Can someone help me with this problem

The value of k for which the system has no solution is k = -16.

To determine the value of k for which the system has no solution, we can examine the system of equations:

x + y + 4z = 0 ...(1)

x + 2y - 2z = 0 ...(2)

4x + 9y + kz = 6 ...(3)

To have no solution, the system of equations must be inconsistent.

The coefficient matrix of the system is:

[tex]\left[\begin{array}{ccc}1&1&4\\1&2&-2\\4&9&k\end{array}\right][/tex]

The determinant of this matrix is given by:

|A| = (1 × 2 × k) + (1 × (-2) × 4) + (4 × 1 × 9) - (4 × 2 × 4) - (9 × (-2) × 1) - (k×1 ×1)

= 2k - 8 + 36 - 32 + 18 - k

= k + 16

For the system to have no solution, the determinant must be equal to zero:

k + 16 = 0

k = -16

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ4

All possible values of b1, b2, b3, b4, and b5 for which the given overdetermined linear system is inconsistent are given by,

b T ≠ [1 + 3c1 - 4c3, 1 - 2c1 + c2 + 4c3, 1, 1 - 4c1 + 4c3, 1 + 5c1 + c2 - 3c3]T

for any constants c1, c2, and c3.

An overdetermined linear system Ax = b must be inconsistent for some vector b.

The given system is, x1 - 3x2 = b1 x1 - 2x2 = b2 x1 + x2 = b3 x1 - 4x2 = b4 x1 + 5x2 = b5

It can be written in matrix form as

Ax = b

where,

A = 1 -3 0 0 0 1 -2 1 0 -4 1 5

and,

x = x1 x2 and

b = b1 b2 b3 b4 b5

Since A has more rows than columns, so it's an overdetermined system.

In an overdetermined system, the matrix A does not have an inverse, thus we can't solve Ax = b exactly.

So, we have to use least-squares to get an approximate solution. However, the least-squares solution doesn't exist if and only if b is outside the column space of A.

i.e. there is no solution to the system Ax = b, so it's inconsistent.

The column space of A is the set of all linear combinations of the columns of A. Hence, we need to find the column space of A.

First, let's find the reduced row echelon form of A using Gaussian elimination.

Row 1 ÷ 11 -3 0 0 0 1 -2 1 0 -4 1 5

Row 2 -R1 + R2 0 1 0 0 0 1 -1 1 4 0 2

Row 3 -R1 + R3 0 4 1 0 0 0 3 1 -4 0 4

Row 4 -R1 + R4 0 -1 0 1 0 0 -1 5 4 0 5

Row 5 -R1 + R5 0 8 1 0 1 0 3 6 -3 0 10

Row 4 + 4R2 0 0 0 1 0 0 3 1 0 0 13

The RREF is given by, 1 0 0 0 -9/11 -3/11 5/11 -1/11 -4/11 0 0 19/11 0 1 0 0 3/4 1/4 -1/4 0 -3/4 0 2/4 0 0 0 0 0 0 0 0 0

The columns corresponding to the pivot columns form a basis for the column space of A, which is a subspace of R5. Hence, we can express the basis as, B = {b1, b2, b3, b4}, where

b1 = (1, 1, 1, 1, 1)b2 = (-3, -2, 1, -4, 5)

b3 = (0, 1, 0, 0, 1)

b4 = (-4, 4, -4, 4, -3)

Thus, the column space of A is spanned by these 4 vectors.

If b belongs to the column space of A, then the system Ax = b will be consistent, otherwise, it'll be inconsistent.

i.e. there is no solution to the system Ax = b.

The coefficients of b in terms of the basis B are given by,

B T b = [1, -3, 0, -4; 1, -2, 1, 4; 1, 1, 0, -4; 1, -4, 0, 4; 1, 5, 1, -3]b T

Thus, the system Ax = b is inconsistent when b is not in the column space of A.

i.e. when,

b T ≠ c1b1 + c2b2 + c3b3 + c4b4

for any constants c1, c2, c3, and c4.

Substituting the values of b1, b2, b3, and b4 in the above equation, we get,

1b1 + 0b2 + 0b3 + 0b4 ≤ 1 1b1 - 2b2 + 0b3 + 4b4 ≤ 1 1b1 + 1b2 + 0b3 + 0b4 ≤ 1 1b1 - 4b2 + 0b3 + 4b4 ≤ 1 1b1 + 5b2 + 1b3 - 3b4 ≤ 1

So, the values of b1, b2, b3, b4, and b5 for which the given system is inconsistent are given by,

b T ≠ [1, 1, 1, 1, 1]T + c1[-3, -2, 1, -4, 5]T + c2[0, 1, 0, 0, 1]T + c3[-4, 4, -4, 4, -3]T

for any constants c1, c2, and c3.

