You are choosing between two different prepaid cell phone planes. The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

You can subtract the right side and factor the result, or you can factor the left side then see what happens.

... 5x² +22x +8 = 5x +2

... 5x² + 2x +20x +8 = 5x +2 . . . . split the x term so we can factor by grouping

... x(5x +2) +4(5x +2) = (5x +2)

Now we can subtract the right side and finish the factoring.

... x(5x +2) +(4 - 1)(5x +2) = 0

... (x +3)(5x +2) = 0 . . . . . the factorization of your equation

_____

If we start by subtracting the right side, we are looking to factor ...

... 5x² +17x +6 = 0

... 5x² +2x +15x +6 = 0 . . . . . split the x-term to help factoring by grouping

... x(5x +2) +3(5x +2) = 0 . . . factor pairs of terms

... (x +3)(5x +2) = 0 . . . . . . . . combine the results

______ _____

Factoring quadratics with the leading coefficient not equal to 1 is similar to factoring when it is equal to 1. Here, (after subtracting the right side), we are looking for factors of 5·6 = 30 that add to 17, the coefficient of the x-term.

... 30 = 1·30 = 2·15 = 3·10 = 5·6

The sums of these factor pairs are 31, 17, 13, 11. We see that the factor pair (2, 15) is the one we want, as its sum is 17. You will note these are the numbers used to divide the x-term for factoring by grouping. We rewrote 17x as 2x +15x. (There are other ways to use these numbers, but this is perhaps the easiest to see and remember.)

Answer:

(5x + 2)(x + 4)

Step-by-step explanation:

So, we have the equation [tex]5x^2+22x+8[/tex] right?

To get the [tex]x^2[/tex] we are going to need 'something' x in the first x slots of our factor form, like this:

(?x ± ?)(?x ± ?)

5 is a prime number, so one of the x's will be a 5x, and the other one a 1x:

(5x ± z)(x ± q)

z * q must be 8, and 5 * q + z must be 22

2 * 4 is 8

Let's plug these values in:

(5x + 2)(x + 4)

Let's multiply this out:

[tex]5x^2+22x+8[/tex]

This matches with our original equation!

So, our answer is:

(5x + 2)(x + 4)

In accordance with Pythagorean theorem, no point is 4 units away from point M.

In this problem we find the coordinates of points A, B, C, whose coordinates are (- 4, 2), (2, 7) and (8, - 6), respectively, and the location of point M, whose coordinates are (- 4, - 6), all set on Cartesian plane. We need to determine if at least one of those three points (A, B, C) are four units away from point M. This can be checked by means of Pythagorean theorem:

AM = √[(- 4 - 2)² + [- 6 - (- 4)]²]

AM = √[(- 6)² + (- 2)²]

AM = 2√10 = √40

BM = √[(- 4 - 2)² + (- 6 - 7)²]

BM = √[(- 6)² + (- 13)²]

BM = √205

CM = √[(- 6 - 8)² + [- 4 - (- 6)]²]

CM = √[(- 14)² + 2²]

CM = 10√2 = √200

There is no point that is four units away from point M.

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The relative minimum from the given graph is located at d.

Given that, the function [tex]f(x)[/tex] is graphed below.

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).

A relative minimum of a function is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood. These are points in which the first derivative is 0 or it does not exist.

From the given graph, point d is a relative minimum.

Hence, the relative minimum from the given graph is located at d.

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The property of equality that are used in each step is:

According to the division property of equality, if both sides of an equation are divided by a common real integer that is not equal to zero, the quotients remain equal. The formula for this is as follows: If a, b, and c are real numbers, with a = b and c 0 respectively, then a c = b c.

Have you ever wondered what rules you have to follow when dealing with inequalities? The division property of inequality is one of those laws, and it basically states that if you divide one side of an inequality by a number, you can divide the other side of the inequality by the same amount.

2((2X/5)+8)= 4(14-(X/5))

2((2X/5)+8)/2= 4(14-(X/5))/2   ---------Division property

(2x/5+8)=2(14-x/5)

((2x/5)+8)=(28-(2x/5)    ---------Distributive property

(2x/5)+8+(2x/5)=28-(2x/5)+(2x/5)  --------Addition property

(4x/5)+8=28

(4x/5)+8-8=28-8    ---------subtraction property

4x/5=20

(4x/5)×(5)=20×(5)  ---------Multiplicative property

4x=100

4x/4=100/4 --------- Division property

x=25      ----------Symmetric property

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Step-by-step explanation:

This is the answer.

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The number of people that like sausage or mushrooms as shown in the Vann diagram is 30.

Venn diagrams are diagrams used to visually depict sets, relationships between sets, and operations on sets

To determine the number of people that like sausage or mushrooms from the Vann diagram, we use the Formula below.

