show that 11/45x15/22=1/6

The given system of linear equations consists of four equations with four variables: x, y, z, and w. To solve the system, we can use various methods, such as Gaussian elimination or matrix operations.

By performing row operations, we can reduce the system to its row-echelon form or solve it directly to find the values of x, y, z, and w. We will solve the system of linear equations using the method of Gaussian elimination. The augmented matrix representation of the system is:

[1 1 2 -1 | -2]

[0 3 1 2 | 2]

[1 1 0 3 | 2]

[-3 0 1 2 | 5]

First, we'll perform row operations to transform the matrix into the row-echelon form:

R2 = R2 - 3R1

R3 = R3 - R1

R4 = R4 + 3R1

The resulting matrix after these operations is:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 -2 4 | 4]

[0 3 1 2 | 5]

Next, we'll perform additional row operations to further simplify the matrix:

R4 = R4 - 3R2

The matrix now becomes:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 -2 4 | 4]

[0 3 1 2 | -19]

Finally, we'll perform the last row operation:

R3 = R3 + 2R2

The matrix is now in row-echelon form:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 0 14 | 20]

[0 3 1 2 | -19]

From this row-echelon form, we can solve for the variables. Starting from the bottom row, we obtain:

3w + z + 2w = -19, which simplifies to 5w + z = -19.

Next, we have 0x + 0y - 5z + 5w = 8, which simplifies to -5z + 5w = 8.

Lastly, x + y + 2z - w = -2.

At this point, we have three equations with three variables: x, y, and z. By solving this simplified system, we can find the values of x, y, and z.

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Answer:

which expressions are we choosing from?

The distance between the points G(-9, 6) and Q(-2, 1) in the coordinate plane is approximately 8.6.

To calculate the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be stated as follows:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the given points are G(-9, 6) and Q(-2, 1).
Step 1: Identify the coordinates of the two points.
G has coordinates (-9, 6) and Q has coordinates (-2, 1).
Step 2: Substitute the coordinates into the distance formula.
Using the distance formula, we can plug in the values as follows:
Distance = sqrt((-2 - (-9))^2 + (1 - 6)^2)
Simplifying the formula:
Distance = sqrt((7)^2 + (-5)^2)
Distance = sqrt(49 + 25)
Distance = sqrt(74)
Step 3: Calculate the square root.
Taking the square root of 74, we get:
Distance ≈ 8.6
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Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

To find the Taylor polynomials centered at x = 0 for the function f(x) = 16tan(x), we can use the Taylor series expansion for the tangent function and truncate it to the desired degree.

The Taylor series expansion for tangent function is:

tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ...

Using this expansion, we can find the Taylor polynomials of degree 2 and 3 centered at x = 0:

Degree 2 Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2!)f''(0)(x - 0)^2

= 16tan(0) + 16sec^2(0)(x - 0) + (1/2!)16sec^2(0)(x - 0)^2

= 0 + 16x + 8x^2

Degree 3 Taylor polynomial:

P3(x) = P2(x) + (1/3!)f'''(0)(x - 0)^3

= 0 + 16x + 8x^2 + (1/3!)(48sec^2(0)tan(0))(x - 0)^3

= 16x + 8x^2

Therefore, the Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

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Answer:

-7x + 2

Step-by-step explanation:

I believe this is the answer. When I see the word "than" I work backwards. So -7 times x plus 2.

Answer:

$806.25  i *think*

Step-by-step explanation:

3% of 750 is 22.5 so add that every year

Year 1 : 750 + 22.50 = 772.50

Year 2 : 772.50 + 22.50 = 795.00

Year 2.5 : 795.00 + 11.25 = 820.50

When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.

We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.

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The function, B(t) which depends on the amount of time, t, in days since the first day of \(B(t) = 2400 \times (5/6)^{(t/2.3)}\)

To understand this problem, let's first talk about what a function is. A function is a rule that takes an input, performs a specific operation on it, and gives an output. In this case, the input is the amount of time, t, and the output is the size of the bee population, B(t).