Hence, all possible values of b1, b2, b3, b4, and b5 for which the given overdetermined linear system is inconsistent are given by,

b T ≠ [1 + 3c1 - 4c3, 1 - 2c1 + c2 + 4c3, 1, 1 - 4c1 + 4c3, 1 + 5c1 + c2 - 3c3]T

for any constants c1, c2, and c3.

Learn more about overdetermined linear system here:

https://brainly.com/question/31360022

#SPJ11

The critical value for the 40% level of significance is 1.96. Therefore, we can reject the Null hypothesis at the 40% level of significance.

In hypothesis testing, the critical value is used to determine the threshold for rejecting or not rejecting the Null hypothesis. The critical value depends on the desired level of significance and the distribution being used. In this scenario, we are conducting a one-sample t-test with a known population standard deviation.

To determine the critical value, we need to consider the level of significance. In this case, the level of significance is 40%, which corresponds to an alpha value of 0.40. Since the test is a one-tailed test (we want to test whether the mean waiting time is significantly more than 3 minutes), we divide the alpha value by 2, resulting in 0.20.

Using a t-distribution table or a statistical calculator, we find that the critical value for an alpha of 0.20 with degrees of freedom equal to the sample size minus 1 (99) is approximately 1.96.

Therefore, if the test statistic falls beyond the critical value of 1.96, we can reject the Null hypothesis at the 40% level of significance.

Learn more about statistic here:

https://brainly.com/question/32201536

#SPJ11

The predicted number of visitors when the temperature is 78° is 888.6 visitors.

The least-squares regression line of the number of visitors, y, at a national park and the temperature, x, is modeled by the equation,

D = 85.2 + 10.3x

We need to find the predicted number of visitors when the temperature is 78°.

Substitute x = 78 in the given equation of regression line:

D = 85.2 + 10.3x= 85.2 + 10.3(78)= 85.2 + 803.4

D = 888.6

To know more about least-squares regression, visit:

https://brainly.com/question/15455036

#SPJ11

Given that the least-squares regression line of the number of visitors, y, at a national park and the temperature, x, is modeled by the equation D=85.2+10.3x.

We need to find the predicted number of visitors when the temperature is 78°.

Option D (fourth) is correct.

To find out this we just need to substitute the given value of x = 78 into the equation of the regression line. So, we get the predicted number of visitors when the temperature is 78° as below:

[tex]D = 85.2 + 10.3 \times 78[/tex]

[tex]D = 85.2 + 803.4[/tex]

D = 888.6

Therefore, the predicted number of visitors when the temperature is 78° is 888.6 visitors.

Hence, option D is correct.

To know more about regression line visit

https://brainly.com/question/7656407

#SPJ11

The distribution of IQ scores is normal, with a mean of μ = 100 and a standard deviation of σ = 10.

Percentage of probability that a randomly selected person will have an IQ less than 90.Solution:We have to find the probability that a randomly selected person will have an IQ less than 90.Using the Z-score formula:Z = (X - μ) / σWhereX = 90μ = 100σ = 10Putting the values into the equation we have:Z = (90 - 100) / 10Z = -1

Using the standard normal distribution table we find that the area to the left of the z-score -1 is 0.1587.That means:P(Z < -1) = 0.1587To find the percentage, we convert it to a percentage by multiplying by 100.0.1587 × 100 = 15.87%Therefore, the probability that a randomly selected person will have an IQ less than 90 is 15.87%.

Know more about standard deviation:

https://brainly.com/question/29115611

#SPJ11

Answer:

793.6

Step-by-step explanation:

793.545=793.55=793.6

Answer:

x = 3

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex]

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{\sqrt{3} }[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by [tex]\sqrt{3}[/tex] )

x = 3

Answer:嘿，我不知道答案，但這段文字很酷

Answer:

find which one my guy im trying to get infinite awnseres srryyyyy

Step-by-step explanation:

Answer:

1. x=24/7

2. x=2

3. x= 11/9

4. x=3/2

5. x=16

6. x=10

7. x=8/9

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

1. x=24/7

2. x=2

3. x= 11/9

4. x=3/2

5. x=16

6. x=10

7. x=8/9

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

The answer to the questions is given in parts.

The standard normal distribution is a normal distribution of data that has been standardized so that it has a mean of 0 and a standard deviation of 1.

The area under the standard normal curve that lies to the right of various values of Z can be calculated using a table of standard normal probabilities, or by using a calculator or computer program. Here, we are given four values of Z and we need to determine the area under the standard normal curve that lies to the right of each value. We can use a standard normal table or a calculator to find these areas.

