A line passes through the two points given in the table find another point that lies on that line

The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

We have,

Step 1: Start with the expression (-4x + 9)².

Step 2: To expand this expression, we use the formula for the square of a binomial: (a - b)² = a² - 2ab + b².

Step 3: In this case, a is -4x and b is 9.

Applying the formula, we have:

(-4x + 9)² = (-4x)² - 2(-4x)(9) + (9)².

Step 4: Simplify each term in the expansion:

(-4x)² = 16x² (square the first term).

-2(-4x)(9) = 72x (multiply -2, -4x, and 9 together).

(9)² = 81 (square the second term).

Step 5: Combine the simplified terms:

(-4x + 9)² = 16x² - 72x + 81.

Thus,

The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

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The combined velocity of the 6000 kg railroad car moving at 5 m/s and the 4000 kg stationary car immediately after the collision, found using the principle of conservation of linear momentum is 3 m/s

The principle of conservation of linear momentum states that the total momentum before and after a collision is the same in the absence of an external force acting on the objects that collide.

The mass of the railroad car, m₁ = 6,000 kg

The speed At which the railroad car is moving, v₁ = 5 m/s

Mass of the stationary car, m₂ = 4,000 kg

v₂ = 0 (the car is stationary)

The mode of motion after the collision = Couple (move) together

The combined velocity can be found using the principle of conservation of linear momentum as follows;

m₁·v₁ + m₂·v₂ = (m₁ + m₂)·v₃
6000 × 5 + 4000 × 0 = (6000 + 4000) × v₃

\(v_3 = \dfrac{6000 \times 5 }{6000 + 4000} = 3\)

The combined velocity of the cars immediately after impact, v₃ = 3 m/s

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Given function is,

To find the Horizontal and vertical shift.

Horizontal shift is defined as any changes which is made by adding or substracting to the variable x in the function.

Vertical shift is defined as any changes which is made by adding or substracting to the variable y in the function.

So in the given function the value inside the root is ( x+2 ). so the horizontal shift is two unit left side.

So in the given function the value out side the root is -3, which directly add it to the variable y.

So the vertical shift is three unit down ( Downwards since negative side ).

So the required answer is 2 units left side and 3 units downwards.

Answer: -1 would be greater than negative two, along with 20, 1000.

-2 is a negative number, so any number that is -1 or higher is greater than -2

Answer:

1,2,3

Step-by-step explanation:

We will use the leg rule

hypotenuse leg

----------------- = --------------------

leg part

y 9+11

------- = -----

11 y

Using cross products

y^2 = 11(20)

y^2 =220

Taking the square root

y = 2 sqrt(55)

Now we can find z using the Pythagorean theorem

11^2 + z^2 = y^2

121 + z^2 = 220

z^2 =99

z = 3 sqrt(11)

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{4}\\ \end{cases} \\\\\\ c=\sqrt{7^2 + 4^2}\implies c=\sqrt{65}\)

The completed missing values are

        4x²   [ 0]   - 1

x      4x³   - 8x² -x

-2     4x³  - 8x²  -x

And the quotient is 4x²   - 1

The functions are given as

4x³ - 8x² - x + 2

x - 2

These functions imply that:

Dividend = 4x³ - 8x² - x + 2

Divisor = x - 2

So, the quotient can be represented as

Quotient = Dividend/Divisor

Substitute the known values in the above equation, so, we have the following representation

Quotient = (4x³ - 8x² - x + 2)/(x - 2)

For the missing values, we have

x      4x³

-2

Divide 4x³ by x

So, we have (complete the dividend)

      4x²

x      4x³   -8x²   -x  +  2

-2

Solving further, we have

      4x²     -8x

x      4x³   -8x²   -x  +  2

-2    4x³   -8x²

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

     -x  +  2

Divide -x by x

So, we have

      4x²   - 1

x      4x³   -8x²   -x  +  2

-2    4x³   -8x²

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

     -x  +  2

     -x  +  2

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

     0

This means that

Dividend = 4x³ - 8x² - x + 2

Divisor = x - 2

Quotient = 4x²   - 1

So, the completed boxes are

        4x²   [ 0]   - 1

x      4x³   - 8x² -x

-2     4x³  - 8x²  -x

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Solving systems of equations by elimination involves manipulating equations so that the variables may be canceled out, resulting in a simpler equation that can be solved. This method is used to solve systems of equations with two or more variables.

