Which table represents a linear function?

Answer:

D

Step-by-step explanation:

it is the only graph with all the points in the table correctly plotted out

Answer:

D.

Step-by-step explanation:

There are negative x values involved (-1 and -2) and positive, so you can discard A and C on that basis.

The value for day -1 should be +4, only graph D shows that.

Answer:

x-intercept(s): (−5,0)

y-intercept(s): (0,−5)

Explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Im also in K12 so Ez Good Luck

Hope this helped!

==========================================================

Explanation:

We start with one block at the very left side. This is algebraically written as \(a_1 = 1\). The small subscript '1' means we're dealing with the first term, and that is set equal to 1. In other words, the first term is 1.

The second term is three since we have three blocks as the next figure down the line. So \(a_2 = 3\). We can then see that \(a_3 = 6\) and \(a_4 = 10\)

The sequence of the first four terms are: 1, 3, 6, 10.

The notation \(a_n = a_{n-1} + n\) tells us "to get the nth term \(a_n\), we add the previous term (\(a_{n-1}\)) to the value of n".

For example, if we wanted the third term, we would add the second term a2 onto the value of n = 2. In order to know a2, we need the diagram or you would have to use the recursive formula to find it.

Furthermore, it means that to find the fifth term \(a_5\), we do the following

\(a_n = a_{n-1} + n\\\\a_5 = a_{5-1} + 5\\\\a_5 = a_{4} + 5\\\\a_5 = 10+5\\\\a_5 = 15\)

The fifth figure will have 15 small little blocks to it. You can draw this out by copying the fourth figure, and then adding 5 smaller blocks to the very bottom portion. The sixth figure is basically a copy of the fifth one, but we have six little blocks along the bottom. This is the "plus n" being applied in the recursive formula.

So the 6th figure will have 15+6 = 21 blocks in total while the 7th figure has 21+7 = 28 blocks. This points us to choice (3).

Side note: These are known as triangular numbers. Note how the gaps between consecutive values of 1,3,6,10,15,21,28 is +2,+3,+4,+5,+6,+7.

Answer:

radius=4/2=2

perimeter =4×side

perimeter =4×4=16 in

area=side²

area=4²

area=16

Answer:

its the first option

Step-by-step explanation:

Answer:

A = (2p + 9) (2p - 9)

B = (x - 9) (x - 4)

Step-by-step explanation:

For A : Rewrite 4p^2 as (2p)^2.

(2p)^2−81

Rewrite 81 as 9^2.

(2p)^2−9^2

Since both terms are perfect squares, factor using the difference of squares formula, a^2 − b^2 = ( a + b ) ( a − b ) where a = 2p and b = 9 .

(2p + 9) (2p − 9)

For B : Consider the form x^2 + bx + c . Find a pair of integers whose product is c and whose sum is b . In this case, whose product is 36 and whose sum is − 13 .

-9, -4

(x - 9) (x - 4)

I hope this helps.

the polynomial expression that represents the area of the soccer field is

5x^2 -16xy +3y^2

given length of a rectangular soccer is 5x -y

and width of a rectangular soccer is x- 3y

find the polynomial expression that represents the area of the soccer field.

we know that the formula for the area of a rectangle is

area= length * width

       =( 5x-y)*( x-3y)

       = 5x^2 -15xy-xy +3y^2

        = 5x^2 -16xy +3y^2

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Answer:

21cm

Step-by-step explanation:

3+4+4+5+5

I so

The price of 1 pound of bananas is $5.25.

To find the price of 1 pound of bananas, we can divide the total cost of the bananas by the total weight purchased. In this case, Aubrey bought 5 pounds of bananas for $26.25.

Let's denote the price of 1 pound of bananas as 'x' dollars.

We can set up a proportion using the given information:

5 pounds / $26.25 = 1 pound / x dollars

To solve for 'x', we can cross-multiply:

5 * x = $26.25 * 1

Simplifying the right side of the equation:

5x = $26.25

Now, divide both sides of the equation by 5 to isolate 'x':

x = $26.25 / 5

Performing the division:

x = $5.25

Therefore, the price of 1 pound of bananas is $5.25.