(a) The area to the right of Z = 0.24 is 0.4052 (rounded to four decimal places).

(b) The area to the right of Z=0.02 is 0.4901 (rounded to four decimal places).

(c) The area to the right of Z=-0.49 is 0.6879 (rounded to four decimal places).

(d) The area to the right of Z=1.89 is 0.0294 (rounded to four decimal places).

Learn more about standard normal distribution here:

https://brainly.com/question/15103234

#SPJ11

Answer:

7. 7.1+5.4+2.9=15.7

10.3+5.4=15.7

8. 373.4 - 152.9 = 220.5

373.4 - 153 = 220.4

220.4 - 0.1 = 220.5

9. 18.25 + 7.99 + 4.75 = 30.99

10. 1.05 + 3 + 4.28 + .95 = 9.28

11. 302.504

12 50.5

Answer:

If both sides of the triangle are exactly equal (which can be assumed they are because of the right angle), then that means EF = FG

Given that information, we can determine that EF is 6.1.

Now, all you have to do is add 6.1 + 6.1 to get 12.2.

EG = 12.2.

Answer:

7/9    

Step-by-step explanation:

7/9

Answer:

7/9

Step-by-step explanation:

Brainliest maaaybe? :)

Therefore, 3 is 6 1/2 of 19.5. Therefore, 30% of 9 is 2.7.  Therefore, 42% of 30 is 12.6. Therefore, 54 is 4 1/2 of 243. Therefore, 1.92 milligrams of antibiotic should be added to 4.8 mL of solution at this rate.

To find the number that is 6 1/2 times 3, we can set up the equation: x = 6 1/2 * 3. Multiplying 6 by 3 gives us 18, and 1/2 of 3 is 1.5. Adding these results, we get x = 19.5. Therefore, 3 is 6 1/2 of 19.5.

To find 30% of 9, we multiply 9 by 0.30 (or 30% written as a decimal). The calculation is 9 * 0.30 = 2.7. Therefore, 30% of 9 is 2.7.

To find 42% of 30, we multiply 30 by 0.42 (or 42% written as a decimal). The calculation is 30 * 0.42 = 12.6. Therefore, 42% of 30 is 12.6.

To find the number that is 4 1/2 times 54, we can set up the equation: x = 4 1/2 * 54. Multiplying 4 by 54 gives us 216, and 1/2 of 54 is 27. Adding these results, we get x = 243. Therefore, 54 is 4 1/2 of 243.

If the recommended rate is 0.8 mg per 2 mL of solution, we can set up a proportion to find the amount of antibiotic for 4.8 mL: (0.8 mg / 2 mL) = (x mg / 4.8 mL). Cross-multiplying and solving for x gives us x = (0.8 mg / 2 mL) * 4.8 mL = 1.92 mg. Therefore, 1.92 milligrams of antibiotic should be added to 4.8 mL of solution at this rate.

Learn more about decimal here:

https://brainly.com/question/30958821

#SPJ11

Answer:

71

Step-by-step explanation:

Answer:

√3

Step-by-step explanation:

                               opposite side         (√3)/2

tan 60 degrees = ------------------------- = ------------ = √3

                                  adjacent side          1/2

Answer:

# 1 the missing side is 11,  20+12+12= 44

Step-by-step explanation:

Answer:

1. 5

2. 4

3. 2

4. 10

Step-by-step explanation:

i did this already. so i knew the answers

The remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.

We can use the remainder theorem to find the remainder when a polynomial is divided by a linear factor.

The remainder theorem states that the remainder when a polynomial f(x) is divided by x - a is f(a). In this case, the polynomial is f(x) = 2x3 - 12x2 + 11x + 2 and the linear factor is x - 5. So, the remainder is f(5).

To find f(5), we can simply substitute x = 5 into the polynomial. This gives us f(5) = 2(5)3 - 12(5)2 + 11(5) + 2 = 7.

Therefore, the remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.

Learn more about remainder theorem here:

brainly.com/question/30242665

#SPJ11

Answer:0

Step-by-step explanation:

Answer:

7uwwjwjwjwjai9qiwjwwiwjb2wuw8ejvewusikwvww

To find the concentration of H+ or H3O+ ions ([H+] or [H3O+]) given a pH value , you can use the formula:

[H+] = 10^(-pH)

Let's calculate the values for two different pH values: pH = 4.0 and pH = 4.8.

For pH = 4.0:

[H+] = 10^(-4.0)

[H+] ≈ 1 × 10^(-4)

Therefore, the concentration of H+ ions ([H+]) at pH 4.0 is approximately 1 × 10^(-4) or 0.0001.

