Determine the surface area and volume

Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

[tex]\log 3+ 9\log x +4 \log y[/tex]

Step-by-step explanation:

Given logarithmic expression:

[tex]\log 3x^9y^4[/tex]

[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\log 3+\log x^9 +\log y^4[/tex]

[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]

[tex]\log 3+ 9\log x +4 \log y[/tex]

The different coordinates after respective rotation are:

1) A'(2, 0)

2) A'(0, -2)

3) A'(-2, 0)

There are different methods of transformation such as:

Translation

Rotation

Dilation

Reflection

Now, the coordinate of the given point A is: A(0, 2)

1) The rule for rotation of 90 degrees clockwise is:

(x, y) →(y,-x)

Thus, we have:

A'(2, 0)

2) The rule for rotation of 180 degrees is:

(x, y) → (-x,-y)

Thus, we have:

A'(0, -2)

3) The rule for rotation of 180 degrees is:

(x, y) → (-y,x)

Thus, we have:

A'(-2, 0)

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Answer/Step-by-step explanation:

C., the first proof we would be given if a little box is shown, which indicates a 90 degree angle at the place where to lines touch  in a T kind of manor. So C is the answer.

Answer:

Step-by-step explanation:

Given the following diagram: We need to find the coordinates of triangle ABC, translate the triangle (-2, 5) and draw the new image on the grid above, and determine the amount each coordinate will move on the x-axis and y-axis during translation.

1. Coordinates of triangle ABC:A = (2, 6)B = (5, 8)C = (6, 3)2. Translation of triangle (-2, 5)The translation of a triangle can be done by adding or subtracting a constant value from the x-coordinates and y-coordinates of each vertex of the original triangle.

For example, if we want to translate a triangle by 3 units to the right and 2 units up, we would add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of the original triangle. Using this method, we can translate the triangle (-2, 5) as follows:

New coordinates of A = (2 + (-2), 6 + 5) = (0, 11)New coordinates of B = (5 + (-2), 8 + 5) = (3, 13)New coordinates of C = (6 + (-2), 3 + 5) = (4, 8)3. New image of triangle (-2, 5)The new image of the triangle (-2, 5) is shown in the following diagram:4. Amount each coordinate moves on x-axis During translation, each coordinate moves 2 units to the right (from -2 to 0).5. Amount each coordinate moves on y-axis During translation, each coordinate moves 6 units up (from 5 to 11).

Therefore, the coordinates of the translated triangle image are (0, 11), (3, 13), and (4, 8).

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The expression for m<3 is 349° - 7x.

To find the measure of angle 3 (m<3), we need to apply the angle sum property, which states that the sum of the angles around a point is 360 degrees.

In the given figure, angles 1, 2, 3, and 4 form a complete revolution around the point. Therefore, we can write:

m<1 + m<2 + m<3 + m<4 = 360°

Substituting the given angle measures, we have:

(x + 6)° + (2x + 9)° + m<3 + (4x - 4)° = 360°

Combining like terms:

7x + 11 + m<3 = 360°

To isolate m<3, we subtract 7x + 11 from both sides:

m<3 = 360° - (7x + 11)

m<3 = 360° - 7x - 11

m<3 = 349° - 7x

Therefore, the expression for m<3 is 349° - 7x.

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The percent increase in recreational boating participation over the sixteen-year period is approximately 8.72%. This means that the number of participants increased by around 8.72% from 52.7 million to 57.3 million.

To determine the percent increase in recreational boating participation over the sixteen-year period, we can use the following formula:

Percent Increase = ((New Value - Old Value) / Old Value) * 100

Using the given information, we have an old value of 52.7 million and a new value of 57.3 million.

Percent Increase = ((57.3 million - 52.7 million) / 52.7 million) * 100

= (4.6 million / 52.7 million) * 100

= 0.0872 * 100

= 8.72%

This increase indicates a positive trend in recreational boating, reflecting a growing interest in this activity over time. Factors such as improved accessibility, marketing efforts, and increasing disposable income may have contributed to this upward trend.