In summary, based on the given information that Aubrey bought 5 pounds of bananas for $26.25, the price of 1 pound of bananas is $5.25.

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The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters

First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:

tan 8 = 4.6/opposite

Solving for the opposite, we get:

opposite = 4.6/tan 8 = 5.8 meters

This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.

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Answer:

so we know:

total of 20 students

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

chemistry has a total of 14 students

1 2 3 4 5 6 7 8 9 10 11 12 13 14

8 students are in physics

1 2 3 4 5 6 7 8

3 are in all of them

1 2 3

1) underline the main 3

total of 20 students

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

chemistry has a total of 14 students

1 2 3 4 5 6 7 8 9 10 11 12 13 14

8 students are in physics

1 2 3 4 5 6 7 8

2) lets bold the physics students, if you are in physics you have to do chem so that means 8 of the chem students also take physics.

total

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14

physics

1 2 3 4 5 6 7 8

3) now we bring biology into the "equation"

off the bat we know 3 are definitely in Biology.

so if 4 study ONLY biology we can cross them off our list see the {}

total

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14 15 16 17 18 19 20

chemistry

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14

physics

1 2 3 4 5 6 7 8

biology

1 2 3

4) so we have a total of 20 students, 3 in all of the classes (underlined), 8 in physics (bolded). If there 14 in chemistry, 4 take ONLY chemistry {}, 8 take chemistry as well (bolded), that leaves two students, so they must belong in biology. lets italicise them.

total

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14 15 16 17 18 19 20

chemistry

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14

physics

1 2 3 4 5 6 7 8

biology

1 2 3 13 14

5) out of our total of 20 students we know 14 of the students classes, so the remaining six must be in biology.

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14 15 16 17 18 19 20

chemistry

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14

physics

1 2 3 4 5 6 7 8

biology

1 2 3 13 14 15 16 17 18 19 20

6) so that was our "diagram" so now lets count how many are in chemistry and biology but NOT physics.

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14 15 16 17 18 19 20

chemistry

-1 2 3 4 5 6 7 8- {9 10 11 12} 13 14

physics

-1 2 3 4 5 6 7 8-

biology

-1 2 3 -13 14 15 16 17 18 19 20

there are 14 students in chemistry and 11 in biology, 5 of them are in both classes so 14-5= 9 and 11-5= 6 9+6=16. BUT 8 of those sixteen are also in -physics- so we arent counting them, we put those students in dashes. so lets count the students out of the dashes. so twelve of them are in chemistry and biology but not physics.

7) so how many are in just biology but not the other classes? lets look at the graph.

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14 15 16 17 18 19 20

chemistry

1 2 3 4 5 6 7 8 {9 10 11 12} 13 14

physics

1 2 3 4 5 6 7 8

biology

1 2 3 13 14 15 16 17 18 19 20

in the class of biology students 1 2 3 13 and 14 take other classes that leaves students 15 16 17 18 19 and 20. so 6 students take ONLY biology.

sorry its long but i hope this helps!

Answer:

X=4

Step-by-step explanation:

Answer:

the real part is part of -12i is 0

Solution

For this case the confidence interval is given by:

(0.27; 0.33)

We can find the estimaed proportion in the following way:

then the sample proportion would be 0.30

Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

There are six even numbers that can be formed from the digits 1, 2, 3, 4, and 5: 2, 4, 12, 14, 23, and 24.

To calculate the number of even numbers, we can first calculate the total number of combinations of all the digits. This is done by multiplying the total number of digits (5) by the total number of combinations of each digit (4). This gives us 5 x 4 = 20.

To calculate the number of even numbers, we then divide this number in half, as half of the combinations will be even numbers. Therefore, 20 divided by 2 = 10 even numbers. Hence, there are six even numbers that can be formed from the digits 1, 2, 3, 4, and 5: 2, 4, 12, 14, 23, and 24.