To write this pattern as a function, we can use exponential growth. Exponential growth is a type of growth where the rate of change is proportional to the current size of the population. In this case, the rate of growth is 5/6, and the current size of the population is B(t). Therefore, we can write the function as:

\(B(t) = 2400 \times (5/6)^{(t/2.3)}\)

This function takes the amount of time, t, in days since the first day of summer, and calculates the size of the bee population, B(t).

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36 square units make up the larger circle's surface area.

We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.

We know that the area of a circle is given by the formula A = πr^2.

We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:

A = πr^2 => r^2 = 9/π => r = sqrt(9/π)

Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:

A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36

So the area of the larger circle is 36 square units

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Answer:

The total time taken by 3 men to trim the hedge would be 80 minutes.

Step-by-step explanation:

1) The time taken by 4 men to trim the hedge is 1 hour or 60 min.

2) One me would take 4 times more time alone i.e. Time taken by only one man would be 4 hours or 240 min.

3) The time taken by 3 men would be 3 times less than time taken by one man i.e. 240/3=80 min.

#of people = 4

time taken for 4 ppl = 1hr / 60mins  

# of people = 3

time taken = 1/x

4 - 1/60

3 - 1/x

cross multiply

x=60/3*4

x=80

hope this helps :)

mark me brainliest :D

To find the volume of the parallelepiped determined by the vectors <1,3,7>, <2,1,5>, and <3,1,1>, we can use the determinant of a 3x3 matrix. The absolute value of the determinant represents the volume of the parallelepiped.

To calculate the volume, we arrange the vectors as columns of a matrix and compute the determinant. The determinant of a 3x3 matrix can be calculated using the formula: determinant = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, i are the corresponding elements of the matrix.

By plugging in the values from the given vectors, we construct the matrix and evaluate the determinant. The absolute value of the determinant will give us the volume of the parallelepiped.

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Answer:

\(42\)

Step-by-step explanation:

Another way to look at this question is: We make 5/6 yards of fabric from each pair of shorts. How many shorts do we need to make 35 yards of fabric.

So, we need to solve this equation for \(x\): \(x*5/6=35\).

We can multiply both sides of the equation by \(6\) to get \(x*5=210\).

We then divide by \(5\) on both sides to get \(x=42\).

So, we can make \(\boxed{42}\) pairs of soccer shorts.

Answer: ..

Step-by-step explanation:

Wed: 0%

Thu: 30%

Fri: 50%

Sat: 80%

Sun: 100%

I got these answers by taking 100, and subtracting the rain percentage from it. For instance, if it was a 45% to rain, and a unknown amount for it to not rain, I would take 100 and subtract 45 from it, resulting in a 55% chance of it not raining.

Given

The expression

To use distributive property to rewrite the expression without parentheses.

Explanation:

It is given that,

Then, by using distributive property,

Hence, the answer is option D) 3x+15.

Answer:

EXPLAINED ON THE ATTACHED

Answer:

C. \(\displaystyle y = 5e^{tan(x)}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Algebra II

Calculus

Derivatives

Derivative Notation

Trig Derivatives

Differential Equations

Antiderivatives - Integration

Integration Constant C

Trig Integration

Logarithmic Integration

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \frac{dy}{dx} = ysec^2(x)\)

x = 0, y = 5

Step 2: Rewrite Differential

Separation of variables

Step 3: Find General Solution

Step 4: Find Particular Solution

∴ Our answer is C.

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Differential Equations

Book: College Calculus 10e

Based on the given information, the estimate for the number of cells in a T75 flask can be calculated by comparing the number of cells in the picture to the field of view area and then scaling it up to the size of the T75 flask.

