find all values of c, such that the following linear system c 1 0 0 c 1 0 1 c x1 x2 x3 = 0 2 2 has (a) one unique solution; (b) no solution; (c) infinite many solutions.

Answer:

x=5

Step-by-step explanation:

6x-14=4x-4

6x-4x =2x

2x-14=-4

-4+14= 10

2x=10

x=5

Answer:

\(\boxed{\sf{x=5}}\)

Step-by-step explanation:

In order to solve this equation, you only need to isolate the term x.

Add 14 from both sides.

\(\sf{6x-14+14=4x-4+14}\)

Solve.

6x=4x+10

Subtract by 4x from both sides.

\(\sf{6x-4x=4x+10-4x}\)

Solve.

2x=10

Divide by 2 from both sides.

2x/2=10/2

Solve.

10/2=5

x=5

Therefore, the correct answer is x=5.

Answer:

7,7, and 7

Step-by-step explanation:

If she vase is cubical we know that all 3 dimensions are the same. This means that x^3 = 343. So we know the answer is the cube root of 343, which is 7

The dimensions of the cubic vase are 7 by 7 by 7.

A three-dimensional object with six congruent square faces is called a cube. The cube's six square faces all have the same dimensions.

Given that the volume of the cubic vessel is 343 cubic inches.

The formula for the volume of a cube of side length a is:

V =a³

Substitute V= 343:

343 = a³

Or, a = ∛343

a = 7

Hence, the dimensions of the cubic vase are 7 by 7 by 7.

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Answer:

The value of b₃ can be expressed as a linear combination of b₁ and b₂, specifically, b₃ = -b₁ - 2b₂.

To understand why this is the case, let's consider the given augmented matrix. The matrix represents a linear system of equations, where each row corresponds to an equation and the columns represent the coefficients of the variables.

In order for the system to be consistent, it means that there must exist a solution that satisfies all the equations. In other words, the system has to be solvable without any contradictions or inconsistencies.

To find the value of b₃, we can perform row operations on the augmented matrix to reduce it to row-echelon form or row-reduced echelon form. However, for this specific problem, we can observe a pattern in the matrix that allows us to directly determine the relationship between the variables.

Looking at the third row of the matrix, we can see that the coefficient of b₃ is 4, and the coefficients of b₁ and b₂ are both positive. To obtain a zero coefficient for b₃, we need to subtract multiples of the other two rows. By subtracting 4 times the first row and adding 2 times the second row from the third row, we eliminate the coefficient of b₃.

Doing the calculations, we get:

-4(4) + 2(-5) + 4(b₃) = 0

-16 - 10 + 4(b₃) = 0

-26 + 4(b₃) = 0

4(b₃) = 26

b₃ = 26/4

b₃ = 13/2

Therefore, we can express b₃ as a linear combination of b₁ and b₂ as b₃ = -b₁ - 2b₂.

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The answer is to find the critical value for constructing the standard deviation  80% confidence interval for the population mean magnesium concentration.


To find the critical value for the 80% confidence interval, we need to use the z-distribution since the sample size is greater than 30 and the population standard deviation is unknown.

The formula for finding the critical value is:
Critical value = z(alpha/2) * (standard deviation / sqrt(sample size))
Where alpha is the level of significance (1 - confidence level), z(alpha/2) is the z-score at alpha/2 level of the standard normal distribution, standard deviation is the sample standard deviation, and sample size is the number of samples.
Using a z-table or calculator, we can find that the z-score at the 40th percentile (80% confidence level) is 1.282.
Plugging in the values, we get:
Critical value = 1.282 * (0.0418 / sqrt(17)) ≈ 0.022
Therefore, the critical value for constructing the 80% confidence interval is approximately 0.022 (rounded to three decimal places).

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Answer:

32% is 0.32

6% is 0.06

93% is 0.93

150% is 1.5

12.5% is 0.125

Hope this helps!

The numbers that will round to 19 when rounded to the nearest whole number are 19.46 and 19.91.