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In the process of determining the credibility of evidence, three key things that should be accomplished are: evaluating the source, assessing the reliability of the information, and considering potential biases or conflicts of interest.

When assessing the credibility of evidence, it is important to first evaluate the source. This involves examining the expertise, authority, and reputation of the individual or organization providing the evidence. A credible source is one that has relevant qualifications, experience, and a history of accurate and reliable information.

Next, it is crucial to assess the reliability of the information itself. This includes examining the methods used to gather the evidence, checking for proper research methodology, and verifying that the data or facts presented are accurate and supported by valid sources. Reliable evidence is based on sound research and trustworthy data.

Lastly, it is essential to consider potential biases or conflicts of interest that may influence the evidence. This involves examining any possible motivations, affiliations, or financial interests that could introduce bias into the information being presented. Understanding the potential biases helps to evaluate the objectivity and integrity of the evidence.

By accomplishing these three tasks—evaluating the source, assessing reliability, and considering biases—the process of determining the credibility of evidence becomes more thorough and reliable, allowing for informed decision-making based on trustworthy and valid information.

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In the process of determining the credibility of evidence, there are three important tasks to accomplish:

Evaluate the source: Assessing the credibility of the source is crucial to determine the reliability of the evidence. Consider the expertise, reputation, and qualifications of the author or organization presenting the evidence. Investigate if they have a bias or potential conflicts of interest that could influence the reliability of the information. Look for reputable sources with a track record of accuracy and reliability.

Examine the methodology: Understanding the methodology used to collect or generate the evidence is essential. Evaluate whether the research design, data collection methods, and analysis techniques are appropriate and rigorous. Look for transparency in how the evidence was obtained, including the sample size, data sources, and potential limitations. A well-designed and well-executed methodology enhances the credibility of the evidence.

Consider corroboration: Corroborating the evidence with multiple independent sources can strengthen its credibility. Look for consistency and agreement among different sources or studies on the same topic. Cross-referencing information with reliable and diverse sources helps reduce the impact of potential biases and increases confidence in the evidence. Multiple sources supporting similar conclusions provide a more robust foundation for credibility.By evaluating the source, examining the methodology, and considering corroboration from multiple sources, you can make informed judgments about the credibility and reliability of the evidence.

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Answer:

686000000000

Step-by-step explanation:

1. We assume, that the number 7000000 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 7000000 is 100%, so we can write it down as 7000000=100%.

4. We know, that x is 9800000% of the output value, so we can write it down as x=9800000%.

5. Now we have two simple equations:

1) 7000000=100%

2) x=9800000%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

7000000/x=100%/9800000%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 9800000% of 7000000

7000000/x=100/9800000

(7000000/x)*x=(100/9800000)*x       - we multiply both sides of the equation by x

7000000=1.0204081632653E-5*x       - we divide both sides of the equation by (1.0204081632653E-5) to get x

7000000/1.0204081632653E-5=x

686000000000=x

x=686000000000

now we have:

9800000% of 7000000=686000000000

The equation for the temperature, d, in terms of t (the number of hours since midnight), is:  d = 16 × sin((π/12) × t) + 55

To find an equation for the temperature, we need to determine the amplitude, period, phase shift, and vertical shift of the sinusoidal function.

The amplitude is half the difference between the high and low temperatures, which is (71 - 39) / 2 = 16 degrees. The period is the number of hours in a day, which is 24 hours. Since the temperature is at its highest point at 12:00 PM (midday), there is no phase shift. The vertical shift is the average of the high and low temperatures, which is (71 + 39) / 2 = 55 degrees.

Putting these values together, the equation for the temperature, d, in terms of t can be written as:

d = 16 × sin((2π/24) × t) + 55

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The low point station and low point elevation are 1366 and 41.36 ft, respectively.

Low point station:

136+20+10+400+10 = 136+60

136+60 = 1366.

