Solve the quadratic equation below for the exact values of x.

Answer:

I know how to do this problem, but before I do, this isn't a live test, correct?

I recognize that your photo is from an eCampus quiz. I want to make sure I don't violate the honor code when answering.

The area of the given rectangle will decrease by 9 % .

What is a rectangle?

The rectangle is a geometrical figure in which opposite sides are equal.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width ).

Area of rectangle is given by = Length ( L ) × Width ( W )

The length of a rectangle is increased by 30%

New length L' = 1.3L

width of the same rectangle is decreased by 30%

New width( W' ) = 0.70W

Now,

New area = L'W'

1.3L × 0.70W = 0.91LW = 0.91 Old area

Hence the percentage decrement

(Old area - 0.91 old area)/old area  × 100 = 9%.

Hence, The area of the given rectangle will decrease by 9 %

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Answer:

width = 8 inches

Step-by-step explanation:

⭐ What is the formula for the perimeter of a rectangle?

We are given that the length is 14 inches longer than the width, and the perimeter of the rectangle is 60 inches.

So, let's substitute these values into the perimeter formula and solve for the width. Let w = width.

[tex]60 = 2(14 + w) + 2(w)[/tex]  Multiply the 2 into the parentheses

[tex]60 = 28 + 2w + 2w[/tex]       Add like terms (terms with the same variable)

[tex]60 = 28 + 4w[/tex]                Subtract 28 on both sides

[tex]32 = 4w[/tex]                        Divide both sides by 4 to isolate the variable

[tex]8 = w[/tex]

∴ The width is 8 inches.

The percent of 3 to 1 is:

Slope Ratio: 3:1 or 3 to 1

Percent Slope: 33%

There is a picture of what the slope is down below:

Therefore, The percent of 3 to 1 is:

Slope Ratio: 3:1 or 3 to 1

Percent Slope: 33%

Using the sample mean and the provided sample size, We can find the sample standard deviation by using the formula  [tex]\sqrt \frac {\sum {(x-\bar x)^{2}}}{n-1}[/tex] .

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

sample mean = [tex]\bar x[/tex]

sample size = n

sample standard deviation = [tex]\sqrt \frac {\sum {(x-\bar x)^{2}}}{n-1}[/tex]

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An equation is considered linear if it is in the form of  [tex]y = mx + c[/tex] where m is the slope of the equation and b is the y-intercept.

Notice how here, x can only be to the power of one. In here, the conditions are just simply m,c ∈ R.

Some examples include [tex]y = 8x + 9, 2y = x-7, 8y=0[/tex] and even some like [tex]x=4[/tex].

As you can see here, all of the following equations are represented using a straight line.

An equation is considered “non-linear” when it is not graphed using straight lines. Some examples include [tex]y = 3x^{2} +8, 4y =2x^{4}-6, y = x^{5} +86[/tex].

In conclusion, a linear equation will always be in the form of , where m is the slope of the equation, and b is the y-intercept of the equation.

Note: To determine if an equation is a linear function, it must have the form  (in which m is the slope and b is the y-intercept). A nonlinear function will not match this form.

In a linear equation, the variables appear in first degree only and terms containing products of variables are absent. But in the case of nonlinear equations, at least one variable is not of the first degree or the equation contains a product of variables.

An equation is linear if its graph forms a straight line. This will happen when the highest power of x is . Graphically, if the equation gives you a straight line then it is a linear equation. Else if it gives you a circle, or parabola, or any other conic for that matter it is a quadratic or nonlinear equation.

If the highest power of x in the equation is one then it is a linear equation else if the power of x is greater than one then it is nonlinear.

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We can determine if this equation is a linear function or a nonlinear function by looking at their graph.

Simplify the equation as closely as possible to the form of y = ax + b.

On a Cartesian Plane, a linear function is a function where the graph is a straight line. The line can go in any direction, but it's always a straight line. The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power. When a linear function is written in its simplest form, it looks like[tex]y = a + bx[/tex], where [tex]a[/tex] and [tex]b[/tex] are both constants. For example, here are some linear functions:

y = 3 + 5x

y = 2 - 6x

y = 4x

On a cartesian plane, a non-linear function is a function where the graph is never a straight line it is always curved may be a parabola, hyperbola or something else. Non-linear functions all have atleast one variable raised to the power of two or more. There's no one formula for non-linear functions because they're all different. For example, here are some non-linear functions:

y = 3x^3 + x^2 - 7

y = 5x^5 - 3x^2 +2

We can determine if this equation is a linear function or a nonlinear function by looking at their graph.