To round a number to the nearest whole number, we look at the decimal part of the number. If it is less than 0.5, we round down to the nearest integer. If it is greater than or equal to 0.5, we round up to the nearest integer.

For the given set of numbers, we can round them to the nearest whole number and check which ones round to 19:

19.46 rounds up to 19

18.48 rounds down to 18

19.91 rounds up to 20

18.82 rounds up to 19

19.33 rounds up to 19

Therefore, the numbers that round to 19 when rounded to the nearest whole number are 19.46 and 19.33.

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Answer:497.76

Step-by-step explanation:

Answer:

Answer C

Step-by-step explanation:

seeing as how the x coordinates of the points are 2,3,4,6,7, we know that the answer must have these numbers, and only these numbers, as the domain. The only answer that has that is answer C.

The particular solution is: y_p = (-1/2)e^(2x). So the general solution to the differential equation is: y = C_1e^(2x) + C_2xe^(2x) - (1/2)e^(2x)

To find a particular solution of y'' - 4y' + 4y = e^(2x), we can use the method of undetermined coefficients. Since the right-hand side is e^(2x), we assume a particular solution of the form y_p = Ae^(2x), where A is a constant to be determined.

Taking the first and second derivatives of y_p, we get:

y'_p = 2Ae^(2x)
y''_p = 4Ae^(2x)

Substituting these expressions into the differential equation, we get:

4Ae^(2x) - 4(2Ae^(2x)) + 4(Ae^(2x)) = e^(2x)

Simplifying and solving for A, we get:

-2Ae^(2x) = e^(2x)

A = -1/2

Therefore, the particular solution is:

y_p = (-1/2)e^(2x)

So the general solution to the differential equation is:

y = C_1e^(2x) + C_2xe^(2x) - (1/2)e^(2x)

where C_1 and C_2 are constants determined by any initial or boundary conditions.

To find a particular solution of the given differential equation, y'' - 4y' + 4y = e^(2x), you can use the method of undetermined coefficients. First, identify the form of the particular solution, which in this case is y_p = Ae^(2x), where A is a constant to be determined. Differentiate y_p twice and plug the results into the given equation to find the value of A. Then, the particular solution will be y_p = Ae^(2x) with the determined value of A.

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Answer:

g(x) = 5^3x is a horizontal stretch of a factor of 3. g(x)= 1/3(5)^x is a vertical stretch of a factor of 3. g(x) = 5^1/3x is a vertical compression of a factor of 1/3. g(x) = 3(5)^3 is a horizontal compression of a factor of 1/3.

The correct option is C as it consists exact domain and range that we need.

What is domain and range?

The domain of a function f(x) is that the set of all values that the function is outlined, and also the range of the operate is that the set of all values that f takes.

The set of all attainable values that qualify as inputs to a operate is thought because the domain of the operate, or it also can be outlined because the entire set of values attainable for freelance variables. .

Main body:

the given function :

{(2,3), (7,9), (4,-7), (6,2), (3,-5)}

domain = (2,7,4,6,3)

range = (3,9,-7,2,-5)

Hence the correct option is C.

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Answer: X= -13/12

Step-by-step explanation:

The transformations that took for mapping ΔA onto ΔB are:

a) Translated the triangle A 2 units to the right,

b) Reflected the ΔA' (translated A) over the y-axis,

c) Reflected the ΔA'' (reflected A) over the x-axis, resulting in ΔB.

The transformation rules are:

a) Translation: (x, y) ⇒ (x + 2, y) (In the right side direction)

b) Reflection over the y-axis: (x, y) ⇒ (-x, y)

c) Reflection over the x-axis: (x, y) ⇒ (x, -y)

The given vertices of triangle A are: (-2, 3), (-5, 3), and (-5, 5).

a) Applying translation by 2 units to the right to triangle A:

(-2, 3) → (-2 + 2, 3) → (0, 3)

(-5, 3) → (-5 + 2, 3) → (-3, 3)

(-5, 5) → (-5 + 2, 5) → (-3, 5)

So, triangle A is translated to triangle A'.

b) Applying reflection over the y-axis to the triangle A':

(0, 3) → (0, 3)

(-3, 3) → (3, 3)

(-3, 5) → (3, 5)

So, triangle A' is reflected as triangle A''.

c) Applying reflection over the x-axis to triangle A'':

(0, 3) → (0, -3)

(3, 3) → (3, -3)

(3, 5) → (3, -5)

Thus, the formed triangle is B at the vertices (0, -3), (3, -3), and (3, -5).

