How can we easily recognize when a system of linear equations is inconsistent or not?

Answer:

(-5) +(+6) +(-2) = (-1)

(-22) -(+8) +(10) =(-4)

Step-by-step explanation:

(-5)+ (+6) is 1 + (-2) is (-1)

(-22)-(+8) is (-14)+(10) is (-14)

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

To know more about parallelepiped, visit:

https://brainly.com/question/30627222

#SPJ11

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

For more questions on: compound interest

https://brainly.com/question/31474686

#SPJ8

Answer:

14 cm

Step-by-step explanation:

1. Recognize that an isosceles triangle will have at least two equal sides. Given the wording of the problem, we can say that we have two equal sides of 4 cm and a third side of 6 cm

2. Define perimeter. The perimeter of a triangle is the length of the continuous line outlining the triangle

3. Add all three side lengths together (4 cm + 4 cm + 6 cm). This will equal 14 cm

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

For more about tangent:

https://brainly.com/question/19064965

#SPJ4

Answer:

9.2(12+10.4)

Step-by-step explanation:

"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.

The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,

we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)

= 13.8 ± (1.96 × 1.088)

= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13

= 15.9313.8 - 2.13

= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].

To know more about average, visit:

https://brainly.com/question/24057012

#SPJ11

The process of counting the number of observations is knowns as Tabulation.

The logical representation of the numerical data written in rows and columns is known as tabulation. It helps in to facilitate the statistical analysis. The data that can be organized in the form of table is termed as tabulation. The data in the table can be represented in a systematic manner. The main objective of tabulation is to present the systematic data in a brief manner.

There are two types of tabulation. They are:

1.Simple tabulation

2.Complex tabulation

A simple example for the tabulation is, The population of the people is divided into religion, caste, gender, age etc.

To know more about tabulation, visit:

https://brainly.com/question/17139731

#SPJ4

The equation sin^2(x) = 1/2 - 1/2cos(2x) is an identity that holds true for all values of x. It can be used to simplify expressions involving sine and cosine functions.

The equation sin^2(x) = 1/2 - 1/2cos(2x) is a trigonometric identity, which means it holds true for all values of x. To understand why this identity is true, we can use the double angle formula for cosine, which states that cos(2x) = cos^2(x) - sin^2(x). Rearranging this formula gives sin^2(x) = cos^2(x) - cos(2x).

Now, we can substitute the identity cos^2(x) + sin^2(x) = 1 into the above equation, which gives sin^2(x) = 1 - cos^2(x) - cos(2x). Rearranging further gives sin^2(x) = 1/2 - 1/2cos(2x), which is the desired identity.

This identity can be useful in simplifying expressions involving sine and cosine functions. For example, if we have an expression with both sin(x) and cos(x), we can use this identity to express everything in terms of sin(x) or cos(x) only.

To learn more about trigonometric click here: brainly.com/question/29156330

#SPJ11

The addition of 11/3 and (-5/6) is about 2.8 which is shown on a number line.

A number line is a representation of real numbers in the form of a graded straight line.

The addition of 11/3 and (-5/6) is:

11/3 + (-5/6)

= 11/3 - 5/6

= (22-5)/6

= 17/6

= 2.8

Hence, the addition of 11/3 and (-5/6) is about 2.8 which is shown on a  number line.

To learn more about the number lines, click here:

https://brainly.com/question/13189025

#SPJ1

Answer:

Part A none

Part B drawn

Step-by-step explanation:

Suppose the transversal intersects a pair of parallel lines it creates two pairs of alternate exterior angles.

Now if we look at the first figure we find that the alternate exterior angle 1 and 4 are equal . Also 3 and 2 are equal.

But <1 and < 2 are not equal . They are supplementary angles. Their sum is equal to 180 degrees.

Similarly angles 3 and4 are supplementary angles.

This situation does not support Ricky's claim. So you will select none in part A.

Now in part B we see that angle 5 &8 are equal and 6 & 7 are congruent.

This refutes Ricky's claims and this can be proved mathematically.

Angles 5 & 6 are supplementary angles. Similarly 7 & 8 are supplementary therefore they cannot be equal as they are unequal and a transversal is drawn not a perpendicular.

The part A none and for part B drawn.

Suppose the transversal intersects a pair of parallel lines it creates two pairs of alternate exterior angles.

Now if we look at the first figure we find that the alternate exterior angle 1 and 4 are equal . Also 3 and 2 are equal.

Two angles are called supplementary when their measures add up to 180 degrees.

But <1 and < 2 are not equal because they are supplementary angles. and the sum is equal to 180 degrees.

Similarly angles 3 and 4 are supplementary angles.

This situation is not support Ricky's claim so select none in part A.

Now for  part B we see that angle 5 &8 are equal and 6 & 7 are congruent.

This refutes Ricky's claims and this can be proved mathematically.

Angles 5 & 6 are supplementary angles. Similarly 7 & 8 are supplementary

Therefore they cannot be equal as they are unequal and a transversal is drawn not a perpendicular.