Solving systems of equations by elimination is a method of finding the solutions to systems of equations with two or more variables. To do this, the equations are manipulated so that the two variables can be canceled out, resulting in a simpler equation. This simpler equation can then be solved using basic arithmetic. Depending on the equations, different methods may be used to manipulate them, such as adding them together or subtracting one from the other. Once the variables have been canceled out, the resulting equation can be solved to find the solution. This method of solving systems of equations can be used for linear equations, quadratic equations, and even more complex systems of equations.

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Answer:

follow the statement below

Step-by-step explanation:

The question you presented here has multiple (un-limited) solutions unless you have another condition to solve for a single solution.

Equation: y = ax² + bx + c

y intercept (0 , 3): c = 3

axis of symmetry x=-5, therefore a corresponding point (-10,3) on the curve

3 = a*(-10)² + b*(-10) + 3

100a - 10b = 0

b = 10a  .... any pair like a=0.5 b=5; a=1 b=10 0r a=2 b=20 ..... all fit the function

y = 0.5x² + 5x +3

y = x² + 10x + 3

y = 2x² + 20x +3

........................

a. The probability that all 5 students are freshmen is 0.26.

b. The probability that there will be 3 freshmen and 2 sophomores is 0.33

a. To find the probability that all 5 students chosen at random are freshmen, we need to calculate the probability of selecting 5 freshmen from a group of 12, divided by the total number of possible 5-person groups that can be formed from the entire organization:

P(all 5 students are freshmen) = (number of ways to select 5 freshmen) / (total number of 5-person groups)

The number of ways to select 5 freshmen from a group of 12 is:

C(12, 5) = 792

where C(n, r) represents the number of combinations of n items taken r at a time.

The total number of 5-person groups that can be formed from the organization is:

C(22, 5) = 3,024

Therefore,

P(all 5 students are freshmen) = 792 / 3,024 = 0.261

So, the probability is 0.261 or approximately 0.26.

b. To find the probability that there will be 3 freshmen and 2 sophomores, we need to calculate the number of ways that this can occur, and then divide by the total number of possible 5-person groups:

P(3 freshmen and 2 sophomores) = (number of ways to select 3 freshmen and 2 sophomores) / (total number of 5-person groups)

P(3 freshmen and 2 sophomores) = [C(12, 3) * C(10, 2)] / C(22, 5)

P(3 freshmen and 2 sophomores) = (220 * 45) / 3,024

P(3 freshmen and 2 sophomores) = 0.328

So, the probability of selecting 3 freshmen and 2 sophomores is 0.328 or approximately 0.33.

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Answer:

(2\(b^{2}\) - 5) (3b + 8)

Step-by-step explanation:

First factor out 2\(b^{2}\) from the first set of parentheses and -5 from the second

2\(b^{2}\) ( 3b + 8)  - 5 (3b + 8)

Next factor out (3b + 8)

(2\(b^{2}\) - 5) (3b + 8)

Answer:

13m

Step-by-step explanation:

volume of sphere = \(\frac{4}{3} * pi * r^{3}\) = 3000π

4r^3/3 = 3000

r^3 =2250

r = ∛2250 = 13.10370 = 13

Answer:

Radius of the sphere is 13.1 m.

Step-by-step explanation:

Volume:

\({ \boxed{ \pmb{volume = { \bf{ \frac{4}{3}\pi {r}^{3} }}}}}\)

Substitute:

\({ \tt{3000\pi = \frac{4}{3} \times \pi \times {( {r}^{3}) } }} \\ \\ { \tt{ {r}^{3} = \frac{3000 \times 3}{4} }} \\ \\ { \tt{r = \sqrt[3]{ \frac{3000 \times 3}{4} } }} \\ { \tt{r = 13.1 \: m}}\)

Answer: 3 / 10

Step-by-step explanation:

It's a 30% chance.

