which is the proper way to enter the following piece wise function into Desmos

This question is asking to create 5 of your own questions, so here are mine with the process on how I got each:

Question 1: Given c(x) = 8x + 32, find the range of c for the domain {1, 3, 5}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 8, and adding by 32.

c(1) = 8(1) + 32 = 8 + 32 = 40

c(3) = 8(3) + 32 = 24 + 32 = 56

c(5) = 8(5) + 32 = 40 + 32 = 72

Range: {40, 56, 72}

Question 2: Given d(x) = x - 7, find the range of d for the domain {-2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, and subtracting 7.

d(-2) = -2 - 7 = -9

d(3) = 3 - 7 = -4

Range: {-9. -4}

Question 3: Given f(x) = 7x + 738, find the range of f for the domain {1.5, 11}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 7, and adding 738.

f(1.5) = 7(1.5) + 738 = 10.5 + 738 = 748.5

f(11) = 7(11) + 738 = 77 + 738 = 815

Range: {748.5, 815}

Question 4: Given g(x) = -2804x + 7268, find the range of g for the domain {50, 75, 256}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -2804, and adding 7268.

g(50) = -2804(50) + 7268 = -140200 + 7268 = -132932

g(75) = -2804(75) + 7268 = -210300 + 7268 = -203032

g(256) = -2804(256) + 7268 = -717824 + 7268 = -710556

Range: {-132932, -203032, -710556}

Question 5: Given h(x) = -3x - 4, find the range of h for the domain {1, 2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -3, and subtracting by 4.

h(1) = -3(1) - 4 = -3 - 4 = -7

h(2) = -3(2) - 4 = -6 - 4 = -10

h(3) - -3(3) - 4 = -9 - 4 = -13

Range: {-13, -10, -7}

b(-3)

b(5)

b(9)

Range

Rest questions

#1

k(x)=2x²-5

Find the range of k for domain {1,2,6}

#2

h(x)=9x³

Find the range of h for domain {9,0,8}

#3

o(x)=6x-7

find the range of o for domain {0,1,9}

#4

p(x)=23x²-5x

Find the range of p for domain {3,4,8}

Answer:

slope = [tex]-\frac{1}{2}[/tex]     if it were in an

Step-by-step explanation:

the graph is a negative and will therefore have a negative slope. to find the slope, pick a point on the graph and find the [tex]\frac{rise}{run}[/tex].

for instance, start with the point (0,1). Then go down 1 and left 2 to get to the next point on the graph (2,0). 1 is the "rise" and 2 is the "run" hence -1/2 being the slope.

you could also use the slope formula: [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

point 1: (0,1)    (x₁ ,y₁)

point 2: (2,0)    (x₂ , y₂)

[tex]\frac{0-1}{2-0} =-\frac{1}{2}[/tex]

Answer:The inverse of the function y = 2x^2 –4 is;. y = √(x +4)/2To find the inverse of the function;We must first solve for x in the equation as follows;y = 2x² - 4y + 4 = 2x²x² = (y +4)/2x = √ (y +4)/2By swapping x and y; we then have;y = √(x +4)/2

The number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.

Given the word:

ESTABROK

Then n = 8

p = 6

The formula for permutation without restrictions

P = n! ( n - p + 1)!

P = 8! ( 8 - 6 + 1) !

P = 8! (8 - 7)!

P = 8! (1)!

P = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 1

P = 40, 320 ways

Thus, the number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.

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The correct option is A. (4, 11) and (0, 7).

The solution of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points: (4, 11) and (0, 7).

Estimate the y-intercept, slope, and express the equation in the form of the y-intercept (y = mx + b) to find the graphed equation. The slope is the difference between the y- and x-axis values.

A graph equation is an equation in graph theory where the unknown is a graph. Isomorphic ideas are one of the key issues in graph theory.

The equations are; y = x + 7 and y = x² - 3x + 7

At the solution, the u-values are equal, which gives;

y = y

x + 7 = x² - 3·x + 7

x² - 3·x + 7 - (x + 7) = 0

x² - 4·x = 0

x·(x - 4) = 0

x = 4, or x = 0

When x = 4, y = 4 + 7 = 11

When x = 0,

         y = 0 + 7 = 7

Therefore, the solution for the equations  y = x + 7 and y = x² - 3x + 7 are are located at points: (4, 11) and (0, 7).