Given that there are 55 cells in the picture, we can use this information to estimate the density of cells in the field of view. The field of view has dimensions of 1.85 mm x 1.23 mm, which gives an area of 2.7095 square millimeters (\(mm^2\)). To calculate the cell density, we divide the number of cells (55) by the area (2.7095 \(mm^2\)), resulting in an approximate cell density of 20.3 cells per \(mm^2\).

Now, to estimate the number of cells in a T75 flask, we need to know the size of the flask's growth area. A T75 flask typically has a growth area of about 75 \(cm^2\). To convert this to \(mm^2\), we multiply by 100 to get 7500 \(mm^2\).

To estimate the number of cells in the T75 flask, we multiply the cell density (20.3 cells/\(mm^2\)) by the growth area of the flask (7500 \(mm^2\)). This calculation gives us an approximate estimate of 152,250 cells in the T75 flask. It's important to note that this is just an estimate, and actual cell counts may vary depending on various factors such as cell size, confluency, and experimental conditions.

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Answer:

  x = 4

Step-by-step explanation:

You want the value of x in the solution to the system of equations ...

Since we have an expression for y, we can substitute for y in the first equation:

  5x -5(-7x +8) = 120 . . . . . . . . use -7x+8 for y

  5x +35x -40 = 120 . . . . . . eliminate parentheses

  40x = 160 . . . . . . . . . . . add 40, collect terms

  x = 4 . . . . . . . . . . . . . divide by 40

__

Additional comment

Then the value of y is ...

  y = -7(4) +8 = -28 +8 . . . . . substitute for x in the second equation

  y = -20

Answer:

Answer:table 4 represent a function

Answer:table 4 represent a function check table 1, second row are equal which automatically disqualified itself

Answer:table 4 represent a function check table 1, second row are equal which automatically disqualified itselfcheck table 2, the same thing in table happens again

Answer:table 4 represent a function check table 1, second row are equal which automatically disqualified itselfcheck table 2, the same thing in table happens againEven in table 3, it still repeat

Answer:table 4 represent a function check table 1, second row are equal which automatically disqualified itselfcheck table 2, the same thing in table happens againEven in table 3, it still repeatBut check the last table, nothing repeat which definitely makes it a function

Answer:

  see attached

Step-by-step explanation:

A function is a relation that has one output for each input value. A table that represents a function will have no repeated inputs.

__

A. there are no repeated x-values. This table represents a function

B. -5 is a repeated x-value. The relation is not a function.

C. -2 is a repeated x-value. The relation is not a function.

D. -4 is a repeated x-value. The relation is not a function.

Answer:

b) 2827

Step-by-step explanation:

Pi*30(squared)=2827m

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

The divergence ▽-F and the curl ▽ × F of the vector field.

F = \((3xye^z, -2y^2ze^z, 5xe^z)\)

▽-F = <\(3ye^z - 4yze^z + 5xe^z\)>

▽ × F =  <\(5xe^z, 3xe^z + 4yze^z, -6yze^z\)>

To compute the divergence ▽-F and the curl ▽ × F of the vector field F = <\(3xye^z, -2y^2ze^z, 5xe^z\)>:
First, let's find the divergence:
▽·F = (∂/∂x)(\(3xye^z\)) + (∂/∂y)(\(-2y^2ze^z\)) + (∂/∂z)(\(5xe^z\))
    = \(3ye^z + (-4yze^z) + (5xe^z)\)
    = \(3ye^z - 4yze^z + 5xe^z\)
Therefore, ▽-F = <\(3ye^z - 4yze^z + 5xe^z\)>
Next, let's find the curl:
▽×F = ( (∂/∂y)(\(5xe^z\)) - (∂/∂z)(\(-2y^2ze^z\)) ) i
         + ( (∂/∂z)\((3xye^z)\) - (∂/∂x)\((-2y^2ze^z)\) ) j
         + ( (∂/∂x)\((-2y^2ze^z)\) - (∂/∂y)\((3xye^z)\) ) k
       = \((5xe^z)\) i + \((3xe^z + 4yze^z)\) j + \((-6yze^z)\) k
Therefore, ▽×F = <\(5xe^z, 3xe^z + 4yze^z, -6yze^z\)>
Note that in this notation, i, j, and k represent the unit vectors in the x, y, and z directions, respectively.

