equivalent (x+ 4)(2r - 1)

The value of h such that the matrix is the augmented matrix of a consistent linear system is 2

For the given matrix to be the augmented matrix of a consistent linear system, we need to check whether the matrix is in row echelon form or not. If the matrix is in row echelon form and the last row is not all zeros, then the linear system is consistent.

We can use elementary row operations to transform the matrix into row echelon form.

\(\left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right]\)

R2 <- R2 - 3R1

\(\left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right]\)

The matrix is in row echelon form. Now, we need to check whether the last row is all zeros or not.

If 6-3h = 0, then the last row will be all zeros, which implies that the linear system is inconsistent.

If 6-3h ≠ 0, then the last row will not be all zeros, which implies that the linear system is consistent.

Therefore, we need to solve the equation 6-3h = 0 to determine the value of h that makes the linear system consistent.

6-3h = 0

3h = 6

h = 2

So, the value of h that makes the matrix the augmented matrix of a consistent linear system is h = 2.

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Using probability concepts, it is found that:

a) Since \(P(A)P(B) \neq 0\), the events are not mutually exclusive.

b) 0.997 = 99.7% probability that the  can does not have a puncture or does not have a smashed edge.

Item a:

Two events, A and B, are mutually exclusive if:

\(P(A \cap B) = 0\)

In this problem:

The problem also states that the probability of neither is \(P(A \cap B) = 0.893\).

Since \(P(A)P(B) \neq 0\), the events are not mutually exclusive.

Item b:

Using Venn probabilities, the "or" probability is given by:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

With the given values:

\(P(A \cup B) = 0.96 + 0.93 - 0.893 = 0.997\)

0.997 = 99.7% probability that the  can does not have a puncture or does not have a smashed edge.

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In the given function H(p) = p/5 + 15, the independent variable is "p" ,

The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.

It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.

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Answer:

hla amgx q tal están queriendo q te ayude yo sé cómo te puedo ayudar para q te saques buenas notas

Step-by-step explanation:

primero me das la corona y te lo digo sii

The expression [(sin  θ)(sec  θ)]² + 1 can be simplified to sec²  θ + 1. This is equivalent to csc²  θ, so the answer is (B).

Based on the information, [(sin  θ)(sec  θ)]² + 1 = (sin²  θ)(sec²  θ) + 1

= (sin²  θ)(1/cos²  θ) + 1

= sin²  θ/cos²  θ + 1

= (sin²  θ + cos²  θ)/cos²  θ

= 1/cos²  θ

= csc²  θ

Therefore, the expression [(sin  θ)(sec  θ)]² + 1 can be simplified to sec²  θ + 1. This is equivalent to csc²  θ, so the answer is (B).

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer: D. 3/12, 3/10, 3/5, 3/4

Step-by-step explanation:

The denomination decreases every time making the fraction bigger

Answer:

84

Step-by-step explanation:

1/4 of class don't play basketball but do play volleyball

so 9/28 of class play both since 4/7 - 1/4 = 9/28

9/28 of class = 27

1/28 of class = 3

class = 3*28

There are 84 girls in the class.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Girls who plays basketball = (3/4)x

Girls who plays volleyball = (4/7)x

Girls who plays both games = 27

Now, Let us consider total girls in the class = x

So we can write it as mathematical equation as;

⇒ (3/4)x +(4/7)x - 27 = x

By taking L.C.M. -

⇒ (21x+16x)/28 - (27) = x

⇒ 37x/28 = x + 27

⇒ 37x = 28x + (27×28)

⇒ 9x = 27×28

⇒ x = (27×28)/9

⇒ x = 3×28

⇒ x = 84

So, There are total 84 girls in the class.

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Answer:

2.00, -6, 10,000 and 43

Step-by-step explanation:

Answer:

a. Only the x-value is given.

Step-by-step explanation:

Taking a look at the graph of both equations, both equations are graphed correctly, because the slope (m) and y-intercept (b) values corresponds of each equation corresponds with what we have on the graph representing each equation.

The solution of two linear equations ought to be in a coordinate pair, (x, y). This means the x-value and it's correaponding y-value of the solution needs to be stated, not just the x-value.

Thus, the correct solution. Of the two linear equations are x = 4, when y = 3.

Solution in coordinate pair form is (4, 3).

Therefore, the statement that describes the error is:

a. Only the x-value is given.

The value of x is 16 and the value of y is 24. The maximum profit is 309,000 dollars.

C(x,y) = 2x²-2xy+y²-9x-10y+11

R(x,y) = 7x+6y

Profit function P(x,y) = R(x,y) - C(x,y)

= 7x+6y - (2x²-2xy+y²-9x-10y+11)

= -2x²-y²+16x+16y+2xy-11

P(x) = -4x+16+2y

P(y) = -2y+16+2x

P(x) = 0

P(y) = 0

-4x+16+2y = 0

-2y+16+2x = 0

-2x+32 = 0

x = 16

y = 24

P(16,24) = 304

Hence the maximum profit is 304,000.

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Answer:

A.

Step-by-step explanation:

Recall, SOHCAHTOA.

Reference angle = Z

Opposite = 35

Adjacent = 12

Hypotenuse = 37

Sin Z = Opp/Hyp

Therefore,

Sin z = 35/37

Answer:

5 parks

7 parks

9 parks

10 months

Step-by-step explanation:

1 month: 5 state parks

2 months:5+2=7 state parks

3 months:7+2=9 state parks

x months : 23 state parks

23-9 state parks = 14 state parks

14/2=7 it means 7 months more

3+7=10 months

10 months : 23 state parks

The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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Answer:

a. My quadrilateral has four equal sides.

Must be: Rhombus.

Could be: Square.

b. My quadrilateral has two sets of parallel sides.

