Eric can choose Plan A or Plan B for his long distance charges. For each plan, cost (in dollars) depends on minutes used (per month) as shown below.

A function can be written as piecewise function if it changes its behaviour ( increasing or decreasing ) about a point.

Here Here,

The given function is : y = 2|x| - 3

Here,

The function will change its behaviour when

| x | = 0

=> x = 0

Now,

If x < 0 , then ;

=> y = 2[–(x)] – 3

=> y = –2x – 3

=> y = – 2x – 3

If x ≥ 0 , then ;

=> y = 2(x) – 3

=> y = 2x – 3

=> y = 2x -3

Hence ,

y = – 2x – 3 , if x < 0

y = 2x - 3 , if x ≥ 0

a. $157.67

Explanation:

>> net income (total amount without the taxes etc...)

. biweekly = $575.50

. per month = $575.50 * 2 = $1,151 (~since it happens 2 times per month)

. per year = $1,151 * 12 = $13,812

>> gross income (total amount with the taxes etc...)

. per year = $17,500

>> amount deducted (~going to taxes etc...)

. per year = $17,500 - $13,812 = $3,688

. per month = $3,688 / 12 =~ $307.33

. per paycheck = $307.33 / 2 =~ $153.67

Answer:

A. [tex]f(\frac{1}{2}\pi)=2[/tex]

B. [tex]x=-2\pi, -\pi, 0, \pi, 2\pi[/tex]

C. [tex][-2, 2][/tex]

Step-by-step explanation:

A:

Since we want to find: [tex]f(\frac{1}{2}\pi)[/tex], all we do is go that that x-value on the function and then go either up or down until we find where the y-value is at that x-value, because [tex]f(\frac{1}{2}\pi)[/tex] is just another way of expressing "the y-value of the function f, at [tex]x=\frac{1}{2}\pi[/tex]

In this case it turns out that the y-value is two, which you can verify by going to that x-value and finding where the y-value is at that point.

So: [tex]f(\frac{1}{2}\pi)=2[/tex]

B.

To find all the x-values such that: [tex]f(x)=0[/tex], we just need to find where the graph crosses the x-axis, also known as an x-intercept. This is because at an x-intercept, the y-value will be equal to zero.

Looking at the graph you can see that these x-intercepts occur at: [tex]x=-2\pi, -\pi, 0, \pi, 2\pi[/tex]

in general you'll notice that all the values are actually separated by a value of pi, so the general formula for a zero in this equation is likely going to be: [tex]x=\pi n\text{ where n is an integer}[/tex], since trigonometric functions are periodic, they repeat.

C.

Looking at the graph you'll notice the value is increasing, then decreasing, then increasing... and so on.

The max value it reaches is two, and the min value it reaches is negative two.

The range of a function is the y-values that the function can output, considering all the possible inputs, or the domain.

In this case no matter the input we can only output values between -2 and 2.

In this interval notation, we use brackets, since the minimum and maximum possible values are included in the range, since the function does output 2 and -2, it doesn't just "approach" it.

So we get a range of: [tex][-2, 2][/tex]

Explanation:

1)

1 kilometer is equal to 1000 meters:

1 km = 1000 m

So,

1m = 1/1,000 km

To complete the table, we can use the rule of three:

a) 1,000 m?

1m - 1/1,000 km

1,000m - x

x = 1/1000 * 1,000 = 1 km

As we can see, we only have to divide the measure in meters by 1000.

b) 3,500 m = 3,500/1,000 = 3.5 km

c) 500 m = 500/1,000 = 0.5 km

d) 75 m = 75/1,000 = 3/40 km = 0.075 km

e) 1 m = 1/1000 = 0.001 km

f) x = x/1,000 = 0.001x km

2)

The relation is:

Y = 0.001x

Where x is the measure in km and x in meter.

Answer:

-b plus or minus square root of b square - 4ac

divided by 2a

where by a is the first term

b is the second term

c is the third term

Step-by-step explanation:

a = 1

b = -5

c = 4

x = 4 & 1

Answer: [tex]4m^{6}[/tex]

Step-by-step explanation:

[tex]\frac{8.4m^{9} n^{5} }{2.1m^{3}n^{5}}[/tex]

Dividing exponents is the same as subtracting the exponents, so

[tex]\frac{m^{9}}{m^{3}} =m^{9-3}=m^{6}[/tex]

[tex]\frac{n^{5}}{n^{5}} =n^{5-5}=n^{0}=1[/tex]

So now our equation looks like

[tex]\frac{8.4m^{6}}{2.1}[/tex]

Now we can divide the numbers

8.4/2.1 = 4

So your final answer is [tex]4m^{6}[/tex]

Answer:

one solution

Step-by-step explanation:

solve it.