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Answer:

x= 95/2  or  x=47.5  or   47 1/2

Step-by-step explanation:

3x + 10 = 5(x - 17)

First Step:

multiply and combine the right side (parentheses)

5 times x = 5x         5 times -17 = -85

3x + 10 = 5x -85

Second Step:

Add like terms ----> which is: 3x and 5x -----10 and -85

BUT since you only want one x on one side, you combine x first.

3x + 10 = 5x -85

-5x         -5x

-2x + 10 = -85

NOW

Third Step:     Add the integers---> 10 and -85

you want to get 10 on the same side as the -85, so you subtract it from BOTH sides.

which brings you:

-2x + 10 = -85

       -10    -10

NOW that we've subtracted -10 from -85 it's technically just adding 85 and 10 then putting a negative sign on it.

so now we have:

-2x = -95

Step Four:

divide -2 from each side to get X alone

-2x = -95

-2      -2

ANSWER:

x=47.5

The value of give operation is =[[0,-4,-28][20.4.-32]]

A rectangular or square array of numbers or variables that are arranged in rows and columns is known as a matrix in mathematics. Elements or entries are the names for individual things in a matrix.

The application of matrix plays a major role in Mathematics, as well as in other fields. It helps in solving linear equations. Matrices are extremely valuable objects that can be found in a wide range of applications. The application of matrices in mathematics is used in a wide range of scientific fields as well as mathematical areas. Engineering mathematics is used in almost every aspect of our lives. In this article, we are going to learn what is a matrix, different matrix operations and the application of matrices in detail.

Some of the matrix's rows and columns define how big it is. A matrix of "m" rows and "n" columns is written as "m*n," where "m" and "n" are the dimensions of the matrix.

We have, c=-4

\(A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right]\)

first, compute the cA.

\(=(-4)\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\cA=\left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\Now, BcA=\left[\begin{array}{ccc}1&2\\-1&3\\\end{array}\right] \left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\\\=\left[\begin{array}{ccc}0&-4&-28\\20&4&-32\\\end{array}\right]\)

The complete question is-

Perform the indicated operation,c=-4,

\(A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right]\)

B(cA)=?

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Answer:

An apple costs £0.25

A banana costs £0.34

Step-by-step explanation:

Let a be apples and b be bananas.

10a+5b=4.2

8a+10b=5.4

Solve for a:

10a+5b=4.2

Subtract 5b from both sides

10a=4.2-5b

Subtract 4.2 from both sides

10a-4.2= -5b

Multiply both sides by -1

-10a+4.2=5b

8a+10b=5.4

Subtract 10b from both sides

8a=5.4-10b

Subtract 5.4 from both sides

8a-5.4= -10b

Multiply both sides by -1

-8a+5.4= 10b

Divide both sides by 2

-4a+2.7=5b

Combine equations:

-4a+2.7= -10a+4.2

Add 10a to both sides

6a+2.7=4.2

Subtract 2.7 from both sides

6a=1.5

Divide both sides by 6

a=0.25

An apple costs £0.25

Solve for b:

10a+5b=4.2

Subtract 10a from both sides

5b= -10a+4.2

Subtract 4.2 from both sides

5b-4.2= -10a

Multiply both sides by -1

-5b+4.2=10a

8a+10b=5.4

Subtract 8a from both sides

10b= -8a+5.4

Subtract 5.4 from both sides

10b-5.4= -8a

Divide both sides by 4

2.5b-1.35= -2a

Multiply both sides by 5

12.5b-6.75= -10a

Multiply both sides by -1

-12.5b+6.75=10a

Combine equations:

-12.5b+6.75= -5b+4.2

Add 12.5b to both sides

6.75=7.5b+4.2

Subtract 4.2 from both sides

2.55=7.5b

7.5b=2.55

Divide both sides by 7.5

b=0.34

A banana costs £0.34

If you would like to check and see if it is true, (I already checked, it is) you can use the formulas I gave at the start of the explanation.