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The complete question is-

Based on the graphs of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points:

A. (4, 11) and (0, 7)

B. (4, 11) and (–7, 0)

C. (–7, 0) and (1.5, 4.75)

D. (1.5, 4.75) and (0, 7)

Answer:

If every line parallel to two lines intersects both regions in line segments of equal length, then the two regions have equal areas. In the case of your problem, every line parallel to the bases of the two parallelograms will intersect them in lines segments, each with a width of ℓ.

There are infinitely many parallelograms with the same area and base due to the variability of the height.

We have,

There is always more than one parallelogram with the same area and base because the height of the parallelogram can vary while keeping the base and area constant.

The formula to calculate the area of a parallelogram is:

Area = base × height

If the base and area of a parallelogram are fixed, we can rearrange the formula to solve for the height:

height = Area/base

Since the height can be any value as long as it satisfies the above equation, there are infinitely many possible heights for a given base and area.

And for each height, there will be a unique parallelogram with that base and area.

Imagine a rectangle as a special case of a parallelogram where all angles are 90 degrees.

For a given base and area, you can have an infinite number of rectangles by varying the height.

Each rectangle will have different side lengths, but they will all have the same base and area.

Thus,

The variability of the height while keeping the base and area constant allows for the existence of multiple parallelograms with the same area and base.

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Answer:

Step-by-step explanation:

plus all of them 5times 10

Hi! ⋇

               - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The first digit of this number is 3², which is 9.

The Number is : 9xx

________

The second digit is: -2·(-4)=8.

The Number is : 98x.

________

The sum of all the digits is 18. This gives us an equation that we can solve in terms of x!

[tex]\multimap\sf{9+8+x=18}[/tex] (x is the digit we are looking for)

Now it takes a little arithmetic to find x :)

[tex]\multimap\sf{17+x=18}[/tex]. Just subtract 17 from both sides to find x!

[tex]\multimap\sf{x=1}[/tex]. And Now, can you see the number!

It's 981, of course :)

Hope this made sense to you!

             - - - - - - - - - - - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\large\it{\overbrace{Calligrxphy}}[/tex]

Answer:

  (a)  3

Step-by-step explanation:

The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.

The degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.

In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).

The conditional probability that, when flipping a non-biased coin four times, there are at least two heads, given that the first flip is a head, is 3/4.

Calculating the Conditional Probability:

Let us assume that getting a head in the first flip of coin is event B

Also, let us assume that getting a head in on of the remaining three flips is A

Then we have to find the probability of A given B, that is, P(A|B).

The formula for conditional probability is given as follows,

P(A|B) = P (A∩B) / P(B)

The probability of getting two heads, P(A∩B) = 3/8

The probability of getting head in the first flip, P(B) = 1/2

∴ P(A|B) = (3/8) / (1/2)

P(A|B) = 3/4

Thus,  the conditional probability of getting at least two heads, given that the first flip is a head is 3/4.

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Answer: B. [tex]12log(x)-4log(y)[/tex]

Step-by-step explanation:

Properties of logs:

[tex]log_{a} (\frac{B}{C} )=log_{A}B-log_{A} C[/tex]

[tex]logA^B = BlogA[/tex]

So, [tex]log\frac{x^{12} }{y^4} =logx^{12} -logy^4 =12log(x)-4log(y)[/tex]

It would be 12 log x - 4 log y (B)

The Slope of the line :

[tex]m=-\frac{1}{5} \approx-0.2[/tex]

Using small, whole integer coordinates, it is simple to manually determine a line's slope. The formula becomes more effective if the coordinates are given greater or decimal values.

Because all horizontal lines have the same y-coordinates, it is important to note that all of them have a gradient of zero. In the slope formula's numerator, this will produce a zero. A vertical line, on the other hand, will have an arbitrary slope because the x-coordinates are constant. When applying the formula, this will lead to a division by zero error.

slope = (y₂ - y₁) / (x₂ - x₁)

Using the two points P=(2,3) and Q=(-3,4) as your input, determine the slope.

