multiply (x – 3)(4x 2) using the foil method. select the answer choice showing the foil method products.

Each edge of the original cube is of length x cm. The diagonal A F has length 20 cm the value of x is 20√2 cm.

Let's label the points in the diagram as follows:

- A, B, C, D are the vertices of the original cube.

- E is the midpoint of the edge BC.

- F is the point where the plane cuts the cube, which is the midpoint of the diagonal AD.

First, let's find the length of the edge EF using the Pythagorean theorem. We know that A F = 20 cm and AE = EF/2, so:

EF² = 2×AE²   (by Pythagoras theorem in triangle AEF)

EF² = 2×(A F/2)²

EF² = A F²/2

EF = √(A F²/2)

EF = 10√2 cm

Next, let's find the length of the diagonal AC using the Pythagorean theorem in triangle AEC. We know that AE = EF/2 = 5√2 cm and EC = x cm, so:

AC² = AE² + EC²

AC² = (5√2)² + x²

AC² = 50 + x²

AC = √(50 + x²) cm

Finally, let's find the length of the diagonal AD using the Pythagorean theorem in triangle AFD. We know that A F = 20 cm and FD = x/2 cm (since F is the midpoint of AD), so:

AD² = AF² + FD²

AD² = 20² + (x/2)²

AD² = 400 + x²/4

AD = √(400 + x²/4) cm

Since AD is a diagonal of the original cube, we know that AD = x√3 cm. Therefore:

x√3 = √(400 + x²/4)

x² × 3 = 400 + x²/4

3x² = 1600 + x²

2x² = 1600

x² = 800

x = √800 = 20√2 cm

Therefore, the value of x is 20√2 cm.

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Answer: The equation \(x-7/8=-3/2\) has a different value of x than the others. The value of x here is -0.625, while in all the other equations, the value of x is 0.625.

Step-by-step explanation: Simplifying the equation \(x+9/8=7/4\), we get:

\(x=7/4-9/8\)

\(x=0.625\)

Simplifying the equation \(x-7/8=-3/2\),  we get:

\(x=-3/2+7/8\)

\(x=-0.625\)

Simplifying the equation \(x+0.875=1.5\), we get:

\(x=1.5-0.875\)

\(x=0.625\)

Simplifying the equation \(x-0.025=0.6\), we get:

\(x=0.6+0.025\)

\(x=0.625\)

Therefore, \(x+9/8=7/4\) has a different value of x than the others.

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The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.

Frequency Distribution:

Digit Frequency

0 3

1 5

2 9

3 5

4 3

5 4

6 4

7 4

8 2

9 1

From the distribution of the digits, it appears that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements.

The frequency distribution of the digits indicates that the heights were reported rather than actually measured. This is because the frequency of the digits is not evenly distributed, which would be expected for a set of actual measurements. For example, the frequency of the digit '2' is more than twice as high as the frequency of the digits '1' and '3', which is not likely to occur in a set of actual measurements.

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Circumference is the distance around the outer boundary of a circle. It can be found using the formulas: C = 2πr or C = πd. It is used in various fields like construction, engineering, and measurement.

Circumference is a fundamental geometric property of a circle. It refers to the distance around the outer boundary or perimeter of a circle. It can be thought of as the circle's "boundary length."

To find the circumference of a circle, you can use a mathematical formula known as the circumference formula or perimeter formula. This formula relates the circumference of a circle to its radius or diameter. There are two commonly used formulas to calculate the circumference:

Using the radius (r):

Circumference = 2πr

In this formula, "r" represents the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. By multiplying the radius by 2π, you obtain the circumference of the circle.

Using the diameter (d):

Circumference = πd

In this formula, "d" represents the diameter of the circle. The diameter is the longest straight line that can be drawn between two points on the circle and passes through the center. By multiplying the diameter by π, you can determine the circumference.

Both formulas provide an accurate measurement of the circumference, but the choice of which formula to use depends on the information available. If you have the radius, you use the first formula, and if you have the diameter, you use the second formula.

The circumference is a crucial measurement when dealing with circles and circular objects. It helps in various real-world applications, including construction, engineering, architecture, physics, and many other fields. Here are a few examples of how the circumference is used:

Construction: When building circular structures such as arches, wheels, or columns, knowing the circumference helps determine the required materials, estimate the amount of material needed, and ensure proper fit and alignment.

Engineering: Circumference calculations are vital in designing gears, pulleys, belts, and other rotating systems. The circumference determines the size and dimensions required for these components to function properly and interact with other machinery.