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Answer:

[tex]\dfrac{28\sqrt{37}}{37} \approx 4.6\; \sf (nearest\;tenth)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Scalar projection}\\\\Scalar projection $=\dfrac{u \cdot v}{|u|}$\\\\where:\\ \phantom{ww}$\bullet$ $u$ is the vector being projected onto.\\\end{minipage}}[/tex]

Given:

Calculate the magnitude of vector u:

[tex]\implies |u|=\sqrt{(-1)^2+(-6)^2}=\sqrt{37}[/tex]

The scalar projection is the magnitude of the vector projection.

Therefore, the magnitude of the projection of vector v onto vector u is:

[tex]\implies \dfrac{u \cdot v}{|u|}=\dfrac{\langle -1, -6\rangle \cdot \langle-4, -4\rangle}{\sqrt{37}}=\dfrac{4 +24}{\sqrt{37}}=\dfrac{28}{\sqrt{37}}=\dfrac{28\sqrt{37}}{37}[/tex]

The value of the function c(n) = 20 + 20n at n = 5 will be 120.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that function, c is defined by the equation c(n) = 20 + 20n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.

The value of the function f(5) will be calculated as,

c(n) = 20 + 20n

c(5) = 20 + ( 20 x 5 )

c(5) = 20 + 100

c(5) = 120

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Answer:

18 and 21

Step-by-step explanation:

We take those two angles as 6x and 7x

133⁰ + 188° + 6x + 7x = 360(Sum of angles of a quadrilateral)

321+13x=360

13x=360-321

13x=39

x=39/13

x=3

6x=6x3=18

7x=7x3=21

In one (1) calendar year, a member may receive illness benefits for a maximum of 120 days. The total number of permitted compensable days for the next year cannot be increased by any unused fraction being carried forward.

Sickness benefits are paid for 91 days across two successive benefit periods and are equal to 70% of the average daily salary.

Enhanced Sickness Benefit: For male and female employees, respectively, this benefit is payable to insured people undergoing sterilization for 7 days and 14 days, and it is equal to their entire salary.

The member's daily Sickness Benefit allotment equals ninety percent (90%) of the credit for his or her average daily wage (ADSC). Up to 120 days can be received from the sickness benefit in a single (1) calendar year.

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Answer:

A. y = –0.2x + 2

Step-by-step explanation:

It is a negative slope and intersects at (0, 2).

Answer: A. y = –0.2x + 2

Step-by-step explanation:

     We see that the answer options are in slope-intercept form, so we will find the slope and the y-intercept of this line to write our equation.

     The line intercepts the y-axis at (0, 2), so the ending of our equation will be "+ 2" for the intercept.

     Next, we will find the slope. We see that for everyone one unit moved downward, there is 5 units right. This becomes a slope of -1/5, which is the same as -0.2.

     Using these details, the correct answer is;

            A. y = –0.2x + 2

Answer:0

Step-by-step explanation:y=1/2x

straight lines are of the y=mx+c

The c value is where the graph cuts the y axis or the y intercept

as there is no value there c=0

or y intercept =0

Answer:

s (50) c (20) s (50) c (20) = 0

Step-by-step explanation:

Hope this helps

4x+5y=20 in slope intercept form would be y= (-4/5)x + 4.

What do you mean by slope?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

4x + 5y = -20

-4x            -4x

5y = -4x - 20

divide it all by 5

y = -4/5x - 4

Slope intercept form is y=mx+b. So you would first subtract 4x from both sides. This ends up being 5y= -4x +20. Then divide both sides by 5. This gets you y= (-4/5)x +4.

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Answer:balls

Step-by-step explanation:

balls

The y-intercept of the equation of the line is 5

The slope-intercept form of a line is given by

Here m is the slope of the line and c be the y-intercept

Here we have

Lincoln is going to use a computer at an internet cafe.  

The equation that represents the total cost of using the computer in t minutes is given by C = t +5  

Here the given equation resemblance the slope-intercept form

y = mx + c  

As we know in y = mx + c

The y-intercept of the line will be c

When we compare C = t + 5 with y = mx + c

=>  c = 5

Therefore,

The y-intercept of the equation of the line is 5

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The square has a 48 centimeter perimeter.

To find the perimeter of the square, we need to calculate its side length. The area of a rectangle is given by its length multiplied by its width, so we can use the given measurements of the rectangle to calculate its area: 25 cm x 16 cm = 400 cm². The area of a square is given by the square of its side length, so we can use the area of the rectangle to calculate the side length of the square: √400 cm² = 20 cm.

