Solve following equations by reducing their augmented matrix to the reduced echelon form
x+2y+z=2
2x+y+2z= -1
2x+3y-z = 9

In order to determine the  height of a box we can use the formula h = V/b or if the given box is a square box or a cube then we can calculate its height by finding the cube root of its volume.

In the formula , V = volume and b = base

Volume is calculated in three dimension , it is the measure of the space occupied by an object . Any given solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

There are various shapes in geometry and all of them have a specific formula to calculate the volume.

The SI unit of volume for a cube is m³.

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The line produced by the equation 3x + 4y=-12 has a slope of -3/4.

To find the slope of a line represented by the equation 3x + 4y = -12, you need to have the equation in the form y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

To put the equation 3x + 4y = -12 in this form, you can start by isolating the y term on one side of the equation:

3x + 4y = -12

4y = -3x - 12

y = (-3/4)x - (12/4)

The slope of the line produced by the equation 3x + 4y=-12 is therefore -3/4.

The complete question is:-

What is the slope of the line given by the equation 3x +4y =- 12?

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Answer: $2.70

Step-by-step explanation:

10% = 0.1

Take 27 times 0.1 = $2.70

-a/b=-5/3  is the slope of the line 5x 3y 15

for

ax+by=c

the slope is -a/b

the slope of paralell lines are the same

find slope

5x+3y=15

-a/b=-5/3

paralell as same slope

the slopes are:

L1: slope 3

L2: slope -3

L3: slope -1/3

So now multiply the slopes of each pair of lines:

L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular

L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular

L1 and L3: (3) *  (-1/3) = -1 => Yes, they are penpendicular.

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can you give a more clearer image if possible, please?

The value of sinx is 1 - 3cosx

What is Trigonometry?

Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. Today, four varieties of trigonometry are used: core, plane, spherical, and analytic. The ratio of the sides and angles of a right triangle is the subject of core trigonometry.

Solution:

1/cosx - tanx = 3

we can write tanx as sinx/cosx

this is because we know that sinx = Perpendicular / Hypotenuse

and cosx = Base / Hypotenuse

so if we divide sinx by cosx we will find that it is equal to Perpendicular / Base which is nothing but tanx

1-sinx = 3cosx

sinx = 1 - 3cosx

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The solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a.

The solution of the equation 2x^2 + 5x + 3 = 0 can be found by using the Quadratic Formula. The Quadratic Formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions are x = (-b +/- sqrt(b^2 - 4ac))/2a. By substituting the given coefficients a = 2, b = 5, and c = 3 into this equation, we can solve for x. First, we calculate the discriminant b^2 - 4ac, which in this case is 25 - 24 = 1. Because the discriminant is positive, the equation has two real solutions. Next, we use the Quadratic Formula to calculate the solutions. To calculate the first solution, we substitute the given coefficients into the formula and solve for x: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3 and -1/2.

Therefore, the solution of the equation 2x^2 + 5x + 3 = 0 is x = -3 and x = -1/2.

Discriminant: b^2 - 4ac = 25 - 24 = 1

Solution 1: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -3

Solution 2: x = (-5 +/- sqrt(1))/2 = (-5 +/- 1)/2 = -1/2

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The required coordinates of point P, following the given coordinate points, are (5.5, -1).

Let's assume that point P has coordinates (x, y). We want to find the coordinates of point P along the directed line segment AB, such that the ratio of AP to PB is 1 to 4.

The coordinates of point A are (8, 0), and the coordinates of point B are (3, -2).

According to the ratio given, we have:

AP/PB = 1/4

Now, we can use the midpoint formula to find the coordinates of point P. The midpoint formula states that the coordinates of the midpoint M between two points (x₁, y₁) and (x₂, y₂) are given by:

Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's use the midpoint formula to find the coordinates of point P:

x = (8 + 3) / 2
  = 5.5

y = (0 + (-2)) / 2
  = -1

So, the coordinates of point P are (5.5, -1).

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The volume of the pyramid is one-third of the product of its height and the area of its base. That is volume of the pyramid is linearly proportional to its height and the area of its base.