Answer:

I dont know the probability scale letters, but the probability of getting a yellow sweet would be 3/10, 0.3, or 30% (they all say the same thing just different ways)

Hope this helps :)

Step-by-step explanation:

The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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The measure of 6.16798 feet are equal to 188 cm.

a dimension in US measurements that is 12 inches long (or wide). The definition of a foot in the Metric System is 0.3048 metres (the foot is defined that way).

The word "foot," which refers to the sole unit of measurement, is pluralized as "foot." In this sense, how far or how long you are measuring determines the mathematical difference between a foot and a foot.

The measurements in feet and feet are often used. They enable us to estimate the size of a person or a group. They can also help us calculate the separation between two spots. The word "foot," which refers to the sole unit of measurement, is pluralized as "foot."

          =188 cm = 6.16798.

           =188 cm = 6.17

Divide the length value by 30.48

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Answer:

a.) 130°

b.) 70°

Step-by-step explanation:

For a given triangle

The sum of all angles on a straight line is equal to 180°

Now,

50° + a = 180°

Subtract 50° from each side we get,

50° - 50° + a = 180° - 50°

a = 130°

Thus, The size of the angle marked a is 130°

The sum of all angles in a triangle is equal to 180°

Now,

b + 50° + 60° = 180°

b + 110° = 180°

Subtract 110° from both side we get,

b + 110° - 110° = 180° - 110°

b = 70°

Thus, The size of the angle marked b is 70°

-TheUnknownScientist 72

Answer:

600⁰00000000000000000

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.

This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).

(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.

First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).

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The false statements are "If you built it, they came" and "If they didn't come, you didn't build it."

The following statements are false:

- If you built it, they came.

- If they didn't come, you didn't build it.

1. **If you built it, they came**: This statement assumes a cause-and-effect relationship between building something and people coming. However, simply building something does not guarantee that people will come. Factors such as marketing, demand, location, and various other factors can influence whether or not people are drawn to what has been built. Therefore, this statement is false.

2. **If they didn't come, you didn't build it**: This statement suggests a direct correlation between people not coming and the absence of your involvement in building it. However, there can be numerous reasons why people may not come to something, even if you were responsible for building it. It could be due to lack of awareness, competition, timing, or other external factors. Therefore, this statement is also false.

The other statements are not false:

- **If they came, you built it**: This statement suggests that if people came, it implies that you were involved in building it. While it is possible that you were involved, there could be other factors that contributed to people coming. So, this statement is not necessarily false.

- **If you didn't build it, they didn't come**: This statement implies that if you were not involved in building it, then people did not come. While it is possible that your involvement could have influenced people's interest, it does not exclude the possibility of people coming for other reasons. Therefore, this statement is not necessarily false.

- **You didn't build it, or they came**: This statement presents two possibilities: either you did not build it, or they came. Both options are plausible and do not contradict each other. Therefore, this statement is not false.

In summary, the false statements are "If you built it, they came" and "If they didn't come, you didn't build it."

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Using the log, the answer to (1/243) ^-x/3 = 4 is \(-x=\log _{\frac{1}{243}}(12)\).

The power to which a number must be increased in order to obtain another number is known as a logarithm.

For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

So, solve using a log as follows: (1/243) ^-x/3 = 4

\(\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}\)

\(\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}\)

\(\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}\)

\(\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}\)

Therefore, using the log, the answer to (1/243) ^-x/3 = 4 is \(-x=\log _{\frac{1}{243}}(12)\).

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The probability of drawing exactly two pair is approximately 0.3954, or about 39.54%.

To calculate the probability of drawing exactly two pair from a deck of cards containing four aces, four kings, four queens, and four jacks, we need to count the number of ways to choose two different ranks for each of the two pairs, and then count the number of ways to choose a fifth card that is different from the ranks of the two pairs.