2y-4=3y-5

-y=-1

y=1

The variables are

C: total cost ($)

S: amount of sugar (tons)

The equation that relates these two variables is;

C = 3250 + 125S

The graph of the equation is:

where C is the dependent variable, and S is the independent variable

We will write it as a fraction in ordet to solve, that is:

We then operate as follows:

We have this, since 1 integer will be equal as a numerator divided by a denominator with equal values. Examples 1 = 2/2, 1 = 45/45, ...

The equation that represent the situation is as follows;

3x + 2y = 34

1 / 2x + 2y = 14

The two number Diego is thinking of are 8 and 5.

He is thinking of two positive numbers.

If we triple the first number and double the second number, the sum is 34.

If we take half of the first number and double the second, the sum is 14.

Therefore, the equation that can be used to solve the situation is as follows:

let

x = first number

y = second number

3x + 2y = 34

1 / 2x + 2y = 14

Therefore,

3x + 2y = 34

1 / 2x + 2y = 14

5 / 2 x = 20

5x = 40

x = 40 / 5

x = 8

3(8) + 2y = 34

2y = 34 - 24

2y = 10

y = 10 / 2

y = 5

Therefore, the two numbers are 8 and 5.

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The probability of matching x successes on n further trials in an experiment with two possible outcomes. There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.

Given that,

The probability of matching x successes on n further trials in an experiment with two possible outcomes is known as the binomial probability (commonly called a binomial experiment).

The following formula gives it:

[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]

Where is the number of distinct combinations of x items drawn from a set of n elements, as determined by the formula below.

[tex]C_{n,x}=\frac{n!}{x!(n-x)!}[/tex]

And p is the probability that anything will happen.

Being aware that employers are monitoring phone calls is a victory in this issue.

43% of adults fear that their employers are listening to their phone calls,

p=43%=0.43

We must locate Four persons were questioned, and none expressed concern about phone call monitoring by companies.

We count four adults, n=4.

Is there a probability of success of 0? If so, then x = 0.

[tex]P=C_{n,x}p^{n}.(1-p)^{n-x}[/tex]

[tex]P=C_{4,0}(0.43)^{0}.(0.57)^{4}[/tex]

P=0.0488

Therefore, There is a 4.88% chance that no one is worried that their employers are listening to their phone calls.

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The Point-Slope form of the equation of a line is:

Where "m" is the slope of the line and this is a point on the line:

You can find the slope of a line using this formula:

In this case, knowing that this line passes through these points:

You can set up that:

Substituting values into the formula and evaluating, you get:

Knowing the slope and coordinates of two points on the line, you can set up these two equations for this line:

1. First equation:

2. Second equation:

The answers are: Option A and Option B.

Answer

(5, 2)

Step-by-step explanation

Point D in triangle DEF is the equivalent to point A in ABC. Similarly, E is the equivalent to B. In consequence, F is the equivalent to C.

We can obtain points D and E by translating points A and B 6 units to the right and 4 units up.

Translation 6 units to the right and 4 units up transforms the point (x, y) into (x+6, y+4). Applying this rule to point C:

C(-1, -2) → (-1+6, -2+4) → F(5, 2)

is it 3, right?

3.- B, angle 1 and angle 8

2.- It's incomplete, Number two it's incomplete I think I need a picture of this problem.

2 .- 4, letter J

Done, bye

Given the figure FGHJ with coordinates

F(0, 5), G(-5, 1), H(5, -7) and J(6, 4)

When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

Therefore, for clockwise rotation, the coordinates of the image of FGHJ becomes

Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'

When we rotate a figure of 90 degrees anti-clockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.

Therefore, the anti-clockwise rotation the coordinates of the image of FGHJ becomes

Note that, the blue graph represents the pre-image FGHJ and the green graph represents the image F'G'H'J'

Out of all the 500 people, how many are Men, shopping at Home Depot?

See the cell crossing "Men" row and "Home Depot" column.

it is 37

Hence, probability of shopper being a men who shops at Home Depot is:

37/500

In decimal:

0.074

In percentage:

Using proportions we know that a 5-oz serving contains 12g of carbohydrates.

