Factoriser A(x)=(x+2)^2

Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

The least common denominator is 4x^2.

Answer:

Step-by-step explanation:

the least common denominator is 4 x^2

(x+1)/4x

3(x+1)/2x^2

To find the common denominator, find the prime factors of each denominator

4x =2*2*x

2x^2 = 2*x*x

We need to take the greatest number of each term

2:  We have two 2's in the first term and one 2 in the second term so we will take two 2's

x: we have one x in the first term and two x's in the second term so we take two x's

common denominator; 2*2*x*x

                                     4x^2

The value of x is 10

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

The large triangle is divided into 2 similar triangles

The ratios of corresponding sides are equal

8/12 = x+4/2x+1

=> 8( 2x+1) = 12( x+4 )

=>  16x+8 = 12x+48

=> 16x-12x = 48-8

=> 4x = 40

=> x= 40/4 = 10

The value of x is 10

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Answer:

Step-by-step explanation:

Answer: −a−5b

Step-by-step explanation:

How to simplify:

1. Rearrange terms

−4−(5−3)

−4−(−3+5)

2. Distribute

−4−(−3+5)

−4+3−5

3. Combine like terms

−4a+3a−5b

−a−5b

The linear system Ax = b is called homogeneous if b = 0; otherwise, it is called inhomogeneous. When all of the constant terms in a system of linear equations are zero, the system is said to be homogeneous. The related homogeneous system of a nonhomogeneous system is obtained by setting the constant term in each equation equal to zero.

There is always one solution, the zero vector, to a homogeneous system. A homogeneous system that has undergone a row operation maintains its homogeneity. It is significant to notice that we frequently exclude the final column of constant terms when representing a homogeneous system as a matrix since row operations would not change that column. So, rather than using an augmented matrix, we employ a standard matrix. There could be no specific solution and an empty solution set in the nonhomogeneous system. In a nonhomogeneous linear system of n equations in n variables, the origin is not always present at the intersection of the solution sets. Although an infinite intersection is still theoretically possible, a single point is still the most likely scenario for the intersection. But, there is also the chance of an empty intersection, which has no solution, as might occur, for instance, when intersecting two parallel lines.

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Based on the above, the graph of the resultant vector is shown in the image attached  (x-axis).

We must do a sum of vectors during the graph creation process before drawing the resulting vector.

Thus, while looking at the attached graph, we can claim that the vectors are:

w = <1, 5>

u = <-3, 1>

v = <4, -3>

So, the sum = u - v + w

Note also that in the sum of the vectors we need to add and subtract the correspondent parts and it will be:

u - v + w

= <-3, 1> - <4, -3> + <1, 5>

= <-3 - 4 + 1, 1 + 3 + 5>

= <-6, 9>

Therefore, Based on the above, the graph of the resultant vector is shown in the image attached  (x-axis).

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Option a is the correct answer. The patient's description of vivid dreams is most likely occurring during rapid eye movement (REM) sleep.

During fast eye development (REM) rest, the mind is exceptionally dynamic, yet the muscles are loose, bringing about the trademark quick eye developments that give this stage its name. It is during REM rest that most dreaming happens. These fantasies will generally be clear, close to home, and frequently strange, and can be serious to such an extent that they might awaken the sleeper. Interestingly, during non-REM rest, the mind is less dynamic, and dreams are ordinarily less striking and vital. The way that the patient depicted clear dreams is serious areas of strength for a that they were in REM rest, as opposed to one of the non-REM stages.

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The Frequency Distribution table is shown below.

The proportion of one event's frequency to all events' frequencies in a statistical experiment.

Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency.

Given:

The Frequency Distribution table is as follow:

Bin                           Frequency     relative Frequency        Cumulative        

                                                                                                Frequency

0- 5000                        4                    4/25 x 100 = 16%            4

5000 - 10000               7                    7/25 x 100 = 28%           4+7 = 13

10000- 15000               7                    7/25 x 100 = 28%            13+ 7= 20

15000 -20000              4                    4/25 x 100 = 16%            20+4= 24

20000-25000              3                    3/25 x 100 = 12%              24+3= 27

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The correct option is A.

A right triangle is a type of triangle in which one of its angles measures exactly 90 degrees (π/2 radians). This angle is called the right angle, and it is located opposite to the longest side of the triangle, which is called the hypotenuse. The other two sides are called the legs of the triangle.