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Answer:

0.090909

Step-by-step explanation:

I used a calculator

Hence, the arrangements to the quadratic equation  (3x-1)(x-2) = 5x + 2 are x = and x = 4.

To unravel the quadratic equation  (3x-1)(x-2) = 5x + 2, let's to begin with grow the cleared out side of the equation:

(3x - 1)(x - 2) = 5x + 2

Growing the condition:

3x^2 - 6x - x + 2 = 5x + 2

Streamlining the condition:

3x^2 - 7x + 2 = 5x + 2

Another, let's move all terms to one side of the condition:

3x^2 - 7x - 5x + 2 - 2 =

Combining like terms:

3x^2 - 12x =

Presently, we have a quadratic condition in standard shape: ax^2 + bx + c = 0, where a = 3, b = -12, and c = 0.

To fathom the quadratic equation, able to calculate out the common calculate of x:

x(3x - 12) =

From this equation, we are able see that the esteem of x can be or unravel for 3x - 12 = 0:

3x - 12 =

Including 12 to both sides:

3x = 12

Isolating both sides by 3:

x = 4

Hence, the arrangements to the condition (3x-1)(x-2) = 5x + 2 are x = and x = 4.

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Answer:

Step-by-step explanation:Angle EDH=Angle FDH, so A must be correct.

Also, we don't have more information to prove B, C, D is right

Answer:

A.

Step-by-step explanation:

An angle bisector is a line, ray, or segment that divides an angle into two equal parts. It divides the angle into two congruent or equal angles. The angle bisector originates from the vertex of the angle and extends towards the interior of the angle. It essentially cuts the angle into two smaller angles of equal measure.

Answer:

chemical reaction that releases heat energy to the surroundings is known as endothermis reaction

a) The distribution of X, the student loan debt of a randomly selected college graduate, is normal with a mean of $25,200 and a standard deviation of $11,200. b) The probability is approximately 7.28%.

c) The middle lies between approximately $22,164 and $28,536.

a. The distribution of X, the student loan debt of a randomly selected college graduate, is a normal distribution (bell-shaped curve) with a mean (μ) of $25,200 and a standard deviation (σ) of $11,200. We can represent this as X ~ N(25200, 11200).

b. To find the probability that the college graduate has between $27,250 and $43,650 in student loan debt, we need to calculate the z-scores for these two values and then find the area under the normal curve between those z-scores.

First, we calculate the z-score for $27,250:

z1 = (X1 - μ) / σ = (27250 - 25200) / 11200 ≈ 1.8304

Next, we calculate the z-score for $43,650:

z2 = (X2 - μ) / σ = (43650 - 25200) / 11200 ≈ 1.6518

Now, we need to find the area under the normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table or a calculator, the probability is approximately P(1.6518 ≤ Z ≤ 1.8304) ≈ 0.0728.

c. To find the middle 20% of college graduates' loan debt, we need to find the range of values that contain the central 20% of the distribution. This range corresponds to the values between the lower and upper percentiles.

The lower percentile is the 40th percentile (50% - 20%/2 = 40%) and the upper percentile is the 60th percentile (50% + 20%/2 = 60%).

Using a standard normal distribution table or a calculator, we can find the z-scores corresponding to these percentiles:

For the lower percentile (40th percentile):

z_lower = invNorm(0.40) ≈ -0.2533

For the upper percentile (60th percentile):

z_upper = invNorm(0.60) ≈ 0.2533

Now, we can convert these z-scores back to the corresponding loan debt values:

Lower debt value:

X_lower = μ + z_lower * σ = 25200 + (-0.2533) * 11200 ≈ $22,164

Upper debt value:

X_upper = μ + z_upper * σ = 25200 + 0.2533 * 11200 ≈ $28,536

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The vertex of h(x) is (-3, 3), and the range is y ≥ 3.