10a+5b=4.2

8a+10b=5.4

a=0.25

b=0.34

                                        C. 17 mm and 53.5 mm

(a)f'(x) = 6x. (b) The critical point of f'(x) occurs at x = 0. (c)The equation for the tangent line with the maximum slope is y = √2.

To compute f'(x), we need to differentiate the function f(x) = 3(\(x^{2}\) + 6) - c with respect to x.

(a) Compute f'(x):

Using the power rule for differentiation, we differentiate each term separately:

f'(x) = 3(2x) - 0 = 6x.

So, f'(x) = 6x.

(b) To find the critical points of f'(x), we set f'(x) = 0 and solve for x:

6x = 0

x = 0

Therefore, the critical point of f'(x) occurs at x = 0.

(c) To find the equations for the tangent lines with maximum and minimum slopes, we substitute the critical point x = 0 into the equation f(x).

For the tangent line with the maximum slope:

Since we want the most positive slope, we consider the value c = -√2 (negative square root of 2). Substituting c = -√2 into f(x), we have:

f(x) = 3(\(x^{2}\) + 6) - (-√2)

= 3\(x^{2}\) + 18 + √2

To find the equation of the tangent line, we take the derivative of f(x) =    3\(x^{2}\) + 18 + √2 with respect to x:

f'(x) = 6x

At x = 0, the slope of the tangent line is f'(0) = 6(0) = 0.

So, the equation for the tangent line with the maximum slope is y = √2.

For the tangent line with the minimum slope:

Since we want the most negative slope, we consider the value c = √2 (positive square root of 2). Substituting c = √2 into f(x), we have:

f(x) = 3(\(x^{2}\) + 6) - √2

Taking the derivative of f(x) = 3\(x^{2}\)+ 18 - √2 with respect to x:

f'(x) = 6x

At x = 0, the slope of the tangent line is f'(0) = 6(0) = 0.

So, the equation for the tangent line with the minimum slope is y = -√2.

Therefore, the equations for the tangent lines to the graph of f(x) with the maximum slope and minimum slope are y = √2 and y = -√2, respectively.

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Answer:

A. y = 8x

Step-by-step explanation:

y is the product, and x is one of the variables that will multiply another number to equal y. So x times a variable equals y, then y divide by x would equal that variable. And in the questions it gave us if y = 48 and x = 6. So we'll use that: 48/6 = 8, the variable is 8. 8 times 6 equals 48 so:

y = 8x

Answer:

i dont even have the first one on my computer

Step-by-step explanation:

Answer:

50 inches

Step-by-step explanation:

Hi there!

\(P=2l+2w\) where l is the length of the rectangle and w is the width of the rectangle

Plug in the length (15 inches) and width (10 inches)

\(P=2(15)+2(10)\\P=30+20\\P=50\)

Therefore, the perimeter of the frame is 50 inches.

I hope this helps!

Answer:

c. anytime

Step-by-step explanation:

if it is stated that a = b, then a always equals b

Answer:

5 and 7

Step-by-step explanation:

Let the two numbers be x and x + 2.

According to Question ,

\(\implies x + x + 2 = 12 \\\\\implies 2x = 12 -2 \\\\\implies 2x = 10 \\\\\implies x =\dfrac{10}{2}\\\\\implies\boxed{ x = 5 }\)

Hence the nos . are 5 and 7

Answer:

(6, 6).

Step-by-step explanation:

The negative before f(x) reflects f(x) in the x-axis so this makes the new vertex equal to (-6, 3), then the + 3 translates it up 3 units so the required vertex is

(-6, 6).