Formula:

n (S ∪ M) = n (S) + n (M) − n (S ∩ M) ................. Equation 1

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the people who like sausage or mushrooms is 30

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Answer & Step-by-step explanation:

This question is just a matter of reading the graph correctly. There is really no explanation for this question. But I'll try my best.

1997 for age 65 or older

Bachelor's degree or higher: The yellow bar starts at 75% and ends at 100%

To find how much percent of people 65 or older had a bachelor's degree in 1997, you subtract...100-75 = 25%

College/associate degree: 75 - 54 = 21%

High school graduates: 54 - 22 = 32%

Less than a High school diploma: 22 - 0 = 22%

Total: 25+21+32+22 = 100%

2007 for age 65 or older

Bachelor's degree or higher: 100 - 69 = 31%

College/associate degree: 69 - 46 = 23%

High school graduates: 46 - 13 = 33%

Less than a High school diploma: 13 - 0 = 13%  

Total: 31+23+33+13 = 100%

Hope this helped :)

The inequality (x - 6) / (x + 5) ≥ (x + 7) / (x + 3) is equivalent to (-15x - 53) / x² + 8x + 15 ≥ 0

Two or more inequalities are equivalent inequalities if they have the same solution set. Similar to equivalent equations, applying properties of Inequality to an inequality produces an equivalent inequality.

In the given inequality

(x - 6) / (x + 5) ≥ (x + 7) / (x + 3)

This can be reduced to

x < -5 or -53/15 ≤ x < -3

In the options given;

(-15x - 53) / x² + 8x + 15 ≥ 0 has the same reduction of x < -5 or -53/15 ≤ x < -3.

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[tex]a_n=80\left(\frac{5}{4}\right)^{n-1}[/tex]is the formula for the nth term of the given sequence.

What is sequence?

In mathematics, a sequence is a list of components, usually numbers, where the components' order is important.

Here, everything fits into a predetermined pattern. In real life, we encounter sequences frequently.

Sequences include things like house numbers in a row, income increases over time (by a set dollar amount or percentage), book pages, etc.

A list of numbers (or other components) that follow a specific pattern is called a sequence.

Olivia, for instance, has been given a job with a starting monthly pay of $1,000 and a $500 annual raise.

Are you able to determine her monthly pay for the first three years? $1000, $1500, and $2000 will be the amounts.

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The required equation is y = 2.5x + 15 which shows the relationship between the number of hours Connor spends writing today,X, and the total number of pages.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Connor has already written 15 pages of his new young adult novel and he will write more today. He expects to write 2.5 pages per hour

Let x represents the number of hours Connor spends writing today and y represents the total number of pages,

According to the given situation, we can write the equation as:

⇒ y = 2.5x + 15

Therefore, the required equation is y = 2.5x + 15.

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The price that Winners wants to pay for the jackets is $82.50

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

45%

= 45 percent

= 45 / 100

= 0.45

The factor 0.71 is a discount factor so we subtract from 1

1 - 0.45 = 0.55

The price Winner wants to pay

= 0.55 * 150

= $82.50

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Answer:

The correct answer is: B. Yes; the other factor is 1 since 1 × 1 = 1.

Step-by-step explanation:

The standard deviation of the sampling distribution of sample means using the given information is 1.8

What does the mathematical term "rounding" mean?

Rounding is a method for estimating a specific number in a situation. To determine how to round a number, look at the next digit in the appropriate position; if it is less than 5, round down, and if it is greater than 5, round up. The precise rounding of decimal figures is referred to as "rounding decimals."

What are the guidelines for rounding off decimal numbers?

To locate the rounding digit, look at its right side.

If the right-side numbers are less than 5, consider them to be equal to zero.

The digit on the right is increased by one and the other digits are treated as zero if the right-side digits are greater than or equal to 5.

The population standard deviation divided by the square root of the sample size, or n, gives the standard deviation of the sampling distribution of sample means, or x, for any given population. Therefore:

For the provided data, the sampling distribution's standard deviation of sample means is [tex]\frac{14}{\sqrt{64} }[/tex], or 1.8.

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Step-by-step explanation:

Mr. Perez bought a living room showcase listed at 150,580 Pesos but discounted into 127,993 pesos. What was the rate of the discount?

(150,580 - 127,993) / 150,580 = 15%

The roster method to write the set A' will be {c, d, e}.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

Let U = {b, c, d, e, f, g, h} and A = {b, f, g, h}.

The roster method to write the set A' will be given as,

A' = U - A

A' = {b, c, d, e, f, g, h} - {b, f, g, h}

A' = {c, d, e}

The roster method to write the set A' will be {c, d, e}.