Measurement: Measuring tapes or flexible rulers often have circumference markings, allowing you to measure curved or circular objects accurately. These measurements are essential for tasks like measuring pipe lengths, determining the size of a circular tablecloth, or creating patterns for clothing.

Sports: In sports like track and field, where races take place on oval tracks, the circumference of the track determines the distance covered in one lap. It is crucial for accurately measuring race distances and setting records.

Astronomy: In celestial mechanics, the circumference of celestial bodies such as planets or asteroids plays a role in calculating their orbits, rotational speed, and other parameters. Precise knowledge of circumference aids in understanding celestial phenomena and predicting their movements.

Understanding the concept of circumference and its applications is essential in various disciplines. It allows us to measure and calculate dimensions accurately, design and build circular structures, and comprehend the behavior of circular objects in the physical world.

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Answer: 92

Step-by-step explanation:

Formula : Sum of first n numbers = Average x n

Given: Average score on first 6 tests= 84

A score on all 8 tests = 86

Then, Sum of first 6 numbers = 84 x 6 = 504

Sum of first 8 numbers = 86 x 8 = 688

Sum of two last numbers = (Sum of first 8 numbers) - (Sum of first 6 numbers)

= 688-504

=184

Average of last two numbers = (Sum of two last numbers )÷2

= 184÷2

= 92

Hence,  the average of your last two test scores = 92.

Answer:

x=6

Step-by-step explanation

2x-2.12=9.88

   +2.12  +2.12

    2x  =   12

12 divided by 2 is 6

x=6

To check you can do 12-2.12=9.88

Using the concept of probability, we can infer that 15 students in a class of 25 are expected to be using smartphones to complete hw.

The ratio of favorable outcomes to all possible outcomes of an event is known as the probability. The number of favorable results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(E) = Number of favorable outcomes/Total outcomes .

Given that, 4 out of 10 teenagers are not using smartphones for H.W.

To find out the number of students using smartphones in a class of 25 students:

4/10 = n/25

n = (4 × 25)/10

n = 100/10

n = 10

10 students will not be using smartphones.

Number of students who are using smartphone = 25-10

Number of students who are using smartphone = 15

Therefore, 15 students in a class of 25 are expected to be using smartphones to complete hw.

The complete question is "4 out of 10 teenagers surveyed say they are not using smartphones to help them complete hw assignments. assuming this survey is fairly accurate, how many students in a class of 25 would you expect to be using smartphones to complete hw?"

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Answer:

The Median is 5

Step-by-step explanation:

The median is the middle number in a set of data, when the data has been written in size order.

0 1 2 4 5 5 5 6 6 6

As there is an even number of data the median is the average of the middle two values.  As the middle 2 values are both 5, then the average of these is also 5.  Therefore, the median is 5.

To find the mean of the set of data, add all the values together then divide by the number of data values:

(0 + 1 + 2 + 4 + 5 + 5 + 5 + 6 + 6 + 6) ÷ 10 = 4

Therefore, the mean is 4.

The Median is a better measure of central tendency as extreme values (outliers) do not affect it.  From inspection of the dot plot, the majority of the data values are 5 and 6.  Therefore, the lower values *could* be outliers, so 5 is a more realistic measure of central tendency.

Answer: c

Step-by-step explanation:

Answer: 219.52 inch^2

Step-by-step explanation:

Given the dimensions of rectangular papaerboard:

Length = 20inches

Width = 16inches

Area of rectangle = Length × width

Area of rectangle = 20 × 16 = 320 in^2

Area of a circle = pi*r^2

Therefore, area of semicircle = (pi*r^2) / 2

Diameter of circle = width of rectangle = 16 inches

Radius = diameter / 2 = 16 /2 = 8inches

Therefore, area of semicircle = (pi*8^2) / 2

= (3.14 × 64) / 2

= 200.96 / 2

= 100.48 inch^2

Therefore, area of paperboard left :

Area of rectangle - area of semicircle

320 - 100.48

= 219.52 inch^2

The  six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane 6x + 3y+ 2z = 8 are ,

Triple integrals are functionally equivalent to double integrals. Triple integrals can be converted into  iterated integrals.

The only trick, as with double integrals, is determining the limits on the iterated integrals. (Drawing in three dimensions is more difficult.)

The triple integral represents W's actual mass. Triple integrals are iterated functions with three variables. Triple integrals are iterated functions with three variables. We are now integrating our function over a three-dimensional figure with volume, rather than a given area.

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The graph of y = -3√(x - 6) is a vertically compressed and reflected square root function that has been translated 6 units to the right compared to the parent function y = √x. The vertex of the graph is located at (6, 0).

