Suppose we have converted the augmented matrix of a system of equations into reduced row-echelon form. How do we then identify the dependent and independent (free) variables?

36π is the surface area of the given cylinder.

To find the surface area of a cylinder, you need to calculate the areas of the two circular bases and the lateral surface area.

The formula for the surface area of a cylinder is:

Surface Area = 2πr² + 2πrh

Given:

Height (h) = 7

Radius (r) = 2

First, let's calculate the area of each circular base:

Area of a circular base = πr²

Area of the top circular base = π(2²) = 4π

Area of the bottom circular base = π(2²) = 4π

Next, let's calculate the lateral surface area:

Lateral surface area = 2πrh

Lateral surface area = 2π(2)(7) = 28π

Now, we can find the total surface area by adding the areas of the bases and the lateral surface area:

Total Surface Area = Area of top base + Area of bottom base + Lateral surface area

Total Surface Area = 4π + 4π + 28π = 36π

Therefore, the surface area of the cylinder with a height of 7 and a radius of 2 is 36π.

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a=2cm. b=50cm. x=?

x=b:a. x=50:2. x=25

Answer:

x = 19

z = 76

Step-by-step explanation:

The angle that is indicated with (8x - 28) is equal to the angle indicated with (6x + 8):

8x - 28 = 6x + 8 transfer like terms to the same side of the equation

8x - 6x = 8 + 28 add/subtract terms

2x = 36 divide both sides by 2

x = 19

The angle indicated with (6x + 8) and the angle indicated with z are supplementary angles:

6x + 8 + z = 180 replace x with the value we found

6*19 + 8 + z = 180 calculate

104 + z = 180 subtract 104 from both sides

z = 76

Answer:

Answer:

The answer is 1825.35

Step-by-step explanation:

Since the first week isn’t included, we only count 4 weeks.

So first, 2000 x 0.03 = 60

(By the way 0.03 is 3%)

2000 - 60 = 1940

Subtracting 2000 by 60 represents the amount of money the aquarium went down in that week.

Then, week 3:

1940 x 0.03 = 58.2

1940 - 58.2 = 1881.8

Now, the last week, week four:

1881.8 x 0.03 = 56.45

1881.8 - 56.45 = 1825.35.

Therefore, 1825.35 after 5 weeks.

Answer:

\(y = \sqrt{7^{2} + 3^{2} }\)

D. 7.6

Step-by-step explanation:

y² = 7² + 3²

y² = 49 + 9

y² = 58

y = (58)^½

y = Rationalize(7.61577310586) ~ 7.6

The opposite of being short $4.28 would be having $4.28 or more. That is a surplus or extra of $4.28.

Surplus refers to an amount or quantity that is left over or in excess of what is needed or used. It can refer to various things, such as:

In finance, a surplus refers to an excess of revenue over expenses, or an excess of assets over liabilities. It means having more of something than is necessary or expected.

Therefore, the opposite of being short $4.28 would be having $4.28 or more. This is often referred to as having a surplus or extra of $4.28.

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The velocity of seawater flowing through a horizontal tube with a variable cross-sectional area, having dimensions of 21cm and 7cm, and manometric pressures of 2.5 N/cm and 3.9 N/cm at the narrow and wide sections respectively, can be calculated using Bernoulli's equation.

According to Bernoulli's equation, the total pressure at any point in a fluid is equal to the sum of its static pressure, dynamic pressure, and potential energy per unit volume. In this case, we can assume that the height difference between the narrow and wide sections is negligible, so the potential energy term can be ignored. Thus, we can write:

where P1 and P2 are the manometric pressures at the narrow and wide sections respectively, ρ is the density of seawater (1.07 g/cm³), V1 and V2 are the velocities at the narrow and wide sections respectively.

Solving for V2, we get:

Substituting the given values, we get:

Therefore, the velocity of seawater flowing through the tube can be calculated using this equation.

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Complete Question:

In a horizontal tube of variable section, the cross sections are 21cm and 7em respectively. If seawater (1.07 g/cm*) flows through the tube and the gauge pressures in the narrowing and wide part are 2.5 N/cm and 3.9N/cm

The required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,

Maximum and minimum points of the function y = 2 sin 2(x + π) + 3. can be determined by drawing the graph of the function, from the graph maximum of point of the function is (-3π/4, 5) and the minimum point is (-π/4, 1).