Therefore for the part A none and for part B drawn.

To learn more about the transversal visit:

https://brainly.com/question/24607467

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

For more such questions on polynomial

https://brainly.com/question/1496352

#SPJ8

Answer:

3/10 shade 3 in

Step-by-step explanation:

The slope can be calculated using the following equation:

Where (x1, y1) and (x2, y2) are two points on the line.

We know that if you buy 6 cans, x = 6, it will cost $3.00, y = 3.

We also know that if we buy zero cans, x = 0, it will cost nothing, y = 0.

So we have the points (0, 0) and (6, 3), so:

So, the slope is 1/2, fourth alternative.

a. The class width for all intervals in this frequency distribution is 3.

b. Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

c. Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

The number of full oscillations that any wave element performs in one unit of time is how we determine the frequency of a sinusoidal wave.

To find the class width, class midpoints, and class boundaries for the given frequency distribution, let's analyze the temperature intervals and frequencies:

Temperature (°F)    Frequency

32-35                      1

36-39                      3

40-43                      5

44-47                      11

48-51                      7

52-55                      7

56-59                      1

(a) Class width:

The class width is the difference between the upper and lower boundaries of each temperature interval. In this case, all the intervals have the same width.

Class width = Upper boundary - Lower boundary

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class width = 35 - 32 = 3

The class width for all intervals in this frequency distribution is 3.

(b) Class midpoints:

The class midpoint is the average value of the upper and lower boundaries of each interval. It represents the central value of the interval.

Class midpoint = (Upper boundary + Lower boundary) / 2

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class midpoint = (35 + 32) / 2 = 33.5

Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

(c) Class boundaries:

The class boundaries are the values that separate each interval. They are calculated by adding or subtracting half of the class width from the upper and lower boundaries.

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35, and the class width is 3.

Lower class boundary = Lower boundary - (0.5 * class width) = 32 - (0.5 * 3) = 32 - 1.5 = 30.5

Upper class boundary = Upper boundary + (0.5 * class width) = 35 + (0.5 * 3) = 35 + 1.5 = 36.5

Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

Note: The class boundaries are inclusive of the lower boundary and exclusive of the upper boundary.

These are the calculations for the class width, class midpoints, and class boundaries for the given frequency distribution.

Learn more about frequency on:

https://brainly.com/question/254161

#SPJ4

To find the class width, subtract the lower class limit from the upper class limit. To find the class midpoints, add the lower and upper class limits and divide by 2. To find the class boundaries, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit.

(a) Class width:

To find the class width, we subtract the lower class limit from the upper class limit. For example, the class width for the first class interval (32-35) is 35 - 32 = 3.

(b) Class midpoints:

To find the class midpoints, we add the lower class limit and the upper class limit and divide the sum by 2. For example, the class midpoint for the first class interval (32-35) is (32 + 35) / 2 = 33.5.

(c) Class boundaries:

To find the class boundaries, we subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. For example, the class boundaries for the first class interval (32-35) are (32 - 0.5) and (35 + 0.5).

https://brainly.com/question/35559032

#SPJ12

Answer:

Surface area of prism A is approximately 12.4 square units.

Step-by-step explanation:

Since prism A and prism B are similar, their corresponding side lengths are proportional. Let's use the scale factor k to represent the ratio of the side lengths of prism B to those of prism A. Then, the volume of prism B is (k³)(27) = 27k³ cubic units. Similarly, the surface area of prism B is (k²)(surface area of prism A).

We are given that the volume of prism B is approximately 512 cubic units. Therefore, we can solve for k:

27k³ = 512

k³ = 512/27

k ≈ 3.62

Now, we can use k to find the surface area of prism A:

surface area of prism B = (k²)(surface area of prism A)

128 = (3.62²)(surface area of prism A)

surface area of prism A ≈ 12.4 square units

Therefore, the surface area of prism A is approximately 12.4 square units.

Answer: x=0, y=3

Step-by-step explanation:

1. We can set both equations equal to each other, 2x+1=4x-1

2. From this, we get -2x=-2, so x=1

3. now we substitute this into any equation of your choosing, I'll be doing y=2x+1

4. From this, we get y=3

5. Substitute both values into the other equation to double check your answer. It works

6. x=0, y=3

Hope this helps!

Answer:

44

Step-by-step explanation:

the smaller triangle is multiples of 9

(9, 18, 27, 36, 45, etc.)

and the bigger triangle is multiples of 11

(11, 22, 33, 44, 55, etc.)

Answer:

44

Step-by-step explanation:

22÷18=11/9

33÷27=11/9

x÷36=11/9

x=11/9×36

x=44

Step-by-step explanation:

Hey there!

The points P1(3,-3) and midpoint is (-2,1). Let (X,y) be the end point.

Note: Find through using midpoint formula.

midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )

Put all values.

(\frac{X+3}{2},\frac{-3+y}{2})

Since they are equal, equating with it's corresponding components.

