You are planning on installing a security system at your home. For Safety First Security, you can get monitoring for $2 a day with a one-time set-up fee of $150. For Home Safety Security, you can get
monitoring for $1.50 a day with a one-time set-up fee of $200. Using substitution, find the number of days for which both companies would cost the same.

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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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:

[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]

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

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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Jose can build a wall in 10 hours. Frank can build the same wall in 15 hours. If they work together, they can paint wall in 6 hours.

The least common multiple, or LCM, of two numbers, such as a and b, is written as LCM in mathematics (a,b). The smallest or least positive integer that is divisible by both a and b is known as the LCM. Finding the prime factors of the provided integers and determining the least common multiple are both steps in the prime factorization process (LCM). For instance, use the prime factorization to couple the multiples that are shown to determine the least common multiple of 12 and 16. Together with the other multiples, list them.

Given,

Jose can build a wall in 10 hours

Frank can build the same wall in 15 hours

Together they can paint in,

Taking LCM

1/10 + 1/15

3/30 + 2/30

5/30

1/6

Time taken = 6 hours

If they work together, they can paint wall in 6 hours.

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If 10x +5 = 100, then x  is less than 10 without solving the equation, x will be multiplied with 10, and if 10 is mulptiplied with 10, it will givess 100, then 100 plus 5 will give 105 which is more than 100.

given the equation as 10x +5 = 100

then the equation can be rearranged as 10x = 100 - 5

this can be rearranged  by substracting 5 from 100, which is

10x = 95

then we can make x the subject of the formula as

x=95/10

= 9.5

hence x= 9.5

Therefore, if 10 is mulptiplied with 10, it will givess 100, then 100 plus 5 will give 105 which is more than 100.

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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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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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The strategy that can be used to prove that the diagonals of a parallelogram bisect each other is congruent triangles .

Given :

Let ABCD is a parallelogram with midpoint M .

To prove that he diagonals of a parallelogram bisect each other we have to go through the following steps:

Angle DBA is congruent to angle BDC.

Angle CMD is congruent to angle AMB.

Triangle CMD is congruent to triangle AMB.

Segment AM is congruent to segment MC.

M is the midpoint of segment AC.

Segment BD bisects segment AC.

Segment BM is congruent to segment MD.

M is the midpoint of segment BD.

Segment AC bisects segment BD.

Hence we have to use the concept of congruent triangles in order to prove that the diagonals of a parallelogram bisect each other.

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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:

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.

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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True. The random() method is a function that generates a random floating-point number between 0 (inclusive) and 1 (exclusive).

This means that the generated number will be greater than or equal to 0 and less than 1. For example, a call to random() might return a value like 0.342341, 0.859203, or 0.000001.

Here is an example of how the random() method can be used in Python to generate a random float between 0 and 1:

import random

# Generate a random float between 0 and 1

x = random.random()

print(x)

The output of this code might be something like 0.342341 or 0.859203.

Therefore, it's true that The random() method is a function that generates a random floating-point number between 0 (inclusive) and 1 (exclusive).

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This means that the generated number will be greater than or equal to 0 and less than 1. For example, a call to random() might return a value like 0.342341, 0.859203, or 0.000001.

Here is an example of how the random() method can be used in Python to generate a random float between 0 and 1:

import random

# Generate a random float between 0 and 1

x = random.random()

print(x)

The output of this code might be something like 0.342341 or 0.859203.

Therefore, it's true that The random() method is a function that generates a random floating-point number between 0 (inclusive) and 1 (exclusive).

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The mean and the standard deviation of the data of the purchase are 4.5 and 1.8 respectively.

According to the question we can interpret that either the candy will be blue or it will not be blue. We use the method of Binomial distribution because the probability of getting a blue candy is not dependent on any other candy. The formula for expected value of the distribution will be

Expected value = E(X) = np

The standard deviation will be

SD = √(np(1 - p))

Now, from the question, n = 15 and the value of p = 30% = 0.3

putting these values we get

Expected value = E(X) = 15×0.3 = 4.5

SD = √(15×0.3(1 - 0.3))

SD = √4.5×0.7

SD = 1.8

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Complete Question:

A candy machine contains over 1,000 pieces of candy, 30% of which are blue. Customers get an SRS of 15 candies in a purchase. Let X= the number of blue candies that a random customer gets in a purchase. Find the mean and standard deviation of X. You may round your answers to the nearest tenth.

The allowable set of values makes up a function's domain. The set of authorized values is the domain of a function.

The set of authorized values is the domain of a function. The x values of a function, like f, are included in this collection (x). The collection of such values serves as a representation of the range of values that can be used as input for a function. The function returns this set of values when we enter an x value.

here ,

Consider the function represented by y = f(x), where x and y are independent variables. If a function f provides a method of efficiently generating a single value y while employing a value for x to that end, the selected x-value is said to fall inside the domain of f.

The range of values that a function can accept is referred to as the domain.

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Answer:

One is 30,000 and the other is 300

Approximately 3.3 inches of rainfall per year.

If central Pennsylvania received only one-third of the usual rainfall in a really dry year, it would be receiving 1/3 * the usual amount of rainfall per year.

In an average year,

     Pennsylvania gets about the same amount of rainfall as a desert, which is typically defined as an area that receives less than 10 inches of precipitation per year.

Therefore, if central Pennsylvania received only one-third of the usual amount of rainfall in a really dry year, it would be receiving,

   1/3 * 10 inches = approximately 3.3 inches of rainfall per year.