The complete question is:-

Compute the divergence ▽-F and the curl ▽ × F of the vector field. (Your instructors prefer angle bracket notation < > for vectors.)

F = \((3xye^z, -2y^2ze^z, 5xe^z)\)

▽-F = _______

▽ × F = _______

Submit Answer

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The divergence ▽-F and the curl ▽ × F of the vector field.

F = \((3xye^z, -2y^2ze^z, 5xe^z)\)

▽-F = <\(3ye^z - 4yze^z + 5xe^z\)>

▽ × F =  <\(5xe^z, 3xe^z + 4yze^z, -6yze^z\)>

To compute the divergence ▽-F and the curl ▽ × F of the vector field F = <\(3xye^z, -2y^2ze^z, 5xe^z\)>:
First, let's find the divergence:
▽·F = (∂/∂x)(\(3xye^z\)) + (∂/∂y)(\(-2y^2ze^z\)) + (∂/∂z)(\(5xe^z\))
    = \(3ye^z + (-4yze^z) + (5xe^z)\)
    = \(3ye^z - 4yze^z + 5xe^z\)
Therefore, ▽-F = <\(3ye^z - 4yze^z + 5xe^z\)>
Next, let's find the curl:
▽×F = ( (∂/∂y)(\(5xe^z\)) - (∂/∂z)(\(-2y^2ze^z\)) ) i
         + ( (∂/∂z)\((3xye^z)\) - (∂/∂x)\((-2y^2ze^z)\) ) j
         + ( (∂/∂x)\((-2y^2ze^z)\) - (∂/∂y)\((3xye^z)\) ) k
       = \((5xe^z)\) i + \((3xe^z + 4yze^z)\) j + \((-6yze^z)\) k
Therefore, ▽×F = <\(5xe^z, 3xe^z + 4yze^z, -6yze^z\)>
Note that in this notation, i, j, and k represent the unit vectors in the x, y, and z directions, respectively.

The complete question is:-

Compute the divergence ▽-F and the curl ▽ × F of the vector field. (Your instructors prefer angle bracket notation < > for vectors.)

F = \((3xye^z, -2y^2ze^z, 5xe^z)\)

▽-F = _______

▽ × F = _______

Submit Answer

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Yes, the graphs of a power function and its inverse are symmetric about the line y=x.

What is an inverse function?

A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

What is a power function?

Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.

Here,

The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.

Hence, the graphs of a power function and its inverse are symmetric about the line y=x.

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Answer:

x = 135°

Step-by-step explanation:

this is a 6-sided polygon so to find the sum of the interior angles you use this formula:  (n - 2)·180°  where 'n' are the number of sides

(6 - 2)·180° = 4(180)° = 720°

2 right angles = 180°

4x + 180 = 720

4x = 540

x = 135°

Answer:

30

Step-by-step explanation:

Let x be his speed at the morning, in miles per hour.

Then his speed after lunch was (x+10) mph.

2x + 3(x+10) = 220.

2x + 3x + 50 = 220

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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In the derivation of Average Variable Cost (AVC), to find its minimum, you need the minimum-slope ray out of the origin to the TVC (Total Variable Cost).

Average Variable Cost (AVC) is calculated by dividing Total Variable Cost (TVC) by the quantity of output. The TVC represents the variable costs incurred in producing a certain level of output.

The minimum point of the AVC curve occurs where the slope of the TVC curve is at its minimum. The minimum-slope ray out of the origin represents the tangent line to the TVC curve at the origin, and this tangent line intersects the TVC curve at its minimum point. The AVC curve takes its minimum value at this point.

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Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.