A pyramid is a solid with a base and rectangle face on the edge of base meeting at a vertex. Generally we consider a right pyramid.

Consider a pyramid of base area A and height h, the volume of the pyramid is one-third of the product of its height and the area of its base, that is the volume formula of pyramid is

V = A × h/ 3

That is

V ∝ A and

V ∝ h

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Answer:

17.5%

Step-by-step explanation:

We know that there are 35 out of 200 allergic to peanut

So we take

35 divided by 200, then times 100% = 17.5%

So, 17.5  of children are allergic to peanut

The probability of getting an ace from a well-shuffled deck of 52 cards is  1/13 and the probability of not getting an ace is 12/13

We can calculate the probability by the following method:

Total number of cards in a pack of cards= 52

Number of ace cards in a pack of cards= 4

Probability of an event= Number of possibilities of that event / Total number of possibilities

(i) If drawing an ace card is considered an event, suppose E, then:

P(E)= Number of ace cards/ Total number of cards

= 4/52

(ii) Probability of any event other than E= 1- Probability of the event E=

If the drawing of a non-ace card is considered an event, suppose E', then

P(E')= 1- the probability of drawing an ace card

= 1- P(E)

= 1-1/13

= (13-1)/ 13

= 12/13

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1) The function is P(t) = 6.79e^ 0.0317t

2) There would be 8.18 million people in 2018

3) It would take 9 years to reach a population of 9 million

4) The doubling time is 22 years

We know that population growth has to do with the increase in the population of a place. Let us recall that population growth occurs exponentially and this would help us as we write the function for the population growth.

a) The population growth function is obtained as;

P(t) = 6.79e^ 0.0317t

t = Number of years since 2012.

b) In the year 2018, six years would have passed hence we have;

P(t) = 6.79e^ 0.0317 * 6

P(t) = 8.18 million people

c) The population would be 9 million when;

9 =  6.79e^ 0.0317t

9/6.79 =e^ 0.0317t

1.33 = e^ 0.0317t

ln(1.33) = 0.0317t

t = ln(1.33)/0.0317

t = 9 years

d) The doubling time would be;

2(6.79) =6.79e^ 0.0317t

2(6.79)/6.79 = e^ 0.0317t

ln 2 =  0.0317t

t = ln 2 / 0.0317

t = 22 years

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The required mean of 2 and 12 is 7.

One kind of average is the mean.

It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.

Add up each value in the set to determine the mean.

So, we have the values:

2 and 12

Mean formula: Sum of terms / Number of terms

Now, solve for the mean of the 2 values using the formula as follows:

Mean: Sum of terms / Number of terms

Mean: 14 / 2

Mean: 7

Therefore, the required mean of 2 and 12 is 7.

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To find the median of a set of numbers, we need to first put the numbers in order from least to greatest. In this case, the ages of the Carnegie children are 3, 9, 18, and 24 years old. Since there are 4 numbers in this set, the median is the average of the middle two numbers, which are 9 and 18. The median of the ages of the Carnegie children is (9 + 18) / 2 = 27 / 2 = 13.5 years old.

To find the mean of a set of numbers, we need to add the numbers together and then divide the sum by the number of numbers in the set. In this case, the sum of the ages of the Carnegie children is 3 + 9 + 18 + 24 = 54 years old. Since there are 4 children, the mean age is 54 years / 4 children = 13.5 years old. Therefore, the mean of the ages of the Carnegie children is 13.5 years old.

Answer:

Median: 13.5

Mean: 13.5

Step-by-step explanation:

To get the median, take the middle value. Since there are two middle values, add them together and divide them by two.

To get the mean, add all the values together and divide the sum by the number of values. In this instance, mean and median are the same.

Answer: the height of this triangle is 55.4 mm

Step-by-step explanation:

[tex]\displaystyle\\Area\ of\ a\ triangle:\ A =\ \frac{ah}{2} \\\\Hence,\\[/tex]

Multiply both parts of the equation by 2:

[tex]2A=ah[/tex]

Divide both parts of the equation by a:

[tex]\displaystyle\\\frac{2A}{a} =h\\\\Thus,\ h=\frac{2A}{a} \\\\h=\frac{2(227.14)}{8.2} \\\\h=\frac{454.28}{8,2} \\\\h=55.4\ mm[/tex]

Answer:

cowboys fan:0  im guessing lol

Step-by-step explanation:

cowboys aren't bad so i'm not complaining:)

The nature of roots of the given quadratic equation is "real and unequal".