Thus, the required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

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Step-by-step explanation:

(1-3i)-(2-i)=

1-2-3i+i=

-1-2i

1-2-3i+i

= -1-2i

Step-by-step explanation:

I simplified it in a simple way by arranging like terms together and did the calculation. Here the like term of 1 is -2 and for -3i it's i. so 1-2= -1 and -3i+i= -2i according to integers rule.

to draw the perpendicular from Y to XZ in triangle XYZ, we need to draw a line through Y that is perpendicular to XZ, label the intersection point as P, and label the lengths of the sides of the triangle.

This perpendicular line will be the height of the triangle and will divide the base (YZ) into two segments of different lengths.

To draw the perpendicular from Y to XZ in triangle XYZ, we can use the following steps:

Draw the triangle: First, draw a line segment YZ of length 5.8cm. Then, draw point Y and point Z such that YZ is the base of the triangle. Finally, draw point X somewhere above the line YZ.

Draw a line through Y perpendicular to XZ: To draw the perpendicular from Y to XZ, we need to draw a line through point Y that is perpendicular to the line XZ. To do this, we can use a compass to draw a circle with Y as the center and a radius of any length greater than half the distance between X and Z. This circle will intersect the line XZ at two points. Choose one of these points and draw a line through it and Y. This line will be perpendicular to XZ.

Label the intersection point: The line we drew in step 2 will intersect XZ at a point. Label this point as P.

Label the lengths: Now that we have drawn the perpendicular from Y to XZ and labeled the intersection point, we can label the lengths of the sides of the triangle. We know that YZ is 5.8cm, YP is the height of the triangle, and PX and XZ are the two legs of the triangle.

In summary, to draw the perpendicular from Y to XZ in triangle XYZ, we need to draw a line through Y that is perpendicular to XZ, label the intersection point as P, and label the lengths of the sides of the triangle. This perpendicular line will be the height of the triangle and will divide the base (YZ) into two segments of different lengths.

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Answer:

  (x, y) = (12, 15)

Step-by-step explanation:

The given expression for y suggests that using substitution would be a good choice for the method of solution.

__

  x +(x +3) = 27 . . . . substitute for y using the second equation

  2x = 24 . . . . . . . subtract 3

  x = 12 . . . . . . . divide by 2

  y = 12 +3 = 15 . . . . use the second equation to find y

The solution is (x, y) = (12, 15).

Let's begin by identifying key information given to us:

Answer:

35 x^4  - 5x^3

Step-by-step explanation:

5x^3 (7x−1)

Distribute

5x^3 (7x) +5x^3 *(−1)

35 x^3 *x - 5x^3

35 x^4  - 5x^3

Answer:

Answer:

35 x^4  - 5x^3

Step-by-step explanation:

5x^3 (7x−1)

Distribute

5x^3 (7x) +5x^3 *(−1)

35 x^3 *x - 5x^3

35 x^4  - 5x^3

Step-by-step explanation:

Answer:

Could be a mix of answers

Step-by-step explanation:

6(x-7y)-300+9y) is what would do

The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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Answer:

A

Step-by-step explanation:

Originally, Mei pays $24 for 12 issues.

Therefore, the cost per issue is:

\(c=\frac{\$24}{12\text{ issue}}=\$2\text{ per issue}\)

With the coupon, Mei pays the same amount of $24 but for 15 issues.

So, the cost per issue now is:

\(c=\frac{\$24}{15\text{ issues}}=\$1.60\text{ per issue}\)

Therefore, the coupon lowered the price of the issue by $0.40.

Our answer is A.

Answer: The coupon lowered the cost per issue by $0.40.

Original price of issue: $2

24 ÷ 12 = 2

Mei added 3 more issues, but she still pays $24.

The answer is A.

Hope this helps you!