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, is one of the most important properties of right triangles. This theorem can be written algebraically as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right triangles also have several other important properties, including:

The acute angles (those that are not the right angle) are complementary, which means that their sum is equal to 90 degrees.

The side opposite the right angle is always the longest side (the hypotenuse).

The legs are always perpendicular to each other.

The altitude (height) from the right angle to the hypotenuse divides the triangle into two smaller triangles that are similar to the original triangle and to each other.

Right triangles are used in many areas of mathematics and science, including trigonometry, calculus, geometry, physics, and engineering. They are also used in practical applications, such as in construction, surveying, and navigation.

In a right triangle EFG, where angle EFG = θ, the sine of θ is defined as the ratio of the length of the side opposite θ (EF) to the length of the hypotenuse (EG). Therefore, the answer is:

A. sin(θ) = EF/EG

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The value of the exponent 'x' in  5ˣ⁻⁵⁵ = 125⁵ is 70.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, An equation in exponents 5ˣ⁻⁵⁵ = 125⁵.

5ˣ⁻⁵⁵ = 5³ˣ⁵.     (as 5³ is 125)

Therefore, x - 55 = 15.

x = 70.

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Answer:

4x+12 ≤ 0 or 4x+1>3

4x ≤ -12 or 4x+1 > 3

x ≤-3 or x >1/2

Answer with Step-by-step explanation:

The time a vehicle is left parked is not a function of the cost of parking because the two variables are not directly related. The cost of parking in this situation depends on how long a vehicle is parked, while the opposite is not true.

This is because the cost of parking is based on an hourly rate, and the maximum cost is capped at $12. So, regardless of how long a car is parked, the maximum cost will always be $12. For example, a car parked for 1 hour will cost $3, a car parked for 4 hours will cost $12, and a car parked for 6 hours will still only cost $12.

On the other hand, the amount of time a car is parked is not limited by the parking cost. A driver may choose to park their car for any length of time within the maximum limit of the parking lot. So, the amount of time parked is not dependent on the cost but rather on the driver's choice and parking lot regulations.

As a result, there is no direct correlation between the length of time a car is parked and the cost of parking, and the length of time a car is parked is not a function of the cost of parking.

The slope of the line passing through the points (-1, 2) and (2, -3) is -5/3

From the question, we are to determine the slope of the line that passes through the points (-1, 2) and (2, -3)

To find the slope of the line passing through the points (-1,2) and (2,-3), we can use the formula

m = (y₂ - y₁)/(x₂ - x₁)

Where m is the slope of the line

and (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given values into this formula, we get

m =(-3 - 2)/(2 - (-1))

m = -5/(2 + 1)

m = -5/3

Hence, the slope is -5/3

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The rank of the 4 x 5 matrix is 2 whose null space is three-dimensional

Matrix is defined as a rectangular array of rows and columns.

Rank of a matrix is defined as the maximum number of linearly independent columns (or rows ) that the matrix has.

Rank–nullity theorem is defined as a theorem described in linear algebra, which says that the dimension of the domain of a map is the sum of its rank and its nullity.

The rank-nullity theorem states that for a matrix A,

rank(A)+nullity(A)= number of pivot columns of A

That implies (the number of pivot columns) - (the null space dimension) = rank

The rank-nullity theorem states that for any matrix A, the rank of A plus the dimension of the null space of A equals the number of columns of A. In other words:

rank(A) + dim(null(A)) = number of columns of A

In this case, we have a 4 x 5 matrix A with null space of dimension 3. Therefore, we can solve for the rank of A as follows:

rank(A) + dim(null(A)) = number of columns of A

rank(A) + 3 = 5

rank(A) = 2

So the rank of the 4 x 5 matrix is 2.

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Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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Step-by-step explanation:

We can divide both of these ratios. If they both come out to be the same number, they are proportional. If different, they are not proportional.

[tex] \frac{0.2}{2.6} = \frac{1}{13} [/tex]

[tex] \frac{0.3}{3.6} = \frac{1}{12} [/tex]

[tex] \frac{1}{13} \: does \: not \: equal \: \frac{1}{12} \: so \: not \: proportional[/tex]

The conversion of 27cm to inch is 10.63 inches.

