -5, x = -10, and x = 10.

Equation is a statement of equality between two expressions that states that they have the same value. Equations can be used to solve problems, model real world situations and describe relationships between different quantities. Equations can be expressed in many different forms, such as linear equations, quadratic equations, exponential equations and more. Equations are a powerful tool for understanding and describing the world around us.

The solutions to the equation 10x²-64 36+6x² are B. x = 5, C. x = -5, E. x=-10, and F. x= 10. These values represent the x-coordinates of the points in which the equation cuts the x-axis. The equation does not have a solution for x= -√√5 or x = √√√5, so these answers are incorrect.

To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1

Option C better choice, the measurement of the line segment RS is equal to x+5.which is difference of segment TR and TS.

A line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints.

There is a point S between the line segments T and R, measure of segment TR is 4x+1 and the measure of segment TS is 3x-4.

we shall find out the measure of RS.

so, length of RS is equal to difference of TR and TS.

Mathematically,

RS=TR-TS

RS=(4x+1) -(3x-4)

RS=4x+1-3x+4

RS=x+5

Hence the length of RS is equal to x+5.

learn more about segment.

https://brainly.com/question/12961019

#SPJ4

Answer:

x=1

Step-by-step explanation:

If y=6x+1, we can substitute that into the original equation, so it would look like 3x+6x+1=10.

Now we just solve for x. Add 3x and 6x to get 9x, and subtract 1 from both sides of the equation, now we have

9x=9, divide both sides by 9 and we end up with x=1.

PS. sorry for the bad handwriting but i attached a photo of how i solved it.

The area of the regular decagon is 496.7 squared unit.

In geometry, a decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon.

To calculate the area of the decagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Learn more about here: https://brainly.com/question/29456443

#SPJ1

To add two mixed numbers, you can separate the whole number and fraction parts. Add the whole numbers together as you normally would, and then find a common denominator to add the fractions. Once you have your sum, you may need to simplify the fraction for your final answer.

To learn more about number refer to:

https://brainly.com/question/17200227

#SPJ1

1/2 is not a whole number.

We know that the whole numbers are numbers that include natural numbers and zero.

That is the set of whole numbers is denotes by W = N ∪ {0},

here N represents the set of natural numbers.

And we know that the natural numbers are nothing but the numbers which can be counted and start from 1 and ends at infinity.

i.e., the set of natural numbers N = {1, 2, 3, . . ., ∞}

and the set of whole numbers W =  {0, 1, 2, 3, . . ., ∞}

A set of whole numbers do not include fractions, decimals, or negative integers.

Here, 1/2 is a fraction (number of the form p/q where q ≠ 0)

So, given number 1/2 is not a whole number.

Learn more about the whole number here:

https://brainly.com/question/29766862

#SPJ4

Answer:

О   XY

Step-by-step explanation:

The chord is a segment that joins two points of a circumference and differs from the diameter because it passes through the central point of the circle.  

The units that is appropriate for the time the number of bacteria is 300 is seconds.

The population of bacteria in a petri dish doubles every 40 seconds. The population of the bacteria is initially 400 organisms.

Therefore, the units that is most appropriate for the time at which the number of bacteria is 300 can be calculated as follows:

The bacteria population doubles every 40 seconds. Therefore, the units appropriate for when the population of the bacteria is 300 is second.

learn more on units here: https://brainly.com/question/30280964

#SPJ1

Answer:  (x*4) - 3= 11.   X = 3.5

Step-by-step explanation

(4x) - 3 = 11 or (x*4) - 3 = 11.

11 + 3 = 14

So then,

14 = x * 4 (or 4x)

14 / 4 = 3.5

so,

X = 3.5

The given point and parallel to the given line is: y - 5 = 0 (Slope is 0)perpendicular to the given line is: y - 5 = -1/6x (Slope is -1/6).

Slope-intercept is a form of linear equation which is written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form of equation is useful for graphing linear equations, as it allows the user to quickly determine the slope and the y-intercept of the equation, which makes it much easier to plot on a graph. It is also helpful for solving linear equations, as the slope and the y-intercept can quickly be determined.

(a) The slope-intercept form of the equation of the line through the given point and parallel to the given line is y = 5. This is because the given line has a slope of 0 and the given point has a y-coordinate of 5, which is the same as the y-intercept of the parallel line.

(b) The slope-intercept form of the equation of the line through the given point and perpendicular to the given line is y = -6x + 5. This is because the given line has a slope of 0 and the line perpendicular to it has a slope of -1/0, which is -infinity. This means that the slope of the perpendicular line is -6 and its y-intercept is 5, which is the same as the given point's y-coordinate.

To know more about slope intercept click-
https://brainly.com/question/1884491
#SPJ1

Answer: 24%

Step-by-step explanation: 48 out of 200 is 24%, meaning that 48 is 24% of 200. To find our answer, we follow two simple steps before we add the percentage symbol, though there can be three steps if we have to round a decimal in a percentage to two digits after the decimal point.

Answer:24%

Step-by-step explanation:

Answer:

Price after discount: $33.75

You saved: $11.25

Step-by-step explanation:

Answer:

3515.3443 grams

Answer: can you help me i cant put a q     i have to points

Step-by-step explanation: plssssssssssssssss      

A customer wanted to purchase a video game and realized that they were short $4.28 to be able to pay. Which value is the opposite of being short $4.28

The Production Possibility Frontier (PPF) is often called the "Opportunity Cost Curve" because it illustrates the concept of opportunity cost.

Opportunity cost is the cost of one alternative in terms of the benefits forgone of the best alternative. In other words, it's the cost of one choice in terms of the best alternative choice.

As we move along the PPF, we can see that as we produce more of one good, we must give up some production of the other good. This trade-off is represented by the slope of the PPF, which is the opportunity cost of producing one good in terms of the other good. The PPF illustrates the relationship between production and opportunity cost by showing the trade-offs that must be made and the opportunity costs associated with different production choices.

To know more on production possibility frontier

brainly.com/question/27833900

#SPJ4

Answer:

(x+8)^2=40

Step-by-step explanation:

x^2+16x+24=0.

Well, to solve for this, you do:

1. (16/2)^2 to find what number should be in place of 24.

That, by the way, is 64.

2. There's no 64! We have to add 64-24 on both sides, which makes the equation

x^2+16x+64=40.

3. Since we know that (16/2)=8, using the completing the square formula, you know that it's going to be a variation of (x+8)^2 or (x-8)^2.

As we are adding for the middle term, it must be (x+8)^2.

4. Answer: (x+8)^2=40.

Sorry if this is too late :)