Low point elevation:

85 - 20 - 23.64 = 41.36 ft.

The low point station and low point elevation are 1366 and 41.36 ft, respectively.

To determine the low point station and low point elevation, the following information is required: the intersection point, the vertical curve length, the percent grades of both lines, and the elevation of the intersection point. We'll need to find the grade point first. It's possible to calculate this as follows:

i = (4.00-2.50)/800,

(4.00-2.50)/800 = 0.001875.

The grade point is the change in grade per station.

The distance from Sta. 136+20 to the low point is 400 ft, so the change in grade is 400(0.001875) = 0.75%.So the low point grade is: 2.50% + 0.75% = 3.25%.

The elevations at the two points are known, and the vertical curve length is given as 800 ft.

The design equation for the vertical curve is: E = elevation, L = distance along curve from point of vertical tangency, and x = distance from point of vertical tangency to low point.

Using the above values, we have the following equations:

E at PVT + (L/2)(G1+G2) = E

at low point E at PVT + (L/2)(G1+G2) = 85 ft,

E at low point = 85 - 800/2(0.04+0.0325),

E at low point = 85 - 23.64,

85 - 23.64 = 61.36 ft.

The low point elevation is 61.36 ft. Finally, we need to find the low point station, which is simply the sum of the distances from the PI to the PVT, the length of the curve, and the distance from the PVT to the low point. The sum of these distances is 10 + 400 + 10 = 420 ft.

Adding this to the PI station, which is 136+20, yields a low point station of 136+60 or 1366.

The low point station and low point elevation are 1366 and 41.36 ft, respectively. To summarize, the grade point and low point grade were first calculated. The vertical curve's design equation was then applied using the percent grades and elevations to find the low point elevation.

Finally, the low point station was calculated by adding up the distances from the PI to the PVT, the length of the curve, and the distance from the PVT to the low point.

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Answer:

1/36

Step-by-step explanation:

A standard die has 6 faces

The numbers 1 through 6 on singly on each face

so the probability of tossing a 1 would be;

1/6

The probability of tossing another 1 would still be same 1/6

So the probability of tossing a 1 and another 1 would be the product of the two tosses as follows;

1/6 * 1/6 = 1/36

Answer:6 people

Step-by-step explanation:

Answer:

To solve the system of equations by the addition method, we need to add the two equations in such a way that one of the variables is eliminated.

Multiplying the first equation by 5, we get:

-5x + 15y = -20

Adding this equation to the second equation, we get:

-5x + 15y = -20

5x - 15y = 20

0x + 0y = 0

This equation tells us that 0 = 0, which is always true. This means that the system of equations has infinitely many solutions, since any value of y will satisfy the equations, and we can then use one of the equations to find the corresponding value of x.

To find a particular solution, we can choose any value of y, say y = 1. Then from the first equation, we have:

-x + 3y = -4

-x + 3(1) = -4

-x = -7

x = 7

Therefore, a particular solution to the system of equations is x = 7 and y = 1. However, there are infinitely many other solutions, since any value of y will satisfy the equations.

To find the velocity as a function of time (v = v(t)), we need to differentiate the position function x(t) with respect to time (t).

Given: x(t) = t^3 - 6t^2 + 9t

a. Velocity as a function of time (v = v(t)):

v(t) = dx(t)/dt

Taking the derivative of x(t) with respect to t:

v(t) = d/dt(t^3) - d/dt(6t^2) + d/dt(9t)

v(t) = 3t^2 - 12t + 9

b. Initial velocity (t = 0):

v(0) = 3(0)^2 - 12(0) + 9

v(0) = 9 m/s

Velocity after 1 second (t = 1):

v(1) = 3(1)^2 - 12(1) + 9

v(1) = 3 m/s

Velocity after 2 seconds (t = 2):

v(2) = 3(2)^2 - 12(2) + 9

v(2) = 9 m/s

Velocity after 3 seconds (t = 3):

v(3) = 3(3)^2 - 12(3) + 9

v(3) = 18 m/s

Velocity after 4 seconds (t = 4):

v(4) = 3(4)^2 - 12(4) + 9

v(4) = 33 m/s

c. Average velocity between 0 and 2 seconds:

Average velocity = (v(2) - v(0)) / (2 - 0)

Average velocity = (9 - 9) / 2

Average velocity = 0 m/s

d. Average velocity between 1 and 3 seconds:

Average velocity = (v(3) - v(1)) / (3 - 1)

Average velocity = (18 - 3) / 2

Average velocity = 7.5 m/s

e. Average velocity between 2 and 4 seconds:

Average velocity = (v(4) - v(2)) / (4 - 2)

Average velocity = (33 - 9) / 2

Average velocity = 12 m/s

f. The particle is at rest when the velocity is equal to zero:

0 = 3t^2 - 12t + 9

Solving this quadratic equation, we find two solutions:

t = 1 second and t = 3 seconds

Therefore, the particle is at rest at t = 1 second and t = 3 seconds.

g. The particle is moving in the positive x-direction when the velocity is positive.

From the velocity equation, we can see that when t > 2, v(t) is positive.

Therefore, the particle is moving in the positive x-direction when t > 2 seconds.

h. Diagram representing the motion of the particle:

```

    ^

    |

    |

    |

-----|-------------->

    |

    |

    |

```

The particle moves to the right along the x-axis.

i. Total distance traveled by the particle during the first five seconds:

To find the total distance traveled, we need to consider both the positive and negative displacements.

Distance traveled = ∫(|v(t)|) dt (from t = 0 to t = 5)

Substituting the velocity function:

Distance traveled = ∫(|3t^2 - 12t + 9|) dt (from t = 0 to t =

5)

To calculate this integral, we need to break it into intervals where the velocity function changes sign.

For t in the interval [0, 1]:

Distance traveled = ∫(3t^2 - 12t + 9) dt (from t = 0 to t = 1)

For t in the interval [1, 3]:

Distance traveled = ∫(-(3t^2 - 12t + 9)) dt (from t = 1 to t = 3)

For t in the interval [3, 5]:

Distance traveled = ∫(3t^2 - 12t + 9) dt (from t = 3 to t = 5)

Evaluating these integrals will give us the total distance traveled by the particle.

j. Displacement of the particle during the first five seconds:

Displacement = x(5) - x(0)

Displacement = (5^3 - 6(5)^2 + 9(5)) - (0^3 - 6(0)^2 + 9(0))

k. Acceleration as a function of time (a = a(t)):

Acceleration is the derivative of velocity with respect to time.

a(t) = dv(t)/dt

Taking the derivative of v(t) = 3t^2 - 12t + 9:

a(t) = d/dt(3t^2) - d/dt(12t) + d/dt(9)

a(t) = 6t - 12

1. To determine if the particle is moving with constant acceleration as a function of time, we need to check if the acceleration is constant (independent of time).

From the equation a(t) = 6t - 12, we can see that the acceleration is not constant since it depends on the value of time (t). Therefore, the particle is not moving with constant acceleration as a function of time.

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The number of different ordered 3-tuples, where each item is an element of set A, can be determined by calculating the Cartesian product of set A with itself three times.

In general, the Cartesian product of two sets A and B is the set of all possible ordered pairs where the first element is from set A and the second element is from set B. Extending this concept to three sets, the Cartesian product will consist of ordered triples.

To find the number of different ordered 3-tuples, we need to consider the cardinality (number of elements) of set A. Let's denote the cardinality of A as n.

The number of different ordered 3-tuples can be calculated as n raised to the power of 3, since each position in the tuple can be filled with any element from set A. In other words, it is equivalent to finding the number of combinations with repetition.

Therefore, the number of different ordered 3-tuples is n^3.

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Answer:

T = 12

Step-by-step explanation:

12/6=2

The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

\(x^2+y^2=r^2\)

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

\(x^2+y^2=16\)

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