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Dividing cubic polynomials by linear divisor

Solving the given matrix operation gives us the solution as: y = -1.4

From the matrix expression given, we can say that the simultaneous equations it represents are:

x - 4y = 8

3x - 2y = 10

We are told to Multiply eq 1 by -3 and add to row 2 and this means we have:

eq 3: -3x + 12y = -24

Adding to row 2 gives us:

10y = -14

y = -1.4

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Answer:

Step-by-step explanation:

The standard form of the equation for the circle is (x - 3)² + (y - 2)² = 8.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = √[(3 - 5)² + (2 - 4)²] = √8

Center, (h, k) = (3, 2).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 2)² = (√8)²

(x - 3)² + (y - 2)² = 8.

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Complete Question:

A circle is shown on the coordinate plane. The graph shows a circle with the origin point A at (3, 2), and a point B on its circumference at (5, 4) and intersects the x-axis at 1 and 5 units. What is the standard form of the equation for the circle?

Answer:

B

Step-by-step explanation:

Vertex form is: y=a(x-h)²+k

Vertex would be (h,k)

Based on this, the only equation in vertex form is B

Answer:

Step-by-step explanation:

B is the easiest way to see vertex because that is the vertex form:

y=a(x-h)²+k     where (h,k) is the vertex

Vertex (2, 27)

Answer: 25/546 chance

Step-by-step explanation:

total is 15 chocolates.

Five are milk, so chance of getting milk is 1/3. second is dark, so 5/14 chance. Then white, so 5/13 chance

1/3*5/14*5/13=25/546

Answer:

D. its a two dimensional object

Answer:

A. It is a polygon

C. It is a one-dimensional object

The shape is a polygon in two dimensions since a polygon must have at least three straight sides.

We would make the bar for the 15-18 age range with a height of 25 on the y-axis of the histogram.

A histogram is a type of chart used to represent the distribution of a set of continuous numerical data. It is a graphical representation that consists of a series of vertical bars, where the height of each bar represents the frequency or count of observations falling within a specific interval or "bin" of values.

To make a histogram, we need to plot the age groups on the x-axis and the corresponding number of tickets on the y-axis. The bars in the histogram should represent the frequency of each age group.

From the given data, the number of tickets bought by people of age 15-18 is 25. Therefore, we would make the bar for the 15-18 age range with a height of 25 on the y-axis of the histogram.

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In A'B'C'D, line segment A'B has a slope of 0 and a length of 5/4

From the question, we have the following parameters that can be used in our computation:

A = (1, 4) and B = (6, 4)

The line AB is a horizontal line that passes through the point y = 4

This means that the slope of the segment A'B' is 0

The length is then calculated as

A'B' = difference in the x-coordinate * scale factor

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

A'B' = (6 - 1) * 1/4

Evaluate

A'B' = 5/4

Hence, the length A'B' is 5/4

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If function "h" is one-to-one function which is having values h(-9) = 5, and h(3) = -4, then the inverse statement is (d) h⁻¹(-4) = 3.

We know that the function "h" is a one-to-one function, so, it has an inverse function (h⁻¹). To find the inverse function, we need to exchange  roles of "x" and "y" and solve for y. This gives:

x = h(y)

y = h⁻¹(x)

The given values of function "h" are h(-9) = 5 and h(3) = -4, we find the values of h⁻¹(5) and h⁻¹(-4):

h(-9) = 5

So, h⁻¹(5) = -9 (by exchanging roles of x and y)

and h(3) = -4

So, h⁻¹(-4) = 3 (exchanging the roles of x and y)

The function "h⁻¹(-4) = 3" is represented in option (d).

Therefore, the correct option is (d).

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The statement "1+1 is the hardest problem in the world" is generally meant to be taken as a joke or a humorous exaggeration.

The phrase may be used ironically to emphasize the difficulty of a seemingly simple task or to highlight the importance of attention to detail. For example, a complex mathematical proof may require multiple steps and involve intricate calculations, but the simplest mistake, such as an error in basic arithmetic, could render the entire proof invalid.