A centimeter is a metric unit of measurement equal to one-hundredth of a meter. It is commonly used in many countries for measuring small distances, such as the length of an object or the height of a person. One centimeter is equal to 0.3937 inches.

To convert 27 centimeters to inches, we can use the following formula:

1 inch = 2.54 centimeters

Therefore, to convert 27 centimeters to inches, we can divide 27 by 2.54:

27 cm ÷ 2.54 = 10.63 inches (rounded to two decimal places)

So, 27 centimeters is approximately equal to 10.63 inches.

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For someone working 24 hours daily, the equivalent hourly wage for a $48,000 yearly salary would be $5.48 per hour.

Assuming that someone works 24 hours a day, 365 days a year, their total number of working hours in a year would be 8,760 hours. To calculate how much an hourly rate would be for a $48,000 yearly salary if someone works 24 hours daily, you can divide the annual salary by the total number of working hours.

Dividing $48,000 by 8,760 hours gives an hourly wage of $5.48. This means that if someone works 24 hours daily, their equivalent hourly wage for a $48,000 yearly salary would be $5.48 per hour.

Additionally, laws and regulations related to working hours vary by country and industry, and many limit the maximum number of working hours per day or week.

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The runner's rate in miles per hour is D * 4/3 miles per hour.

Distance is a measure of the physical space between two objects or points. It is the length of the shortest path between two points in space. Distance can be measured in different units, such as meters, kilometers, miles, feet, or inches, depending on the scale of the objects or the purpose of the measurement.

In geometry, the distance between two points in a Euclidean space can be calculated using the Pythagorean theorem or the distance formula. The distance formula is expressed as:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where d is the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane. This formula can be extended to three dimensions by adding a third term to the equation.

Distance can also be calculated using other methods, such as GPS (Global Positioning System) or by measuring the time it takes for an object to travel from one point to another, using the speed of light or sound.

In everyday life, distance is a fundamental concept used in various contexts, such as navigation, transportation, sports, and communication. It plays a significant role in determining the time and effort required to travel between two points and is often used as a basis for making decisions.

We can use the formula:

rate = distance / time

where distance is the distance traveled by the runner and time is the time taken to travel that distance.

Given that the runner travels 2/3 of the marathon distance in 10 minutes, we can find the total distance of the marathon by dividing the distance traveled by 2/3:

total distance = distance traveled / (2/3) = distance traveled * 3/2

Let's denote the total distance of the marathon as D. Then:

D = distance traveled * 3/2

distance traveled = D * 2/3

We know that the time taken to travel 2/3 of the distance is 10 minutes. Let's convert this to hours:

10 minutes = 10/60 hours = 1/6 hours

Now we can calculate the runner's rate:

rate = distance / time = (D * 2/3) / (1/6) = (D * 4/3) / 1 = D * 4/3

So the runner's rate in miles per hour is D * 4/3 miles per hour.

Note that we don't have a specific value for the total distance D of the marathon, so we cannot give a numerical answer. We can only express the runner's rate in terms of D as:

runner's rate = D * 4/3 miles per hour

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Answer:

19.72

Step-by-step explanation:

Answer:  p = 4

Step-by-step explanation:

Because 3 * 4 + 3 = 15 which is then multiplied by 4 equaling 60

Answer:

p=4

Step-by-step explanation:

4(3p +3) = 60

12p + 12 = 60

        -12   -12  

___________

12p = 48

p = 4

Any number that can be expressed as a ratio of two integers is called a rational number.

Any number that can be expressed as a ratio of two integers is called a rational number. The word "rational" comes from the word "ratio", which means a comparison of two quantities. In other words, a rational number is a number that can be written in the form p/q, where p and q are integers and q is not equal to 0. For example, 2/3, -5/7, and 1 are all rational numbers, while pi (π) and √2 are not rational because they cannot be expressed as a ratio of two integers.

Rational numbers can be positive, negative, or zero. They can also be expressed in different forms, such as mixed numbers or decimals. However, it is important to note that not all decimals are rational. A decimal is rational if and only if it either terminates or repeats indefinitely. For example, 0.25, 0.5, and 0.333... are all rational decimals, while 0.7 and 0.1234567891011121314... are not rational.

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Answer:

To find the measure of angle A, we substitute the given expression into the formula for the measure of an angle:

A = 12x + 12 degrees

To find the measure of angle C, we substitute the given expression into the formula for the measure of an angle:

C = 3x + 18 degrees

The measure of angle B is already given as 15 degrees.