Thus, the perimeter of the square is equal to 4 times its side length, or 4 x 20 cm = 80 cm.

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The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.

V∝ n at constant P and T

V = constant × (n)

Vn = constant

This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.

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To simplify a complex fraction expression, first identify the numerator and denominator of each fraction.

A complex fraction is a fraction that contains one or more fractions in the numerator, denominator, or both. This type of fraction requires additional steps to simplify and can often be reduced to a simpler fraction or a whole number. Complex fractions are also known as compound fractions or nested fractions.

Then, factor each fraction into its simplest form by dividing each numerator and denominator by their greatest common factor. Finally, combine the fractions by multiplying the numerators and denominators. This will result in a simplified expression.

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The factors of the quadratic expression 3x² + 7x + 2 are 3x + 1 and x + 2.

We know for a quadratic expression of the form ax² + bx + c, the sum of the roots is -b/a and product of the root is c/a.

So in the given case

a = 3

b = 7

c = 2

Let the roots be α and β, therefore

α + β = -b/ a = -7/ 3

Also αβ = 2/3

We can find α and β by trial and error method. Else using the identity (a+b)² = a² + 2ab + b² and  (a-b)² = a² - 2ab + b², we get

(a - b)² = (a + b)² - 4ab

Therefore

(α - β)² = (α + β)² - 4αβ

(α - β)² = (-7/ 3)² - 4×2/3

(α - β)² = 25/9

Assuming α>β,

α - β = 5/3

So solving α + β = -7/ 3 and α - β = 5/3, α = -1/ 3 and β = -6/3 = -2

Therefore simplifying

3x² + 7x + 2

= 3(x + 1/3)(x + 2)

= (3x + 1)(x + 2)

--The question is incomplete, answering to the question--

"What is the factor of 3x² + 7x + 2?"

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Answer:

One is 30,000 and the other is 300

Relation between base and height of parallelograms is a function  [tex]f(x)=\frac{48}{x}[/tex].

Relations called functions provide an output for each input. The characteristic that every input is associated to exactly one output defines a function as a relation between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Based on the values listed in the table for the parallelograms' base length and height, you can see that the base length grows by one unit, giving you the numbers 1, 2, 3, and 4. When base length increases by one unit, height reduces by 1/x, as shown in the following example:

Height and base length have the following relation:

[tex]f(x)=\frac{48}{x}[/tex]

where x is the base length and f(x) is the height. 

[tex]f(1)=\frac{48}{1}= 48\\f(2)=\frac{48}{2}=24\\f(3)=\frac{48}{3}=16\\f(4)=\frac{48}{4}=12\\f(6)=\frac{48}{6}==6[/tex]

Relation between base and height of parallelograms is a function  [tex]f(x)=\frac{48}{x}[/tex].

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Therefore , we can explain square roots to the child with the help of following explanation and examples.

A number's square root, which is the result of multiplication by itself, yields the original number. Some examples of exponents are squares and square roots. Imagine the number twenty five. Additionally, this can be expressed as expression of  5x5.

Here,

The square root is the same as the square in every way. You could think of it as the square's "root" or the number that was utilized to create the square.

The square root symbol is as follows:√

For example: √9 = √3*3 = 3

√25 = √5*5=5

√4 =  √2*2 = 2

are the square roots of the following numbers .

Here we can see it is very easy to calculate the square root

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Answer:No answer

Step-by-step explanation: Simplify like terms first if possible

on LS=-X+10X=9X

9X=9X+5

We need to get Xs on one side to solve equation

We aim to have the Xs on the left side

we take 9X from both sides

9X-9X=9X-9X+5

0=5

No solution

The steps for solving an algebraic problem can be summarized as follows Identify the problem and what you need to find (the variable). Determine what information you have about the problem, including any equations or other relevant information. Develop a plan for how to approach the problem and solve the variable. Implement your plan and perform the necessary calculations to solve for the variable. Check your solution to make sure it makes sense in the context of the problem and that it satisfies the original equation or conditions.

There are several basic steps that can help you solve algebraic equations in grade 6:

Here's an example of how to use these steps to solve an equation:

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A negative number is not a real number which, squared, is negative.  Hence square root of -4 undefined

What is the square root?

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is √ ​.Finding the square root of a number is the opposite of squaring a number.

According to the given question:

A negative number is not a real number which, squared, is negative.

You can't get square a number and get a negative. If you square a negative number, it'll become positive, therefore you can't square root a negative number because it doesn't exist. Hence square root of -4 is undefined.

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The answer to your Question is 3:8