In this context, the phrase "1+1 is the hardest problem in the world" could be used to underscore the importance of checking and double-checking even the most basic assumptions and calculations in complex problem-solving.

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Answer:

  C) x = 5 if and only if x + 5 = 10

Step-by-step explanation:

You want to identify the biconditional statement among those that are given.

A conditional statement is of the form ...

  If P, then Q.

The converse of the above conditional statement is ...

  If Q, then P.

When both the statement and its converse are intended, the statement can be written as the biconditional ...

  If and only if P then Q.

The given example of a biconditional statement is ...

  x = 5 if and only if x +5 = 10.

__

Additional comment

This can be abbreviated ...

  Iff P then Q

meaning "if P then Q, and if Q then P", or "if and only if P, then Q."

After 4 years, the investment of $700 at 4% compounded daily results in a future value of $821.45.

The future value represents the present value or investment compounded at an interest rate periodically for a certain number of years.

The future value can be determined using the FV formula or an online finance calculator.

N (# of periods) = 1,460 days (4 years x 365)

I/Y (Interest per year) = 4%

PV (Present Value) = $700

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $821.45

Total Interest = $121.45

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14 students excel in all three subjects.

Let's use the Principle of Inclusion-Exclusion to solve this problem.

Let A be the set of students excelling in Arts, B be the set of students excelling in Science, and C be the set of students excelling in Mathematics.

|A| = 24, |B| = 16, |C| = 13

|A ∩ B| = 16, |B ∩ C| = 13, |A ∩ C| = 12

Let x be the number of students who excel in all three subjects.

|A ∩ B ∩ C| = x

We are given that 2 students excel in none of the subjects.

So, |A ∪ B ∪ C| = 52 - 2 = 50

Using the Principle of Inclusion-Exclusion:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|

Substituting the given values, we get:

50 = 24 + 16 + 13 - 16 - 13 - 12 + x

Solving for x, we get:

50 = 24 - 12 + x

x = 38 - 24

x = 14

So, 14 students excel in all three subjects.

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Michio's answer not correct. He made a mistake when he was trying to convert the equation to logarithmic form. The right answer is  2.57

Looking at the equation 2(3)ˣ = 34, the best way to convert to logarithm is by isolating x.

we divide  2(3)ˣ = 34 by 2 on both side.

= (3)ˣ = 17

In logarithm form 3 becomes the base of the log

x = log₃(17)

x= 2.578

The answer above is based on the information seen in the picture.

Michio wanted to find the value of x in the equation 2(3)ˣ = 34. He first converted the equation to log₃2x = 17. Next, he wrote 2x = 3¹⁷ and used a calculator to find x = 64,570,081.5. Was his answer correct? If not, what was his mistake and what is the right answer? Justify your answer.

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Therefore, the slope of line s is equal to (d + b) / (a - c).

In mathematics, the slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those same two points. In other words, the slope is the change in the y-coordinate divided by the change in the x-coordinate. If the slope is positive, the line is increasing from left to right and has an upward direction. If the slope is negative, the line is decreasing from left to right and has a downward direction. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical. The concept of slope is important in various fields of mathematics, science, and engineering, as it helps to describe the relationship between two variables and make predictions based on that relationship. It is also used in calculus to find the rate of change of a function, and in geometry to find the equation of a line or the angle between two lines.

Here,

Since line s is parallel to line t, it has the same slope as line t. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, the points on line t are (a, -b) and (-c, d), so the slope of line t is:

slope of t = (d - (-b)) / (-c - a)

slope of t = (d + b) / (a - c)

Since line s is parallel to line t, it has the same slope as line t:

slope of s = (d + b) / (a - c)

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The correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

What is decagonal pyramid?

A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.

Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.

We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.

Hence the correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

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Answer is 16.4. Hope this helpsAnswer:

Step-by-step explanation:

The volume of the cuboid is 58 cubic units.