To find the vertex of the quadratic function h(x), we can use the formula x = -b/2a, where the quadratic function is in the form [tex]ax^2 + bx + c[/tex].

From the given table, we can observe that the x-values of the vertex correspond to the minimum points of the function.

The minimum point occurs between -4 and -3, which suggests that the x-coordinate of the vertex is -3. Therefore, x = -3.

To find the corresponding y-coordinate of the vertex, we look at the corresponding h(x) value in the table, which is 3. Hence, the vertex of the function h(x) is (-3, 3).

To determine the range of h(x), we need to consider the y-values attained by the function.

From the table, we see that the lowest y-value is 3 (the y-coordinate of the vertex), and there are no other y-values lower than 3. Therefore, the range of h(x) is all real numbers greater than or equal to 3.

The vertex of h(x) is (-3, 3), and the range is y ≥ 3.

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The vertex of the quadratic function is (-4, 12).

The range of h(x) is [3, ∞).

To find the vertex and range of the quadratic function h(x) based on the given table, we can use the properties of quadratic functions.

The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be determined using the formula:

x = -b / (2a)

The domain of h(x) is all real numbers, we can assume that the quadratic function is of the form h(x) = ax² + bx + c.

Looking at the table, we can see that the x-values are increasing from left to right.

Additionally, the y-values (h(x)) are increasing from -6 to -4, then decreasing from -4 to -1.

This indicates that the vertex of the quadratic function lies between x = -4 and x = -3.

To find the exact x-coordinate of the vertex, we can use the formula mentioned earlier:

x = -b / (2a)

Based on the table, we can choose two points (-4, 4) and (-3, 3).

The difference in x-coordinates is 1, so we can assume that a = 1.

Plugging in the values of (-4, 4) and a = 1 into the formula, we can solve for b:

-4 = -b / (2 × 1)

-4 = -b / 2

-8 = -b

b = 8

The equation of the quadratic function h(x) can be written as h(x) = x² + 8x + c.

Now, let's find the y-coordinate of the vertex.

We can substitute the x-coordinate of the vertex, which we found as -4, into the equation:

h(-4) = (-4)² + 8(-4) + c

12 = 16 - 32 + c

12 = -16 + c

c = 28

The equation of the quadratic function h(x) is h(x) = x² + 8x + 28.

The range of the quadratic function can be determined by observing the y-values in the table.

From the table, we can see that the minimum y-value is 3.

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The cross section of the geometric solid is (d) rectangle

From the question, we have the following parameters that can be used in our computation:

The geometric solid

Also, we can see that

The geometric solid is a cylinder

And the cylinder is divided vertically

The resulting shape from the division is a rectangle

This means that the cross section of the geometric solid is (d) rectangle

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The shape of the cross-section for the geometric solid given in the diagram is a rectangle.

The cross section of the geometric solid represents the shape which extends beyond the actual geometric solid which is a cylinder.

A rectangle has opposite side being equal. This means that the width and and length are of different length.

Therefore, the shape of the cross-section is a rectangle.

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The z - score z = (x - μ)/σ equals z = (p' - p)/[√(pq/n)]

The z-score is the statical value used to determine probability in a normal distribution

Given the z-score z = (x - μ)/σ where

We need to show that

z = (p' - p)/√(pq/n)

We proceed as follows

Now, the z-score

z = (x - μ)/σ

Substituting in the values of μ and σ into the equation, we have that

So, z = (x - μ)/σ

z = (x - np)/[√(npq)]

Now, dividing both the numerator and denominator by n, we have that

z = (x - np)/[√(npq)]

z = (x - np) ÷ n/[√(npq)] ÷ n

z = (x/n - np/n)/[√(npq)/n]

z = (x/n - p)/[√(npq/n²)]

z = (x/n - p)/[√(pq/n)]

Now p' = x/n

So, z = (x/n - p)/[√(pq/n)]

z = (p' - p)/[√(pq/n)]