Therefore, the measures of the three angles are:

Angle A = 12x + 12 degrees

Angle B = 15 degrees

Angle C = 3x + 18 degrees

Answer:

Step-by-step explanation:

5, 4, 3, 7, 6, 10, 9, 13, 12, 16, 15

Answer:

Step-by-step explanation:

The volume of a cylinder with a diameter of 34 m and a height of 27 m is 24501.42 m³.

A cylinder is a three-dimensional figure that has a rectangular body but is rolled up which gives it a round shape with two circles for its top and bottom. We see a lot of cylinders around us all the time.

Here, we have been told that the diameter of the cylinder is 34 which means that the radius is 34/2 = 17 m.

Furthermore, we have also been told that the height of the cylinder is 27 m.

We already know that the volume of a cylinder can be calculated using

= πr²h

Using the values, we get -

= 3.14 * 17 * 17 * 27

= 24501.42 m³.

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The highest 5% of all IQs in the N(100, 15) Normal model are bounded by a value of 124.68, while the lowest 30% are bounded by a value of 92.64. The middle 80% of IQs are bounded by values between 80.77 and 119.23.

In the Normal model N(100, 15):

The highest 5% of all IQs are bounded by a z-score of 1.645, which corresponds to a value of 100 + (1.645 * 15) = 124.68. This means that an IQ of 124.68 or higher is in the top 5% of all IQs in this model.

The lowest 30% of the IQs are bounded by a z-score of -0.524, which corresponds to a value of 100 + (-0.524 * 15) = 92.64. This means that an IQ of 92.64 or lower is in the lowest 30% of all IQs in this model.

The middle 80% of the IQs are bounded by z-scores of -1.282 and 1.282, which correspond to values of 100 + (-1.282 * 15) = 80.77 and 100 + (1.282 * 15) = 119.23, respectively. This means that IQs falling between 80.77 and 119.23 are in the middle 80% of all IQs in this model.

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Answer:

x = 3 units

Step-by-step explanation:

These two triangles are similar figures, which means the ratio of the lengths of their corresponding sides are equal:

[tex]\frac{Side AB}{Side AC} = \frac{Side DE}{Side CE}[/tex]

= [tex]\frac{24}{2x} = \frac{56}{3x + 5}[/tex]

Cross-multiplication is applied:

= [tex](24)(3x + 5) = (56)(2x)[/tex]

Parenthesis are expanded by using the Distributive Law:

= [tex]72x + 120 = 112x[/tex]

Bring all the like terms together and then isolate x:

= [tex]120 = 112x - 72x[/tex]

= [tex]120 = 40x[/tex]

= x = [tex]\frac{120}{40}[/tex]

∴ x = 3 units

The average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Given that, the total cost to produce by James shirts is represented by a function, f(x) = 5x²+6.

We are to find the average rate of change of the total cost as his shirt production increases from 10 to 20.

The average rate of change is given by =

f(b) - f(a) / b-a, where a and b are given intervals,

Here, we have, a = 10 and b = 20

f(b) = 5(20)²+6 = 2006

f(a) = 5(10)²+6 = 506

The rate of change =

2006 - 506 / 20-10

= 1500 / 10

= 150

Hence, the average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

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If Juan baked 250 cookies in 2 hours, then he can make approximately 2.08 cookies in one minute.

The unitary method involves finding the value of one unit and then using that to find the value of any number of units.

In this problem, the unit we are interested in is cookies per minute. We need to find out how many cookies Juan can make in one minute, given that he can make 250 cookies in 2 hours.

To find out how many cookies Juan can make in one hour, we can use the unitary method as follows:

1 hour = 60 minutes (since there are 60 minutes in one hour)

So, if Juan can make 250 cookies in 2 hours, he can make:

250 cookies / 2 hours = 125 cookies per hour

Using the unitary method again, we can find out number of cookies Juan can make in one minute:

1 hour = 60 minutes

So, Juan can make:

125 cookies / 60 minutes = 2.08 cookies per minute

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Answer:

$2945.8

Step-by-step explanation:

226.60 multiplied by 13 is 2945.8.  

To check the answer you divide 2945.8

and 13 to get 226.60 or 226.6