\frac{3 + x}{2} = - 2

-2 = 3 + x

-4 -3= x

Therefore, X= -7.

Now,

\( \frac{ - 3 + y}{2} = 1\)

\( - 3 + y = 2\)

Therefore, y= 5

Therefore, the other end point is (3,5).

Hope it helps...

The angle of 'x' is 87°  

The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another is always equal.

Here we have

Two lines are intersected at the point and forms four angles      

As we can see that given angles are vertically opposite angles  

=> x = 82°    

Therefore,

The angle of 'x' is 87°  

Learn more about Vertically Opposite Angles

https://brainly.com/question/18045519  

#SPJ1

Answer:

Step-by-step explanation:

To understand the transformation better we will take a point B first.

Coordinates of B → (3, 0)

When we rotate this point by 180° counterclockwise about the origin, rule to be followed,

(x, y) → (-x, -y)

By this rule, coordinates of B'' will be,

B(3, 0) → B''(-3, 0)

Now we translate the point B by 2 units right.

Rule for the translation is,

(x, y) → [(x + 2), 0]

Following this rule,

B''(-3, 0) → B'[(-3+2), 0]

             → B'(-1, 0)

We can conclude with the statement, "Figure ABCD was rotated by 180° about the origin followed by the translation of 2 units to the right" to get the new figure A'B'C'D' similar to pre-image ABCD.

Answer:

y = 2x

Step-by-step explanation:

We know

They earn $2 for each cup of lemonade they sell. So, the equation is

y = 2x

The pooled standard deviation is approximately 10.28.

The formula for calculating the pooled standard deviation, sp, is:

\(sp = \sqrt{((n_1-1)s_1^2 + (n_2-1)s_2^2)/(n_1+n_2-2)]}\)

where \(s_1\) and \(s_2\) are the standard deviations of the two samples, and n1 and n2 are the sample sizes.

Substituting the values given, we get:

\(sp = \sqrt{((15-1)(10^2) + (25-1)(13^2))/(15+25-2)]}\)

\(sp = \sqrt{[(1410^2 + 2413^2)/38]}\)

\(sp = \sqrt{[(1400 + 4056)/38]}\)

\(sp = \sqrt{[5456/38]}\)

sp ≈ 10.28

Therefore, the pooled standard deviation is approximately 10.28.

To learn more about standard deviation visit:https://brainly.com/question/23907081

#SPJ11

The total amount of cost of Franklin's family using a non-network provider will be $24,725.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

They had 17 physician visits, 9 specialist visits, and 4 physical therapist appointments at $90 each. They also had a hospital charge of $21,675 with an admission charge of $350.

Then the total charge is given as,

T = 17 × $90 + 9 × $90 + 4 × $90 + $21,675 + $350

T = $1,530 + $810 + $360 + $21,675 + $350

T = $24,725

The total amount of cost of Franklin's family using a non-network provider will be $24,725.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Franking Family pays a total of $24,725.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Franklin Family spend on 17 physician visits, 9 specialist visits, 4 physical therapist appointments at $90 each.

They also had a hospital charge of $21,675 with an admission charge of $350.

So, total they had paid

= 17(90) + 9(90) + 4(90) + 21675 + 350

= 1530 + 810 + 360 + 21675 + 350

= $24,725

Learn more about unitary Method here:

https://brainly.com/question/22056199

#SPJ1

If A,B, and C are three collinear points such that AB=10 units and AC=15 units, the length of BC is  5 units.

This is because of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, AB + AC = 25, which is greater than the length of BC, which is 5.  

To calculate the length of BC, we can use the Pythagorean theorem. The formula is a² + b² = c², where a and b are the sides of the triangle and c is the hypotenuse. In this case, we have a = 10 and b = 15, so c² = 10² + 15² = 325. To find c, we take the square root of both sides, so c = √325 = 18.25. Since BC is the hypotenuse, its length is 18.25, but since its endpoints are collinear, the length of BC is 5 units.

To  know more about the inequality theorem refer to the  link brainly.com/question/1163433

#SPJ4

The sampling distribution of x for a sample size of 30 is N(16642, 423.27), for a sample size of 50 is N(16642, 328.08), for a sample size of 100 is N(16642, 232.00), and for a sample size of 400 is N(16642, 116.00).

The sampling distribution of x for itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400 can be determined using the formula for the standard error of the mean (SEM):

SEM = σ / √n

where σ is the standard deviation and n is the sample size.

For a sample size of 30:

SEM = 2320 / √30 = 423.27

For a sample size of 50:

SEM = 2320 / √50 = 328.08

For a sample size of 100:

SEM = 2320 / √100 = 232.00

For a sample size of 400:

SEM = 2320 / √400 = 116.00

The sampling distributions of x for itemized deductions for this population of taxpayers for each of the sample sizes are normal distributions with a mean of $16,642 and the corresponding SEM values calculated above.

For more similar questions on taxpayers:

brainly.com/question/29746342

#SPJ11