P=(x1,y1) and Q=(x2,y2) are two points on a line, and the slope of that line is given by :

                                 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

we have that:

                        [tex]x_{1}=2, y_{1}=3, x_{2}=-3, y_{2}=4[/tex]

Fill in the blanks in the slope calculation,

                                    [tex]m=\frac{(4)-(3)}{(-3)-(2)}\\\\=\frac{1}{-5}\\\\=-\frac{1}{5}[/tex]

Reaction:  the slope of the line is =[tex]m=-\frac{1}{5} \approx-0.2[/tex]

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The value of the probability P(A∪B) is 39/50

The given parameters are:

P(A)= 9/20

P(B) = 3/5

P(A∩B) = 27/100

To calculate the probability P(A∪B), we make use of the following equation

P(A∪B) = P(A) + P(B) - P(A∩B)

So, we have:

P(A∪B) = 9/20 + 3/5 - 27/100

Evaluate the expression

P(A∪B) = 78/100

Simplify

P(A∪B) = 39/50

Hence, the value of the probability P(A∪B) is 39/50

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Answer:

El río mide:

300000 metros.

Step-by-step explanation:

1 km = 1000 metros

300 km = 300 * 1000 = 300000 metros

...

The number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.

In this question,

Positive integers are 0,1,2,3,4,5,6,7,8,9

Total number of integers = 10

This can be solved by permutation concepts.

Case 1: 4-digit positive integers with no repeated digits,

First digit, cannot be zero. So remaining 9 digits.

Second digit, can be any digit other than the first digit. So 9 digits.

Third digit, can be any digits other than first and second. So 8 digits.

Fourth digit, can be any digits other than first, second, third digit. So 7 digits.

Thus, Number of ways of 4-digit positive integers with no repeated digits ⇒ (9)(9)(8)(7)

⇒ 4536 ways.

Case 2:  4-digit positive integers, there may be repeated digits, but all digits are odd

Odd integers are 1,3,5,7,9

Number of digits = 5

In this case, we can repeat the digits. So all places can have 5 possibilities.

Thus number of ways of 4-digit positive integers with repeated digits, but all digits are odd = (5)(5)(5)(5)

⇒ 625 ways.

Hence we can conclude that the number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.

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It is necessary to imagine the sum of the areas between each z-score and the average.

Given as the ratio of the area under the normal curve between two z-scores, both above average.

The  Z score accurately measures the number of standard deviations above or below the mean of the data points.

The formula for calculating the z-score is

z = (data points – mean) / (standard deviation).

It is also expressed as z = (x-μ) / σ.

Therefore, to find the percentage of the area under the normal curve between two z-scores, both above the mean, you need to look at the sum of the areas between the z-score and the mean.

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The interval where the function is negative is (–∞, –6)

The function is given as:

[tex]f(x) = \sqrt[3]{x + 6}[/tex]

Set the radicand to less than 0

x + 6 < 0

Subtract 6 from both sides

x < -6

Rewrite as an interval notation.

(–∞, –6)

Hence, the interval where the function is negative is (–∞, –6)

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The probability that any given car will have a brake failure if it is make a is 0.0065%

The complete question is added as an attachment

From the table in the question, we have:

P(Brake failure|car a) = 0.0065%

The above represents the required conditional probability

Hence, the probability that any given car will have a brake failure if it is make a is 0.0065%

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Answer: The probability that any given car will have a brake failure if it is making A, is 0.0065%.

Step-by-step explanation:

I got it right on Edmentum!

The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

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No, The resulting prediction would be more or less reliable than your original one.

Importance:

Prediction is a forecast or a prophecy. An example of a prediction is a psychic telling a couple they will have a child soon, before they know the woman is pregnant. A statement of what will happen in the future.

Predictions provide a reference point for the scientist. If predictions are confirmed, the scientist has supported the hypothesis. If the predictions are not supported, the hypothesis is falsified. Either way, the scientist has increased knowledge of the process being studied.

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Answer: A

Step-by-step explanation:

Each value of x maps onto only one value of y.

The probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.

Given:

The square's length is 10 units.

The circle's diameter is equal to two units.

To Determine:

It is necessary to determine the probability that the target's white section and black circle will both be hit.

Solution:

The square's area is 10 x 10 or 100 units.

The shaded circle's area is given by  πr² = 3.14 (1)² = 3.14 units.

The white area has a surface area of (100 - 3.14) = 96.86 units.

Probability of an event = The number of favorable events /Total number of events

The probability that it will occur in the shaded area = 3.14/100 = 0.0314  (The probability is close to 0).

The probability of hitting the white section is equal = 96.86/100= 0.9686.

(The probability is quite near to 1)

Hence, the probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.

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1. The given function is growth.

The percent of growth is 43%.

The initial value is 1500.