For pH = 4.8:

[H+] = 10^(-4.8)

[H+] ≈ 1.6 × 10^(-5)

Therefore, the concentration of H+ ions ([H+]) at pH 4.8 is approximately 1.6 × 10^(-5) or 0.000016.

Learn more about approximately here:

https://brainly.com/question/31695967

#SPJ11

Based on estimated sales of 2,000 cups of coffee per week and the amount of coffee required for each cup size, it is recommended to purchase approximately 46.875 pounds of coffee.

To determine the amount of coffee needed for 2,000 cups of coffee per week, we need to consider the size of each cup and the amount of coffee required for each size.

According to the information provided, small cups use 1 shot of espresso, medium cups use 2 shots, and large cups use 3 shots.

Since each shot requires approximately 7 grams of coffee (or about 1/64 of a pound), a small cup would require approximately 1/64 of a pound, a medium cup would require approximately 2/64 (or 1/32) of a pound, and a large cup would require approximately 3/64 of a pound.

Let's calculate the total amount of coffee required for 2,000 cups based on these proportions. Assuming a certain distribution of cup sizes, we can estimate the average number of shots per cup.

Let's assume that 40% of the cups are small, 40% are medium, and 20% are large.

With these proportions, we can calculate the total amount of coffee required.

(0.4 * 2,000 * 1/64) + (0.4 * 2,000 * 2/64) + (0.2 * 2,000 * 3/64) = 62.5 + 125 + 46.875 = 234.375

Therefore, to meet the estimated sales of 2,000 cups of coffee per week, it is recommended to purchase approximately 46.875 pounds of coffee.

To learn more about total amount visit:

brainly.com/question/2683720

#SPJ11

Answer:

d=18 feet

Step-by-step explanation:

The volume of a sphere is represented by the equation [tex]V=\frac{4}{3}\pi r[/tex]³, where r is the radius. If the volume is 972[tex]\pi[/tex],

[tex]972\pi =\frac{4}{3}\pi r[/tex]³

Divide [tex]\pi[/tex] from each side,

[tex]972=\frac{4}{3} r[/tex]³

Multiply each side by 3/4 to get rid of the fraction,

[tex]r[/tex]³[tex]=729[/tex]

Using the cube root, we find that 729 is actually a perfect cube.

[tex]r=9[/tex]

Now, the diameter is 2 times the radius, so

9×2=18

So, the measure of the diameter is 18 feet.

Answer:

[tex]2l + 2w[/tex]

Step-by-step explanation:

We know that a rectangle has four sides. And each pair of opposite sides are equal. We can set the length to [tex]l[/tex] and the width to [tex]w[/tex]. Since we know that both variables have a side that is equal to it, we know that the sum of the sides is[tex]l+l+w+w = 2l + 2w[/tex].

Answer:

Step-by-step explanation:

12 boxes of hay

Answer:48 bunches of hay

Step-by-step explanation:4 hunches for $9, therefore 108/9=12 and 4x12=48 bunches of hay

Answer:

Apartment 1 is his best option

Answer: Apartment 1

Step-by-step explanation:

The equation of the quadratic graph is: [tex]y = \frac{1}{8}(x - 3)^2 + 4[/tex]

In a quadratic graph, the focus and the directrix determine the shape and position of the parabola. The focus (3,4) represents the vertex of the parabola, and the directrix y=8 is a horizontal line.

To evaluate the equation of the quadratic graph, we use the vertex form of a quadratic equation, which is [tex]y = a(x - h)^2 + k[/tex], where (h,k) represents the vertex.

The focus coordinates indicate that the vertex is at (3,4). Thus, h = 3 and k = 4.

Since the directrix is a horizontal line, its equation takes the form y = c, where c is a constant. In this case, the directrix equation is y=8, meaning the distance from the vertex to the directrix is 4 units (8 - 4 = 4).

Using the formula [tex]a =\frac{1}{4p}[/tex], where p is the distance from the vertex to the focus (or directrix), we find that [tex]p = \frac{4}{2} = 2[/tex].

Substituting the values into the vertex form equation, we get:

[tex]y = a(x - 3)^2 + 4[/tex]

To evaluate the value of a, we use the formula a = 1 / (4p), where p = 2. Substituting this value, we have:

[tex]a = \frac{1}{4*2} = \frac{1}{8}[/tex]

Therefore, the equation of the quadratic graph is:

[tex]y = \frac{1}{8} (x - 3)^2 + 4[/tex]

Hence, the equation of the quadratic graph with a focus of (3,4) and a directrix of y=8 is [tex]y = \frac{1}{8} (x - 3)^2 + 4[/tex].

To know more about quadratic graph refer here:

https://brainly.com/question/14879503
#SPJ11