Nature of Roots:

Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.

Depending on the value of the discriminant, we discuss the following cases for the nature of the root:

Case 1: D = 0

If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.

Case 3: D < 0

If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.

Case 4: Perfect Square with D > 0

If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.

Case 5: D > 0 and Not Perfect Square

If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.

According to the Question:

The given quadratic equation:

9x²-6x-2 = 0

Here, a = 9, b = - 6 and c = -2

To Find: the nature of roots of the given quadratic equation.

∴ Discriminant, D = b²-4ac

= (-6)² - 4×9×(-2)

= 36 -36(-2)

= 36 + 72

=108

Since,

D = 108 > 0, the roots are real and unequal.

Hence, the nature of roots of the given quadratic equation is "real and unequal".

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Answer:

1. has ordered both a gown and a yearbook: 54%

2. has ordered a yearbook or a gown: 58% + 54% = 112%

3. has ordered neither a yearbook nor a gown: 100% - (58% + 54%) = 88%

4. has ordered a yearbook but not a gown: 54% - 15% = 39%

Step-by-step explanation:

Answer: The answer is option 1

Step-by-step explanation

The given equation is [tex](p^{2} r^{3} /pr^{4} )^{2}[/tex]

 [tex](p^{2} r^{3} /pr^{4})^{2}[/tex]  =  [tex]p^{4} r^{6} /p^{2}r^{8}[/tex]  (the given equation whole square is applied)

[tex]p^{4} r^{6} /p^{2} r^{8}[/tex]  =  [tex]p^{2} /r^{2}[/tex]   (the p and r are canceled out )

Therefore the correct answer is  [tex]p^{2} /r^{2}[/tex]

Answer:

Congruent means the same shape but perhaps moved or rotated or reflected

Similar means a shape that has been enlarged by a scale factor

Step-by-step explanation:

The circumference of the circle with a radius of 4 inches is 8π inches.

The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure.

Given that the radius of the circle is 4 inches. The circumference of the circle will be calculated by the formula,

Circumference = 2πr

Circumference = 2 x π x 4

Circumference = 8π inches

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The area henry' rectangular kitchen island top with length 35. 5 inches and width 46. 75 inches is 1659. 625 inch².

The word "area" means an open area. A shape's area is calculated using its length and width. Length is one-dimensional and measured in units such as feet (ft), yards (yd), and inches (in). Area is defined as the total space occupied by a planar (2-D) surface or shape of an object. It is measured in units such as square feet (ft²) and square inches (in²)

Let " l " be length of rectangular island top and "w" be width of it.

We have , l = 35.5 inches , w = 46.75 inches

We have to calculate the area if henry' rectangular kitchen iland top.

let "A" be area of rectangular island top .

As discuss above, Required Area , A = l × w

=> A = 35.5 inches × 46.75 inches

=> A = 1659.625 inch²

Hence, required area is 1659.625 square inches.

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The limit of h(x) as x approaches infinity is ∞, and as x approaches 0, is undefined due to division by zero.

x h(x)

1 2 + 2

2 1.41 + 1

4 2 + 0.25

8 2.83 + 0.125

16 4 + 0.0625

To find the limit of h(x) as x approaches infinity, we see that h(x) = √(x) + 2/x - 5. As x increases without bounds, the square root of x and 2/x both approach infinity, but the value of -5 is constant. Therefore, the limit of h(x) as x approaches infinity is infinite.

To find the limit of h(x) as x approaches 0, we see that h(x) = √(x) + 2/x - 5. As x approaches 0, the value of the square root of x approaches 0, and the value of 2/x approaches infinity. However, the value of -5 is constant. Therefore, the limit of h(x) as x approaches 0 is -5 + ∞, which is undefined.