2. The rate of decay is 20% per day.

3. a. The exponential equation representing the sales after x months for the given situation is 3500000(0.97ˣ).

b. The monthly sales after 8 months will be $274,310.1758.

4. Between months 5 and 6, the website gains more members. The difference between the two sites for this period is 2700 members.

An exponential function is of the form f(x) = (a)(bˣ), where a is the initial value, and b is the exponential factor.

When b > 1, we have growth, and when b < 1, we have decay or depreciation.

1. Given function, f(x) = 1500(1.43ˣ).

The exponential factor in this function is 1.43, which is greater than 1, thus we have growth.

The percent of growth = (1.43 - 1)*100% = 43%.

The initial value = 1500.

2. Given an equation, y = 75(.8ˣ).

The exponential factor in this function is 0.8, and x signifies the days passed.

Thus, the rate of decay = (1 - 0.8)*100% per day = 20% per day.

3. Initial value = $350,000.

Rate of depreciation = 3% per month.

a. Thus, the equation for the sales after x months can be given as:

f(x) = 350000(1 - 0.03)ˣ = 350000(0.97ˣ).

b. To find the monthly sales after 8 months, we substitute x = 8.

Sales = 350000(0.97⁸) = $274,310.1758.

4. Initial members for both sites = 100.

For site a:-

Members double each month.

This makes an exponential equation, f(x) = 100.(2ˣ), where x is the number of months.

The growth between months 5 and 6 can be calculated as:

f(6) - f(5) = 100.(2⁶) - 100.(2⁵) = 6400 - 3200 = 3200.

For site b:-

500 new members are added each month.

This makes a linear equation, f(x) = 100 + 500x, where x is the number of months.

The growth between months 5 and 6 can be calculated as:

f(6) - f(5) = (100 + 500*6) - (100 + 500*5) = 3100 - 2600 = 500.

Thus, between months 5 and 6, the website a gains more members. The difference between the two sites for this period is 2700 members.

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Answer:

D (the last choice)

Step-by-step explanation:

Taking the fourth root of each element individually:

49^(1/4) = sqrt(7)

(d^8)^(1/4) = d^2

(e^2)^(1/4) = sqrt(e)

Multiplying them back together:

sqrt(7) * d^2 * sqrt(e) = d^2 * sqrt(7e)

Answer:

The last bubble (that of which is cut from the screen) is simplified.

Step-by-step explanation:

The provided equation is simplified by following these steps:

[tex](49d^{8}e^2)^\frac{1}{4}[/tex]

= [tex](49)^\frac{1}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]

[tex](7)^\frac{2}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]

=[tex]\sqrt{7} (d^2)(\sqrt{e})[/tex]

Figure 1 was translated using the rule (x', y') ⇒ (x -9, y + 2) to produce figure 2.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

Figure 1 was translated 9 units left and 2 units up using the rule (x', y') ⇒ (x -9, y + 2) to produce figure 2.

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Basic nutrients a 12-year-old needs are:

The following are the nine nutrients that a youngster should consume on a daily basis:

Therefore, basic nutrients a 12-year-old needs are given.

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The fill up of the missing points are:

Using the image attached, one can see that m<1 and m<2 creates a kind of  linear pair hence one can say they are both supplementary using the law of LINEAR POSTULATE THEOREM.

Based on the fact that the supplementary angles add up to 180 degrees, therefore:

m<1 + m<2 = 180   - will be equation 1

Since the interior angles m<2 and m<3 are known to be equal based on the CONGRUENCE POSTULATE THEOREM. Therefore

m<2 = m<3 ---  will be equation 2

Then place eqn. 2 into eqn. 2

m <1 + m <3 = 180

This connote that m<1 and m<3 are supplementary.

Hence, The fill up of the missing points are:

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The work done in lifting the block is 3430 J

From the question, we are to determine the work done in lifting the block

Using the formula,

Work done = mgh

Where m is the mass

g is the acceleration due to gravity

and h is the height

From the question,

m = 50.0 kg

g = 9.81 m/s²

h = 7.00 m

Putting the parameters into the formula,

Work done = 50.0 ×9.8 × 7.00

Work done = 3430 J

Hence, the work done in lifting the block is 3430 J

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Answer:

no solution

Step-by-step explanation:

y = (1/3)x - 4

3y - x = -7

put the first equation into the second

3(1/3)x - (3)4 - x = -7

x - 12 - x = -7

-12 = -7 can never be true so this is no solution