A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;

volume of cuboid = length x width x height

From the given question, we have;

the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;

volume of cuboid = length x width x height

                             = 2.9 x 5 x 4

                             = 58

The volume of the cuboid with the given dimension is 58 cubic units.

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Piston movement compresses air in Small compressors type of air compressor

Piston movement compresses air in small compressors. Small compressors, also known as portable compressors, are commonly used for home improvement projects, powering tools, and inflating tires or other objects. The piston moves back and forth inside a cylinder, compressing air and increasing its pressure. The compressed air is then stored in a tank until it is needed to power a tool or inflate an object.

Small compressors are generally less powerful than medium or industrial compressors, but they are more affordable, portable, and easier to use for smaller tasks. They can be powered by electricity or gasoline, and they come in a range of sizes and capacities to meet different needs. Overall, piston-driven small compressors are an efficient and cost-effective way to compress air for various applications.

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The probability that the team wins the debate is 0.6475

P(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)

= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)

= 0.6475

Therefore, the probability that the team wins the debate is 0.6475.

In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:

Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.

Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.

Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.

If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.

Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.

Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.

Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.

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The calculated value of the maximum possible value of the objective function is 46

From the question, we have the following parameters that can be used in our computation:

Objective function, F = 5x + 6y

The coordinates of the feasible region are

(0, 6), (1, 6.5) and (2, 6)

Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation, so, we have the following representation

F(0, 6) = 5(0) + 6(6) = 36

F(1, 6.5) = 5(1) + 6(6.5) = 44

F(2, 6) = 5(2) + 6(6) = 46

The maximum value above is 46 at (2, 6)

Hence, the maximum possible value of the objective function is 46

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The solution of the given system of equations is (1, 2.5)

From the graph attached, it van be seen that two intersecting lines represent the system of equations.

And the solution of the system of equations is a common point where these lines intersect.

The graph shows both the line are intersecting each other at (1, 2.5).

Therefore, the solution of the given system of equations will be (1, 2.5).

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The values of the expression are,

⇒ x₂ = - 9.4

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

Given that;

Expression is,

e²ˣ = - 2x - 1

Hence, Function is,

⇒ f (x) = e²ˣ + 2x + 1 = 0

⇒ f' (x) = 2e²ˣ + 2

Now, By newton's method;

⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))

⇒ x₂ = x₁ - f (x₁) / f' (x₁)

⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)

⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)

⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)

⇒ x₂ = - 68 / 7.2

⇒ x₂ = - 9.4

⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))

⇒ x₃ = x₂ - f (x₂) / f' (x₂)

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

Thus, The values of the expression are,

⇒ x₂ = - 9.4

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

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The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.

In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.

On the y-axis, the graph represents the number of laps the swimmer is completing.

When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:

Number of laps remaining----------Time (in minutes)

30 --- 0

27 --- 1

24 --- 2

21 --- 3

18 --- 4

15 --- 5

12 --- 6

9 --- 7

6 --- 8

3 --- 9

0 --- 10

From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.  

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Answer:

The graph will be a circle with center (0, 2) and radius 6.

Answer: √2/2

Step-by-step explanation: Starting from the positive x-axis (angle 0), we rotate the ray counterclockwise by 45 degrees, or π/4 radians. Since the point on the unit circle corresponding to 45 degrees lies on the line y = x, its coordinates are (cos(45), sin(45)) = (√2/2, √2/2).

Answer:

number 1111q

Step-by-step explanation:

the answer is 1

The number of bacteria present at 5 hours is 148.413. The Option B is correct.

In exponential growth, a population's growth rate stays the same regardless of population size which makes the population grow faster and faster as it gets larger.

To get number of bacteria present at 5 hours, we need to evaluate the function [tex]f(5) = e^5.[/tex]

Using a calculator, we get:

[tex]f(5) = e^5\\f(5) = 148.413159103\\f(5) = 148.413.[/tex]

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