So, the z - score is z = (p' - p)/[√(pq/n)]

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Answer:

c) 54 feet

Step-by-step explanation:

Let the  side of the square be x

perimeter = 4x

⇒ 36 = 4x

⇒ x = 36/4 = 9 feet

Each side is 9 feet

When we join the two squares, it becomes a rectangle with

b = 9

l = 9 + 9 = 18

The perimeter of a rectangle is 2(l + b)

perimeter = 2(18 + 9)

= 2(27)

= 54 feet

Answer:

Option (c) 54 feet

Step-by-step explanation:

Perimeter of one square is 36 feet.

Side of square = 36 / 4 = 9 feet

When combined together one side of each square merged.

So, the perimeter of rectangular shape will be;

(9+9+9) + (9+9+9)

27 + 27

54 feet.

Answer:

(x + 13)(x - 7) = 69

x² + 6x - 91 = 69

x² + 6x - 160 = 0

(x + 16)(x - 10) = 0

x = 10, so the area of the original square is 100 m².

The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

  - x + 3y = 350    (Equation 1)

  - 2x + 4y = 625   (Equation 2)

2. Multiply Equation 1 by 2:

  - 2(x + 3y) = 2(350)

  - 2x + 6y = 700    (Equation 3)

3. Subtract Equation 2 from Equation 3:

  - (2x + 6y) - (2x + 4y) = 700 - 625

  - 2x - 2x + 6y - 4y = 75

  - 2y = 75

4. Simplify Equation 4:

  -2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

  y = 75 / -2

  y = -37.5

6. Therefore, the resulting equation is:

  -5y = -375

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Answer:

9

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

?

Answer:

y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)

Step-by-step explanation:

To simplify the given expression, we can expand it using the distributive property:

(5/8x + y^5)(y^5 - 5/8x)

Expanding the expression yields:

= (5/8x * y^5) + (5/8x * -5/8x) + (y^5 * y^5) + (y^5 * -5/8x)

= (5/8xy^5) - (25/64x^2) + y^10 - (5/8xy^6)

Combining like terms, we have:

= y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)

Hope this help! Have a good day!

Answer:

[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4

Step-by-step explanation:

(8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex]) - (4 + [tex]x^{3}[/tex] + 6x)

= 8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4 - [tex]x^{3}[/tex] - 6x

= 2x + [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4

= [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4

Answer:

Multiply to remove the fraction, then set it equal to 0 and solve.

Exact Form: x = −124/5

Decimal Form: x = −24.8

Mixed Number Form: x = −24 4/5

Please give the brainliest, really appreciated. Thank you

Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

The initial stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], the resultant stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex] and the induced force in the bar when the temperature reaches 50°C is 100.03 kN.

To calculate the initial stress in the tie bar, we can use the formula:

Stress = Load/Area

The area of the tie bar can be calculated using the formula for the area of a circle:

Area = π * [tex](diameter/2)^2[/tex]

Plugging in the values, we get:

Area = π * [tex]10 mm^{2}[/tex] = π *[tex](5 mm)^2[/tex] = 78.54 [tex]mm^2[/tex]

Converting the area to square meters, we have:

Area = 78.54 [tex]mm^2[/tex]* (1 m^2 / 1,000,000 [tex]mm^2[/tex]) = 7.854 × 1[tex]0^-5 m^2[/tex]

Now we can calculate the initial stress:

Initial Stress = 100 kN / 7.854 ×[tex]10^-5 m^2[/tex] = 1.273 × [tex]10^9 N/m^2[/tex]To calculate the resultant stress when the temperature rises to 50°C, we need to consider the thermal expansion of the tie bar. The change in length can be calculated using the formula:

ΔL = α * L0 * ΔT

Where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature.