The limit of h(x) as x approaches 0 is undefined.

You could also say that the function is not defined at x = 0, meaning that the limit as x approaches 0 does not exist.

It's worth noting that the original function is not defined when x=0 as we are dividing by x, so it's impossible to calculate the limit of this function at that point.

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The median when the mean is 48 and the mode is 15 is 37.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

For instance, what is the median of our data set if we know that we have a mean of 10 and a mode of 4?

Since the Mean - Mode is 3, we may state that 10 - 4 equals 3. (10 – Median).

According to some algebra, the median of our data is 8 because 2 = (10 - Median).

So, the values are:
Mean = 48

Mode = 15

Formula: Mean – Mode = 3(Mean – Median)

Now, calculate the median using the formula as follows:

48 – 15 = 3(48– Median)

33 = 144 - 3Median

3Median = 144 - 33

3Median = 111

Median = 111/3

Median = 37

Therefore, the median when the mean is 48 and the mode is 15 is 37.

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The factor of x³y³ is x.x.x.y.y.y or x²xy²y.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x³y³

This can be factorized as,
x.x.x.y.y.y

or

x²xy²y

Thus,

The factor is x.x.x.y.y.y or x²xy²y.

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Answer:

Right angle triangles

Step-by-step explanation:

the only type of triangles that can be solved with pythagorem theorem is right angle triangles. otherwise you would need to use a different formula

The statement that is true is there are no outliers in this distribution.

What is distribution ?

Selling and providing goods and services to customers is the process of distribution. The phrase is used to refer to marketing channels that are employed to contact clients in various contexts and geographical locations.

There are four different categories of distribution channels: direct selling, selling through middlemen, dual distribution, and reverse logistics networks.

The delivery of goods from manufacturers to end users is ensured by a network of distributors or intermediaries known as a distribution channel. It is also in charge of sending payments made by clients for purchases made by producers.

In this scenario, the noticeable outliers in the data sets are 200 and 210. Thus, a statement which is not true about the data provided in the box plot above, is that there are no outliers in this distribution

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Tommy and Zach will be 16 miles apart after 2.90 hours.

Let the time taken for Tommy and Zach to run until they are 16 miles apart be t hours.

Tommy runs North at a speed of 5 miles per hour.

Therefore, the distance covered by Tommy in t hours is 5 multiplied by t hours:

=5t miles

Zach runs East at a speed of 8 miles per hour.

Zach started running 2 hours later so that he would run for (t - 2) hours.

Distance covered by Zach in (t - 2) hours running at a speed of 8 miles per hour :

=8(t - 2) miles

Since they are now 16 miles apart, Pythagoras's theorem, a²+ b² = c², is applied.

[8(t - 2)]²+ (5t)² = 16²

64(t - 2)² + 25t² = 256

64(t² + 4 - 4t) + 25t² = 256

64t² + 256 - 256t + 25t² = 256

89t² -256t + 256 - 256 = 0

89t² - 256t = 0

t( 89t - 256) = 0

(89t - 256) = 0

9t = 256

= 256÷9

t = 2.90 hours

Therefore, for 2.90 hours, Zach and Tommy will be 16 miles apart.

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Answer:

C. Substitution

Step-by-step explanation:

Substitution is the final answer to an equation. So, the answer is C

Answer: C. Substitution

Arithmetic mean of the data set 4, 5, 0, 10, 8 and 3  is '5'

As per the question the given data set is :

4 , 5 , 0 , 10 , 8 and 3

Number of observations in given data set are '6'

We have to determine the value of arithmetic mean of the data

Arithmetic Mean is simply the mean or average for a set of data or a collection of numbers.

Arithmetic mean is defined as the ratio of sum of all observations in given data set to the total number of values.

Arithmetic mean ( AM ) formula is

AM = (sum of all observations in given data set) ÷ (total number of observations)

Sum of all observations in given data set :

= 4 + 5 + 0 + 10 + 8 + 3

= 30

Arithmetic mean :

[tex]=\frac{30}{6}[/tex]

= 5

Therefore arithmetic mean of the given data set 4, 5, 0, 10, 8 and 3  is 5.

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