Answer:

3 m/s

Step-by-step explanation:

final speed= initial speed x Acceleration + time

= 0 m/s x 5 m/s2 + 3 s

= 0 m/s + 3 s

= 3 m/s

Answer:

A. {y = 3x + 1 y =− 3x + 7

B. {y = 3x + 1 y = x + 1

Step-by-step explanation:

The required options are

A. {y = 3x + 1 y =− 3x + 7

B. {y = 3x + 1 y = x + 1

C. {y = 3x + 1 y = 3x + 7

D. {x + y = 10 x + y = 12

For option A

y = 3x + 1 and y =− 3x + 7

Equating both expression

3x+1 = -3x+7

3x+3x = 7-1

6x = 6

x = 6/6

x = 1

Since y = 3x+1

y = 3(1)+1

y = 4

For y = 3x + 1 and y = x + 1

Equate both expression

3x+1 = x+1

3x-x = 1-1

2x = 0

x = 0

Substitute x = 0 into y= x+1

y = 0+1

y = 1

c) {y = 3x + 1 and y = 3x + 7

Equate both expression

3x+1 = 3x+7

3x - 3x = 7-1

0x = 6

x = 6/0

X = infinity

the roots have infinite number of solutions

d) x + y = 10.... 1

x + y = 12 .... 2

Add both equations

2x+2y = 22

x+y = 11

Since we have one equation with tei unknown hence the equation has infinite number of solutions

The correct answers are A and B

Answer:

2850

Step-by-step explanation:

We know that only 19% of people prefer the sedans, so we have to find 19% of 15,000. Set up a proportion: \(\frac{19}{100}=\frac{x}{15000}\), cross multiply and get 2850.

Answer:

2850 sedans per month

Step-by-step explanation:

19 % want sedans

They expect to sell 15000 cars

Take the number of cars and multiply by the percent sedans

19% * 15000

Change to decimal form

.19*15000

2850

By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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The scale factor of the two rectangles show a common ratio of 4/5

A scale factor in geometry is a ratio that indicates how much a figure has been extended or shrunk.

When two figures are comparable, the scale factor is the ratio of any matching lengths in the two figures.

A scale factor of higher than 1 indicates expansion, whereas a scale factor of less than 1 indicates decrease. The figure is the same size as the original when the scale factor is 1.

The dimensions of comparable figures can be calculated using scale factors. For instance, we can use the scale factor to determine the length of the corresponding side of the smaller rectangle if we know the scale factor between two identical rectangles and the length of one of its sides of the larger rectangle.

In the given figure;

12/15 = 36/45

Let's find the ratio here;

4/5 =4/5

The scale factor is 4/5

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The number of black and white socks Tim has is :

Let the Number of white and black socks be x and y respectively.

Hence, Total number of socks can be expressed Mathematically as :

x + y = 74 - - - (1)

Since, he has 1 pair (2) more white Than black socks ;then

Number of white socks = 1 + number of black socks

x = 2 + y - - - (2)

Therefore ;

2 + y + y = 74

2 + 2y = 74

2y = 74 - 2

2y = 72

y = 72 / 2

y = 36

x = 2 + y

x = 2 + 36

x = 38

Black socks = 36

Black socks = 36White socks = 38

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Answer: 4,5

Step-by-step explanation:

The actual length of the Olympic-size swimming pool which is drawn by Christina on the scale model is 50 meters.

Scale factor is the factor which is used to enlarge or smaller the original figure.

Scale factor is the ratio of representation measurement of the figure to the original figures.

Christina drew a scale model of an Olympic-size swimming pool using a scale in which 3 centimeters represents 10 meters.

Thus, the scale factor is for cm to m,

\(r=\dfrac{3}{10}\rm\)

The length of the pool in her drawing is 15 centimeters. Let the length of the actual pool is x cm. Thus,

\(\dfrac{15}{x}=\dfrac{3}{10}\\x=50\rm \; m\)

Thus, the actual length of the Olympic-size swimming pool which is drawn by Christina on the scale model is 50 meters.

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Step-by-step explanation:

y-Intercept = (0 , -5)

Slope / m = -4

y - y1 = m(x - x1)

y + 5 = -4(x - 0)

y = -4x - 5 → Equation

The value assigned to variable y in the given expression "x = 0; y = (x > 0) ? 10 : -10;" is -10.

In the given expression "x = 0; y = (x > 0) ? 10 : -10;", the variables x and y are being assigned values based on a conditional statement.

First, the value of x is assigned as 0.

The conditional statement (x > 0) checks whether the value of x is greater than 0. In this case, since x is equal to 0, the condition evaluates to false.

The ternary operator ? : is used to specify different values for y based on the outcome of the conditional statement. If the condition is true, the value assigned to y would be 10. On the other hand, if the condition is false, the value assigned to y would be -10.

In this case, since the condition (x > 0) is false, the value assigned to y is -10, as indicated after the colon :.

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