The induced force in the bar can be calculated using the formula:

Induced Force = Initial Stress * Area + E * α * ΔT * Area

Plugging in the values, we get:

Induced Force = (1.273 × 10^9 N[tex]m^2[/tex] * 7.854 × [tex]10^-5 m^2[/tex]) + (200 × [tex]10^9[/tex] N/[tex]m^2[/tex] * 14 × [tex]10^-6[/tex] /K * (50 - 15) K * 7.854 × [tex]10^-5 m^2[/tex])

Simplifying the equation, we find:

Induced Force = 100.03 kN

Therefore, the initial stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], the resultant stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], and the induced force in the bar when the temperature reaches 50°C is 100.03 kN.

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The probable question may be:

A rigidly held tie bar in a heating chamber has a diameter of 10 mm and is tensioned to a load of 100 kN at a temperature of 15°C. What is the initial stress, the resultant stress and what will be the induced force in the bar when the temperature in the chamber has risen to 50°C? E= 200 GN/ m2 and the coefficient of linear expansion of the material for tie bar = 14 × 10−6 /K.

Answer:

X intercepts: (-2, 0), (2, 0)

Y intercept: (0, 4)

Edited because I forgot to put in point form earlier. Depends on whether your teacher wants it in point form. If not, ignore the 0s.

Step-by-step explanation:

X intercepts are the points where a line crosses the x axis. Y intercepts are the points where a line crosses the y axis.

Answer:

A. x-intercept: (-2,0), (2,0)

A. y-intercept: (0,4)

Step-by-step explanation:

If you want to find the x and y-intercept of a line, you need to know its equation. But don't worry, it's not as hard as it sounds. Here are some tips to help you out.

One type of equation is y = mx + c, where m is the slope and c is the y-intercept. This means that the line crosses the y-axis at c. To find the x-intercept, just plug in y = 0 and solve for x. You'll get x = -c/m. Easy peasy!

For example, if the equation is y = 2x + 4, then the y-intercept is 4 and the x-intercept is -2.

Another type of equation is ax + by + c = 0, where a, b and c are constants. To find the x-intercept, plug in y = 0 and solve for x. You'll get x = -c/a. To find the y-intercept, plug in x = 0 and solve for y. You'll get y = -c/b. Piece of cake!

For example, if the equation is 3x + 2y - 6 = 0, then the x-intercept is 2 and the y-intercept is -3.

Now you know how to find the x and y-intercept of a line from its equation.Let us understand the calculations to find the x and y intercept, through the steps in the below table.

The slope of a line that is perpendicular to the given line x + 6y = 3 is 6.

To determine the slope of a line that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.

The equation of the given line is x + 6y = 3.

To find the slope of the given line, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:

x + 6y = 3

6y = -x + 3

y = (-1/6)x + 1/2

From the equation y = (-1/6)x + 1/2, we can see that the slope of the given line is -1/6.

To find the slope of a line that is perpendicular, we take the negative reciprocal of -1/6.

The negative reciprocal of -1/6 can be found by flipping the fraction and changing its sign:

Negative reciprocal of -1/6 = -1 / (-1/6) = -1 * (-6/1) = 6

Therefore, the slope of a line that is perpendicular to the given line x + 6y = 3 is 6.

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1a.) The amount that the eldest son received would be =GHç 1,360

b .) The amount received by the daughter would be =G Hç 2176

c.) The difference between the amount the two sons received would be =GHç1,904

For 1a.)

The amount that the land is worth= $8,600

The amount received for various purposes= $1,800

The remaining amount shared to the sons= 8,600-1800= $6,800

The percentage amount received by the eldest son= 20% of 6800

That is;

= 20/100×6800/1

= 136000/100

= $1,360

The remaining amount= 6800-1360= $5,440

For 1b.)

The ratio that the remaining amount was shared between the other son and the daughter = 3 : 2 respectively.

The total ratio= 3+2=5

For daughter= 2/5× 5440

= 10880/5 = 2176

The other son= 5440-2176 = 3264

For 1c.)

The difference between the amount the two sons received would be =3264-1,360 = GHç1,904.

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