Must be: Parallelogram.

Could be:  Rectangle, Rhombus, Square

c. My quadrilateral has four right angles.

Must be: Rectangle.

Could be: Square.

Explanation:

b. A quadrilateral with two sets of parallel sides must be a parallelogram. It could also be a rectangle, a rhombus, or a square. However, a rectangle, rhombus, or square is also a parallelogram, so a parallelogram is the "must be" shape.

c. A quadrilateral with four right angles must be a rectangle. It could also be a square, but a square is a special type of rectangle, so a rectangle is the "must be" shape.

Answer:

a)  Must be a rhombus.
     Could be a square, a rectangle, a parallelogram, a trapezoid, or a kite.

b)  Must be a parallelogram.
     Could be a square, a rectangle, a kite, or a rhombus.

c)  Must be a rectangle.
     Could be a square, a kite, a rhombus or a parallelogram.

Step-by-step explanation:

The six basic types of quadrilaterals are:

A quadrilateral by definition is a four-sided shape. Therefore, it is possible for all types of quadrilateral to have four equal sides. However, for it to be a square and a rhombus, it must have four equal sides.

The interior angles of a square are all right angles, and its opposite sides are parallel. So as we haven't been told anything about the interior angles of the quadrilateral, or if any of its sides are parallel, we can conclude that:

The types of quadrilateral that can have two sets of parallel sides are square, rectangle, rhombus, parallelogram and kite (all squares are kites).

The interior angles of a square and a rectangle are 90°.

The side lengths of a rhombus are congruent.

As we haven't been told anything about the interior angles or the side lengths of the quadrilateral, we can conclude that:

All quadrilaterals, apart from a trapezium, can have interior angles that are all right angles. However, for a quadrilateral to be a square or a rectangle, it must have interior angles that are right angles.

As we don't know if the side lengths of the quadrilateral are equal, we cannot know if it's a square. Therefore, we can conclude that:

The area of the composite figure is 122.5 square inches

Based on the problem statement, we have the following dimensions from the question

The area of the composite figure is the sum of individual areas

So, we have

Area = Isosceles right triangle + Rectangle + Another isosceles triangle

By applying the formulas, we have

Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3

Evaluate

Area = 122.5

Hence the area is 122.5 sq inches

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Answer:

Step-by-step explanation:

Use similarity here. The ratio will look like this:

\(\frac{height of Jack}{length of Jacks shadow}=\frac{height of beanstalk}{length of stalks shadow}\)

using the numbers provided:

\(\frac{15}{10}=\frac{x}{100}\) and then cross multiply:

10x = 1500 so

x = 150

Therefore, the beanstalk is 1500 feet tall

The circumference of the circle having a diameter of 38 mm will be 119.32 millimeters.

Given that:

Diameter, d = 38 mm

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let d be the diameter of the circle. The circumference of the circle will be given as,

C = πd units

The circumference of the circle will be given as,

C = 3.14 x 38

C = 119.32 mm

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sum of two angles of triangle are equal to the exterior angle of triangle

Answer:

Below.

Step-by-step explanation:

a + b + c = 180 degrees        (angles in a triangle)

c + d = 180 degrees              ( adjacent angles).

So, subtracting the 2 equations:

a + b + c - c - d = 0

a + b - d = 0

a + b = d.

Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Answer:

The circumference of the circle is 94.2m.

Step-by-step explanation:

The circumference of a circle is:

C = pi•d

Fill in the diameter which was given, 30m.

C = pi•30

use 3.14 for pi

C = 3.14 • 30

C = 94.2

The circumference is 94.2m

Answer:

1.The  equation of best fit is ŷ = 2.69152X + 3.45818.

Step-by-step explanation:

The correct image include the following: B. Green: image A.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.

In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.

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The equivalent ratios are 6:3, 24:12 and 18:9.

According to the question,

We have the following information:

We have a table where number of people and  benches are given.

(Note that equivalent ratios mean that when we simplify it then the ratio should be equal to the original ratio.)

Now, we will find the equivalent ratios column-wise:

In first column, we have 6 and 3.

6:3

Now, in second column, we have:

_:12

Now, dividing 12 by 3, we have 4.

Multiplying 4 into 6:

24:12

Now, in third column, we have:

18:_

Dividing 18 by 6:

18/6 = 3

Multiplying 3 by 3:

18:9

Hence, the equivalent ratios are 6:3, 24:12 and 18:9.

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Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

Answer:

y = -1/4 x+4 is blue

y = 1/2 x+4 is green

y = 3x is red

y = -1/2x is purple

y = 3 is black

y = -1/4 x+4 is blue, y = 1/2 x+4 is green, y = 3x is red, y = -1/2x is purple and  y= 3 is black

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

y = -1/4 x+4 is blue

The slope is -1/4

y = 1/2 x+4 is green

Slope is 1/2

y = 3x is red

Slope is 3

y = -1/2x is purple

Slope is -1/2

y = 3 is black

Hence, y = -1/4 x+4 is blue, y = 1/2 x+4 is green, y = 3x is red, y = -1/2x is purple and  y= 3 is black

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Answer:

It would be B. 815.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

On edge

Answer:

The area is 72.

Step-by-step explanation:

2 * 6 = 12

6 * 10 = 60

60 + 12 = 72

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Answer:

72 units squared

Step-by-step explanation:

6x2=12

10x6=6

60+12=72

Answer:

One side - 15 feet

Second side - 4 feet

Third side - 13 feet

Step-by-step explanation:

Let's call the sides A B and C, respectively.

We know that:

A = B + 11

C = B + 9

and that

A + B + C = 32

Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.

A + B + C = (B + 11) + B + (B + 9) = 32

3B + 20 = 32

3B = 12

B = 4

The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).