So, the carbohydrates in a 5-oz serving:

Now, calculate as follows:

Therefore, using proportions we know that a 5-oz serving contains 12g of carbohydrates.

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Answer:

The correct option is D

The accumulated interest after 10 years is $2,125.00

Explanation:

We have the following parameters:

Principal (P) = $2,500

Rate (R) = 8.5%

Time (T) = 10 years

To calculate the interest after 10 years, we use the formula:

The interest is $2,125

Based on the equation, each girl received the following Algebra test scores:

An equation is a mathematical expression that claims that two values are equivalent.

Equations use the equation symbol (=) to illustrate the equality of two or more expressions.

Algebraically, let Alyssa's algebra test score = x

Let Jennifer's test score = x + 8

The total of their two tests = 180

x + x + 8 = 180

2x + 8 = 180

2x = 180 - 8

2x = 172

x = 86 (172/2)

Alyssa's test score = 8 points lower

Shareable points = 172 (180 - 8)

Each received 86 points from the shareable points

Alyssa's test score = 86 points

Jennifer's test score = 94 points

Check:

86 + 94 = 180

94 = 8 points greater than 86

Thus, using an equation, we can conclude that Alyssa scored 86 points on the Alegra test, which is 8 points less than Jennifer's 94 points.

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Solution:

Given the system of equations:

1) The graphs of the system of equations are as shown below:

2) Values of x for which

From the graph of the system of equations, the points at which the graph functions cut or intersect each other, give the solution of the system of equations.

Thus, in the graph of the system of equations, the functions intersect each other at the point (1,1) and (5,1) as shown below:

Thus, the values of x for which f(x) = g(x) are

Answer:

Step-by-step explanation:

since 30 liters is ten times 3 liters, you must mulitply all of the amounts of dye liters (not green because we know its 30) by 10. this would make a ratio of 90:30:150. Now, add them all up to equal 270 liters of purple dye in total.

When you locate the coordinates of A it is (-4, 1)

Locate the coordinates of A', it is : (4, 5)

This implies, 8 was added to the x coordinate and 4 was added to the y-coordinate

Hence, the transformation is;

(x + 8, y+4)

we have that

Part c)

the probability is equal to

P=0.14+0.27+0.58

because is the sum of

x=1, x=2 and x=3

Part D

the probability is

P=0.01+0.14+0.27

because is less than or equal 2

Given the terminal point of Θ:

Let's find the value of Θ.

In polar coordinates, we have the points as

Where:

R is the radius and Θ is the angle.

We know in rectangular coordinates, we have:

x = R * cosΘ

Y = R * sinΘ

Thus, to find the value of Θ, we have:

Solve for Θ.

Take the inverse cosine of both sides:

ANSWER:

Answer: 16.94285714

Step-by-step explanation: 2/35 is 0.05714285714. 13+2+2 = 17.

17- 0.05714285714 is 16.94285714.

We are given the following two points

We are asked to find the equation of the line that passes through these points.

Recall that the equation of the line in slope-intercept form is given by

Where m is the slope and b is the y-intercept.

The slope of the line is given by

Let us substitute the given values into the slope formula

So, the slope of the equation is 0

The equation of the line becomes

Now let us find the y-intercept (b)

Choose any one point from the given two points

Let choose (-4, -1) and substitute it into the above equation

Therefore, the equation of the line in slope-intercept form is

Note that this equation has 0 slope that is why mx part becomes 0

Mary has scored 78, 60, 82, 94, and 88 on her previous fice tests.

What score does she need on her next test so that her average (mean) is 80?

Let x be the next test score

Recall that the mean is given by

We have the following information,

mean = 80

sum of test scores = 78 + 60 + 82 + 94 + 88 + x = 402 + x

total number of tests = 6

So, let us substitute these values into the above formula

Therefore, Mary need to score 78 on her next test so that her mean is 80

we need to make revenue-cost and then maximize

simplify

now, to maximize, we need to find the derivate and make it equal to 0

so, the maximum profit is at x = 6

we have that

Vertical asymptote at x=3

so

The denominator could be (x-3)

Horizontal asymptote at y=2

so

Degree on Top is Equal to the Bottom

The numerator could be equal to 2x and the leading coefficient of the denominator is 1

therefore