Find the point on the curve y = -x^2 - 2 that is closest to the point (0, 1)

Reduced matrix to its reduced echelon form Original Matrix:

[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,4)

Pivot Columns (Original): 1, 2, 4

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,4)

Pivot Columns (Reduced): 1, 2, 4

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column

4. Divide row 2 by 3 to get the coefficient 2/3 in the third column

5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column

6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column

Exercise 4:

Original Matrix:

[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,3)

Pivot Columns (Original): 1, 2, 3

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,3)

Pivot Columns (Reduced): 1, 2, 3

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract row 1 from row 3 to get the leading 1 in the third column

4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column

5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column

6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively

7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column

8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column

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The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles

Distance is defined as the quantity that describes the space that exists between two locations in a field.

The number of miles Tonya covered on Saturday = 3 ⅓ miles

The number of miles that Tonya covered on Sunday = 2 ⅘

Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.

That is; 3⅓ - 2⅘ ( change to single fraction form)

= 10/3 - 14/5

= 50-42/15

= 8/15

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A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.

A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.. The weight of each backpack will be recorded in order to calculate the mean and standard deviation of the sample. To calculate the mean, the total weight of the five backpacks will be added together and then divided by the number of backpacks in the sample (5). To calculate the standard deviation, the weight of each backpack will be subtracted from the mean and the resulting difference will be squared. All of the squared differences will then be added together, divided by the number of backpacks in the sample (5), and the square root of this result will be taken. This will give us the standard deviation of the sample. These calculations will provide us with valuable information about the weights of the backpacks in the sample, which can then be compared to the weights of the backpacks in the population.

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No, these data do not allow us to infer that the mean number of commercials watched is greater than 15.

To make such an inference, we would need to know the population mean number of commercials watched, along with the population standard deviation. We can use the sample data to calculate the sample mean and sample standard deviation. The sample mean (X) is the sum of the data values divided by the number of observations. The sample standard deviation (s) is calculated using the equation s = √(sum of (x-X)² / (n-1)) , where n is the number of observations. With the sample mean and standard deviation we can then use a t-test to determine if the population mean is significantly greater than 15.

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The amount of sugar present in the milk chocolate bar is, 12000   milligrams.

Given,

Amount of milk chocolate bar = 20.00 grams

Amount of sugar = 12.00 grams

The conversion used for grams to milligram is :

1 gram = 1000 milligram

As per question we are given that, 12 grams of sugar

As, 1 gram of sugar = 1000 milligram of sugar

So, 12.00 grams of sugar = (12/1) x 1000

                                          = 12000 milligrams of sugar

Therefore, the amount of sugar present in the milk chocolate bar is, 12000 milligrams.

(b) THe reduced size is 3 g

3 g bar has 12x3/20 g of sugar

i.e 7.2 g

hence , he amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g is 7200mg.

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The centroid of the given triangle is =(5.3 , 7.3)

The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.

The centroid formula of a given triangle can be expressed as,

C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)

where,

C denotes the centroid of a triangle

x1,x2,x3  are the x-coordinates of the 3 vertices.

y1,y2,y3  are the y-coordinates of the 3 vertices

To find: Centroid of a triangle.

We are taking the Cordinates of the traiangle XYZ

as x1,y1,x1,y2,x3,andy3

so,Given parameters are,

(x1,y1)=(-2,6)

(x2,y2)=(4,10)

(x3,y3)=(14,6)

Using centroid formula,

The centroid of a triangle = ,

 =-2+4+14/3  6+10+6/3

 =5.3 7.3

The centroid of a triangle is ==(5.3 and 7.3)

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Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.

Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.

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The equation of a line passing through the terminal point of a vector a and in the direction of vector b is  r = a + λb.

In math the equation of a straight line is y = m x + c

where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.

Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.

Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,

=> r = a + λb.

Where λ refers the constant term.

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Answer:

0.750

Step-by-step explanation:

Yellow sections: section 2 and section 3

Number of yellow sections: 2

Number of non yellow sections: 6

Total sections: 8

p(not yellow) = 6/8 = 0.75

Answer:

0.750

Step-by-step explanation:

you take a quarter and then you divide and think  

The denominator could be any real value

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

Fraction = same denominator

Such that the numerators are 5 and 7

This means that the fractions can be represented as

Fractions = 5/x and 7/x

There is no restriction on the possible value of x

hence, the denominator is any value

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The domain of each expression is given as follows:

1. All real values except y = 0 and y = 2.

2. All real values.

3. All real values except y = 0 and y = -7.

The domain of an expression is composed by the set of all the possible input values that the expression can assume.

For an expression that is a fraction, the denominator cannot be zero, hence:

For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.

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The number of scarves in 4 hours is 9.6

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

Rate = 3 scarves in 75 minutes

Time = 4 hours

The number of scarves is then calculated as

Scarves = Rate * Time

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

Scarves = (3/75 minutes) * 4 hours

Evaluate the product

Scarves = 9.6

Hence, the number of scarves is 9.6

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By adding (81.7-23.456)+(78.44+2.72), we get 139.404

Use the three rules below to calculate the number of significant figures in a number:

Non-zero digits are always meaningful.

Any zero between the first and second significant digits is significant.