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There were 7.76 billion chees produced until 2006 and  8.99 billion cheese produced until 2014.

The mathematical model can be used in the solving of a particular problem. Most importantly, we could use the mathematical models to be able to solve a problem or make predictions about the future.

We can now use the model that is shown as ;y=7.1(1.03)ˣ where x = the number of years after 2003.

a) For the year 2006, we can see that the number of years that ahs past is three years hence;

y = 7.1(1.03)^3

y = 7.76 billion chees

b) For 2014 we have 8 years thus we can write;

y = 7.1 (1.03)^8

y = 8.99 billion cheese

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Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

[tex]\textsf{I.} \quad \dfrac{58}{67}=0.86567...[/tex]

[tex]\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058[/tex]

[tex]\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58[/tex]

[tex]\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058[/tex]

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

The slope of the lines are -2/9 and 14/3.Given the coordinates of two points on the line, use the slope formula to determine the slope of the line.

Explanation:

m = (-8 - -6)/(3 - -6)

   = -2/9.

m = (-6 - 8)/(-6 - -3)

   = -14/-3 = 14/3.

The slope of the lines are -2/9 and 14/3.  

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Answer:

?? There are 27 students!

11+13 = 24 students play those sports

How can there be 5 students who play neither sport! I'm kind of confused!

Step-by-step explanation:

Answer:

22 / 27

Step-by-step explanation:

See Venn diagarm below

Answer:

[tex]n=126[/tex]

Step-by-step explanation:

Using the formula for the sum of the angles of an [tex]n[/tex]-sided polygon, the sum of the angles is [tex]180(n-2)[/tex] degrees.

An exterior angle is supplementary to the corresponding interior angle. Using the given angle measures, the sum of the angles is [tex]2(180-50)+127+135+173n=522+173n[/tex] degrees.

Equating these two results,

[tex]180(n-2)=522+173n \\ \\ 180n-360=522+173n \\ \\ 7n-360=362 \\ \\ 7n=882 \\ \\ n=126[/tex]

Answer:

n=126

Step-by-step explanation:

180(n−2)=522+173n

180n−360=522+173n

7n−360=362

7n=882

n=126

Answer:

Step-by-step explanation:ask a pro

Answer: None of these

Step-by-step explanation:

[tex]3^x+2 > -1\\\\3^x > -3\\\\3^x \geq 0 \forall x \in \mathbb{R} \implies x \in (-\infty, \infty)[/tex]

The number line that contains each of these points marked is given by the image presented at the end of the answer.

It depends if the number to be plotted is an integer or if it is a decimal.

The numbers that will be plotted in this problem are defined as follows:

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After 598 years the population of the country will be 677 million

The exponential model of the population is

A = 371.4 e^ (0.0241×t)

Where A is the total population in t years

t is the number of years

The population of the country = 677 million

677 million = 677e^8

Therefore the exponential equation will be

6.77 × [tex]10^8[/tex] = 371.4e^(0.0241t)

e^(0.0241t) = 6.77 × [tex]10^8[/tex] / 371.4

Divide the terms

e^(0.0241t) = 1822832.526

0.0241t = ln(1822832.526)

t = ln(1822832.526) / 0.0241

Divide the terms

t = 598.17

t ≈ 598 years

Hence, after 598 years the population of the country will be 677 million

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The solutions to the absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0,  |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 are 1/6, 1, 2/15 and no solutions respectively

An absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.

In the questions given;

Question 1

|3x - 1| - |2x + 5 - (5 - x)| = 0

x = 1/6

Question 2

|2(x + 1) - 4| - 4| = |2 - 2(2 - x)|

x = 1

Question 3

|(x - 2) / 4| - 1/3 = x

x = 2 / 15

Question 4

1/2|x - 3| - 1 = |x - 3| + 2

This equation does not have a solution

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Step-by-step explanation:

Form of an exponential function is

[tex]y = a \times b {}^{x} [/tex]

where a is the initial value, and b is the rate of growth

We know that when x=2

[tex]100 = a \times b {}^{2} [/tex]

when x=4

[tex]2500 = a \times b {}^{4} [/tex]

If we divide these two quantities we would get

[tex]25 = b {}^{2} [/tex]

[tex]b = 5[/tex]

So our rate of common growth is 5,

so b=5

[tex]y = a \times 5 {}^{x} [/tex]

We need to find the initial value, this means we solve for a.

[tex]100 = a \times 5 {}^{2} [/tex]

[tex]100 = a \times 25[/tex]

[tex]4 = a[/tex]

So our equation is

[tex]y = 4(5) {}^{x} [/tex]

or

[tex]y = 4 \times 5 {}^{x} [/tex]