This amount of rainfall is significantly less than the average rainfall in Pennsylvania and would qualify as a desert if it persisted over a long period of time.

Hence, Approximately 3.3 inches of rainfall per year.

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The height of the tree, calculated according to the details of shadow and Sofia's height, to the nearest hundredth of a meter is 5.83 meters.

The tangent of angle of elevation will be equal to the ratio of height of tree ÷ distance from the tip shadow. The tangent will be same for both tree and the girl. Le the height of tree be x.

x/23.55 = 1.35/(23.55-18.1)

Performing subtraction on Right Hand Side of the equation

x/23.55 = 1.35/5.45

Rewriting the equation with x

x = (1.35×23.55)/5.45

Performing multiplication on Right Hand Side of the equation

x = 31.79/5.45

Performing division on Right Hand Side of the equation

x = 5.83 meters

Thus, tree is 5.83 meters tall.

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By using compound interest, there will be$554.68in the account after 2 years.

Compound interest is interest that is calculated on the original principal of a loan or deposit, as well as on any accumulated interest from previous periods.

Compound interest is calculated using the following formula:

Compound interest = P * (1 + r/n)^(nt) - P

To calculate the total amount in the account after 2 years, we can use the following formula:

Total amount = P * (1 + r/n)^(nt)

In this formula, P is the principal amount (the initial deposit of $500), r is the annual interest rate (5.2%), n is the number of times that interest is compounded per year (12 in this case, since the interest is compounded monthly), and t is the number of years for which the interest is compounded (2 in this case).

Substituting the given values into the formula, we get:

Total amount = $500 * (1 + 0.052/12)^(12*2) = $554.68

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The expression be written as 4 × -3 = -12, which can be simplified to -3 × 4 = -12. Therefore, the answer for M4 = -12 is -3.

M4 = -12 is an algebraic expression that is asking us to solve for the value of M. To solve, we can start by rewriting the expression as 4 × -3 = -12. This can be simplified to -3 × 4 = -12.Now, it is easier to see that the value of M is -3. This is because when we multiply -3 by 4, we get -12. Since -12 is the same value as the original equation, M must be equal to -3.To summarize, M4 = -12 is an algebraic expression that can be simplified to -3 × 4 = -12. Solving for M, we end up with M = -3. This is because when we multiply -3 by 4, we get -12, which is the same value as the original equation.

M4 = -12

4 × -3 = -12

-3 × 4 = -12

M = -3

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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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Answer:

If his old mirror had a side length of 9cm, that means the area would be 81cm (9 times 9)

For the circles:

A radius of 8: 201.06

A radius of 7: 153.94

A radius of 5: 78.54

The only one of these answers that is remotely close to dominics original mirror would be C: the radius of 5. 81 is close to 78.5!

We solve log2 value by following logarithm laws.

Logarithm is the alternating way of expressing an exponent. The power at which a number is needed to raise so as to obtain the other values is called logarithm.

log2 is termed as log base 2 or binary logarithm. It is called the inverse of the power of two function.

As stated earlier that Log base 2 is an inverse expression of the power 2.

Suppose N is a real positive number and x is the number of exponents.

Now, logarithm form of this exponent is written

as log2 N = x

2∧x = N

Besides, we can directly get the log2 value by using calculator.

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1) Quadrilateral [tex]ABCD[/tex] with diagonal [tex]\overline{AEC}[/tex] bisecting [tex]\angle DAB[/tex], [tex]\overline{BE}[/tex], [tex]\overline{DE}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle BAE \cong \angle EAD[/tex] (definition of an angle bisector)

3) [tex]\overline{AE} \cong \overline{AE}[/tex] (reflexive property)

4) [tex]\triangle BAE \cong \triangle DAE[/tex] (AAS)

5) [tex]\overline{AB} \cong \overline{AD}[/tex] (CPCTC)

6) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

7) [tex]\triangle BAC \cong \triangle DAC[/tex] (SAS)

8) [tex]\overline{BC} \cong \overline{DC}[/tex] (CPCTC)

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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Answer:

3

Step-by-step explanation:

Real zeros are the times when the graph intercepts the x-axis or, in other words, when y = 0.

In this graph, the polynomial intercepts the horizontal (x) axis 3 times!

This means there are 3 real zeros.

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:balls

Step-by-step explanation:

balls

The value of p is -1, and the coordinates of the focus are (-1,0) The equation of the directrix is 1.

The general equation for this parabola is

y^2 = 4px

To Find the value of p:

We are told that the equation of the problem is y^2 = -4x

And the general formula is

y^2 = 4px

From there, we can deduce that

p = -1, because y^2 = 4(-1)x = -4x

This means that p = -1

To Find the focus:

To find the focus we can see the equations attached below for the focus, vertex, and directrix.

In these cases, the equations still apply, even though the variable is inverted, we just need to adjust it

y^2 = -4x

=>x = (-1/4)*y^2

x = a*y^2 + b*y +c

Focus: ((4ac -b^2  + 1)/4a, -b/2a)

But, b = 0 and c = 0

=>(1/4a,0) = (1/4(-1/4),0) = (-1,0)

Focus =  (-1,0)

To Find the directrix:

The equation is x = c - (b^2 + 1).4a

But, b = 0 and c = 0

x = -4*a

x = -4* (-1/4) = 1

x = 1

Directrix x = 1

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