The total number of ways to draw 5 cards from the deck is:

C(16, 5) = (16 choose 5) = 4368

Now, let's count the number of ways to draw exactly two pair:

Choose two ranks for the first pair: C(4, 2) = 6 ways to do this.

Choose two ranks for the second pair: C(4-2, 2) = C(2, 2) = 1 way to do this.

Choose the rank of the fifth card: C(12, 1) = 12 ways to do this.

Now, we need to count the number of ways to distribute the chosen ranks among the 5 cards:

Choose two cards of the first rank: C(4, 2) = 6 ways to do this.

Choose two cards of the second rank: C(4-2, 2) = C(2, 2) = 1 way to do this.

Choose one card of the third rank: C(4, 1) = 4 ways to do this.

The total number of ways to draw exactly two pair is:

6 * 1 * 12 * 6 * 1 * 4 = 1,728

Therefore, the probability of drawing exactly two pair is:

1,728 / 4,368 = 0.3954 (rounded to 4 decimal places)

So the probability of drawing exactly two pair is approximately 0.3954, or about 39.54%.

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Answer:

25.5 feet because of some

Step-by-step explanation:

.,........

Answer:

Step-by-step explanation:

Answer:

1 feet = 12 inch

so, 3 feet = 36 feet

therefore, 3 feet is greater than 30 inch

Answer:

Yes, 3o inches is greater than 3 feet

Step-by-step explanation:

Answer: Hello, I can help!

The probability that Jerry will have to wait for the bus for more than five minutes is 0.3. Therefore, the probability that he will not have to wait for more than five minutes is 0.7 (since the sum of the probabilities of all possible outcomes is 1).

The probability that Jerry does not wait for more than five minutes on any one day is 0.7. The probability that he does not wait for more than five minutes on all 5 days is:

0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807

Therefore, the probability that Jerry does not wait for more than five minutes all 5 days this week is 0.16807 or about 16.81%.

Step-by-step explanation: rest easy my friend:)

Answer:

To answer this question, we need to use the binomial probability formula:

P(X = k) = nCk * p^k * (1 - p)^(n - k)

where n is the number of trials, k is the number of successes, p is the probability of success, and nCk is the number of combinations of k elements out of n.

In this case, n = 5 (the number of days in a week), k = 5 (the number of days that Jerry does not wait for more than five minutes), and p = 0.7 (the probability that Jerry does not wait for more than five minutes on any given day).

Plugging these values into the formula, we get:

P(X = 5) = 5C5 * 0.7^5 * (1 - 0.7)^(5 - 5)

P(X = 5) = 1 * 0.16807 * 1

P(X = 5) = 0.16807

Therefore, the probability that Jerry does not wait for more than five minutes all 5 days this week is about 16.8%.

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Answer:

50m/s

Step-by-step explanation:

Since we are not told what to find, we can as well look for two speed of the car in meter per seconds

If the car travels at a constant speed of 100 meters per 4 seconds, the we can say;

100 meters = 4seconds

Since we want to know the speed in metres per second, we will say;

X meters = 1second

Equating both

100 meters = 4seconds

X meters = 1seconds

Cross multiply

4×X = 200×1

4X = 200

Divide both sides by 4

4X/4 = 200/4

X= 50

Hence the of the car in meter per seconds is 50meters per second

The function that takes an input, adds 2, and then multiplies by 3 is a linear function with two operations: addition and multiplication. It can be represented by the equation y = 3(x + 2), where x is the input and y is the output.

To describe the function that adds 2 to the input and then multiplies by 3, we can break it down into two steps. First, we add 2 to the input, which can be represented by (x + 2). This expression ensures that the input is increased by 2.

The next step is to multiply the result by 3. Multiplying the expression (x + 2) by 3 gives us 3(x + 2). This step ensures that the increased input is further multiplied by 3.

Combining the two steps, we have the equation y = 3(x + 2), where y represents the output of the function. This equation indicates that the input (x) is first incremented by 2 and then multiplied by 3 to produce the final output (y).

Therefore, the function that takes an input, adds 2, and then multiplies by 3 can be described by the equation y = 3(x + 2).

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