Only the last zero or trailing zeros in the decimal section are important.

Numbers Have Rules INCLUDING a Decimal Point

START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.

STOP COUNTING FOR SIGNIFICANT FIGURES.

Non-zero numbers are ALWAYS meaningful.

After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.

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Given that IJ = 2, we know that IJ is the radius of the circle.

The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:

(x/360) * pi * 2^2 =

Solving for x:

x = (180/pi)*

We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.

The height of the building that cast the shadow 98 feet will be 61.25 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.

Let 'h' be the height of the building. Then the equation is given as,

h / (90 + 8) = 5 / 8

h / 98 = 5 / 8

h = 98 x 5 / 8

h = 12.25 x 5

h = 61.25 feet

The height of the building that cast the shadow 98 feet will be 61.25 feet.

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The exponent form that represents the side length of the square is √x

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

Area = x in.²

The area of a square is calculated as

Area = Side length²

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

Side length² = x

Take the square root of both sides

Side length = √x

Hence, the expression is √x

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Answer: Maybe if you post the question

Step-by-step explanation:

The image that gives the translation of the polygon six units to the left and two units upward is given as follows:

The fourth graph.

(which is the third graph if we consider that the first is the original image).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

For the translation 5 units left, we have that:

The bottom segment of x = 1 to x = 4 will assume coordinates of x = -5 to x = -2.

For the translation 2 units up, we have that:

The vertical segment from y = 1 to y = 3 will assume coordinates from y = 3 to y = 5.

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IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.

The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.

We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.

In another sentence, we were told that the size of the transistor today  is expressed as  1 × 10^-2

We can then know the difference in size will  which will be

= 1 × 10^4 / 1 × 10^-2

= 1 × 10^6

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complete question:

Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?

Answer:

1

Step-by-step explanation:

We have g(f(2))

Working from the inside out, we start with f(2)

So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2

Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)

Now we can go to the other graph, g(x) and find where X is -2.

That's where we find the point (-2,1)

Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1

Now we can conclude g(f(2)) = 1

Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

What is the graph?

A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.

To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).

Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

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answer

no

steps

February ends on the 28th this year 2023

leap year February ends on the 29th

Answer:

No, there is no value of a that makes the statement |a| = -2 true.

Step-by-step explanation:

The absolute value of a number is the distance of that number from zero on the number line. It is always non-negative, so it can't be -2. The absolute value of a number is denoted by two vertical lines on either side of the number like this |a|.

For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. In both cases, the distance from zero is 5.

In the statement |a| = -2, the absolute value of a is -2, which is impossible as the absolute value can't be negative. Therefore, there is no value of a that makes the statement true.

Answer:

  no

Step-by-step explanation:

You want to know if there's any value of the variable 'a' that would make its absolute value be -2.

The absolute value of a number is always positive. There is no such thing as a number whose absolute value is negative, not -2 or any other negative number.

  such a value of 'a' Does Not Exist (DNE)

Answer:

Step-by-step explanation:

You want the number of lines of symmetry of the 4-leaved rose shown in the figure.

The figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.

The petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)

The figure maps to itself when rotated 90° or 180°.

Answer: 22 vaccines

Step-by-step explanation:

first, reduce the amount that doctors leave out from the total amount of a vial

6 - 0.5 = 5.5

next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give

5.5/ 0.25 = 22 vaccines

The product of the binomial factors is x² + 16x + 64

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

(x+8)2

Express properly

So, we have

(x+8)²

Using the square of a binomial sum, we have

(x+8)² = x² + 2 * x * 8 + 8²

Evaluate

(x+8)² = x² + 16x + 64

Hence, the solution is x² + 16x + 64

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For function f(x)= x² + 7 and g(x)= x² + 2,

a) f(x) + g(x) = 2x² + 9

b) f(x) - g(x) = 5

c) f(x) . g(x) = x⁴ + 9x² + 14

d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]

Consider given functions  f(x)= x² + 7 and g(x)= x² + 2

a) To find addition of functions: f(x) + g(x)

f(x) + g(x)

= (x² + 7) + (x² + 2)

= x² + x² + 7 + 2             .............(associative property of addition)

= 2x² + 9                       ................(combine like terms)

b) to find subtraction of functions : f(x) - g(x)

f(x) - g(x)

= ( x² + 7 ) - (x² + 2)

= 7 - 2

= 5

c) To find multiplication of functions: f(x).g(x)

f(x) . g(x)

= ( x² + 7 ).(x² + 2)

= x² (x² + 2) + 7(x² + 2)

= x⁴ + 2x² + 7x² + 14

= x⁴ + 9x² + 14              ................(combine like terms)

d) To find division of functions: f(x)/g(x)

[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]

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Slope between the points (1,7) and (-5, -11) is m = 18/6 as a decimal m = 3

The slope of a hill describes its steepness. The steepness of a line follows a similar pattern. The rise between two points, which is the vertical change, is divided by the run, which is the horizontal change between those same two points, to determine the slope.

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

step1:

calculate the slope m using the slope formula

slope m=y2-y1/x2-x1

with (x₁, y₁ )=(1,-5) and (x₂, y₂ ) =(-5,-11)

step2:

m=-11-7/-5-1=-18/-6=18/6

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