The parent function y = √x represents a square root function with its vertex at the origin (0, 0). When graphing y = -3√(x - 6), the graph undergoes several transformations.

Translation:

The term "x - 6" inside the square root function indicates a horizontal translation. The graph is shifted 6 units to the right. The vertex, which was originally at (0, 0), will now be at (6, 0).

Amplitude:

The coefficient in front of the square root function (-3) affects the amplitude of the graph. Since the coefficient is negative, the graph is reflected vertically. This means that the graph is upside down compared to the parent function. The negative coefficient also affects the steepness of the graph.

The absolute value of the coefficient (3) represents the vertical compression or stretching of the graph. In this case, since the coefficient is greater than 1, the graph is vertically compressed.

Combining the translation and reflection:

By combining the translation and reflection, we find that the graph of y = -3√(x - 6) is a vertically compressed and reflected square root function. It is shifted 6 units to the right compared to the parent function. The vertex is located at (6, 0).

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volume= 16/3, A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

limits

z= 0 to z = 4-y-2x

y= 0 to y = 4- 2x

x= 0 to x= 2

volume

v= \(\int\limits^2_0 \int\limits^4_0 \int\limits^4_0 dzdydx\)

v= \(\int\limits^2_0 \int\limits^4_0 (4-y-2x) dydx\)

v= \(\int\limits^2_0 ( 4y- y^{2} / 2 - 2xy) ^4^-^2^x _0\)

dx= \(\int\limits^2_0 [ 16-8x - 16+ 4x^2 - 16x / 2 - 8x+ 4x^2 ] dx\)

v= \(\int\limits^2_0 [ 8+ 2x^2- 8x] dx\\\)

= [ 8x + 2x^3 / 3 - 8x^2 / 2 ] ^2_0

= [16+ 16/3- 16]

v= 16/3

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Complete Question

Question: Sketch The Tetrahedron Enclosed By The Coordinate Planes And The Plane 2x+Y+Z=4. Use A Triple Integral To Find The Volume Of The tetrahedron

Answer:

0.6 I'm also sorry if I get it wrong

In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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Answer:

The answer is C.

Step-by-step explanation:

Answer:

Area = 36 squ. unit

Step-by-step explanation:

According to the Question,

by using these points a quadrilateral is formed with two opposite sides 7 and 5 and with height 6 (Refer in the diagram).

Area = 1/2 * (sum of opposite side) * height

Area = 1/2 * (7+5) * 6

Area = 3*12

Area = 36 squ. unit

Answer:

36

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

use Pythagoras Theron

a^2+b^2=c^2

let ms know if you have further questions

Using Pythagorean theorem

\(\\ \sf\longmapsto H^2=P^2+B^2\)

\(\\ \sf\longmapsto H^2=(5√3)^2+5^2\)

\(\\ \sf\longmapsto H^2=75+25\)

\(\\ \sf\longmapsto H^2=100\)

\(\\ \sf\longmapsto H=10\)

Answer:

Step-by-step explanation:

Answer:22,000

Explanation:

21.933=21.930

21.930= 21.900

21.900 = 22,000

Answer:

Step-by-step explanation:

F(x) is simply another way of saying y. We are given the x value of -10. We can substitute this in for x and find y.

f(-10) = 7(-10) - 5

f(-10) = -70 - 5

f(-10) = -75

Answer:

Rewrite the equation in term of  

x

and  

y

.

f

(

x

)

=

2

x

2

−

7

x

+

5

Rewrite the equation in vertex form.

Tap for fewer steps...

Complete the square for  

2

x

2

−

7

x

+

5

.

Tap for more steps...

2

(

x

−

7

4

)

2

−

9

8

Set  

y

equal to the new right side.

y

=

2

(

x

−

7

4

)

2

−

9

8

Use the vertex form,  

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of  

a

,  

h

, and  

k

.

a

=

2

h

=

7

4

k

=

−

9

8

Find the vertex  

(

h

,

k

)

.

(

7

4

,

−

9

8

)

Step-by-step explanation:

Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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Antidisestablishmentarianism

Answer:

B

Step-by-step explanation:

It's a guess

Answer:

y is the dependent variable and x is the independent variable

Step-by-step explanation

The number on the right of the equal sign is always the independent variable and the number on the left is always the dependent variable.

independent variable = dependent variable +5

The inverse of a number is it's reciprocal. Divide 1 by the number to obtain its reciprocal.

For example, the reciprocal of 5 is 1/5, and the reciprocal of 0.5 is 2. The reciprocal of a number x is denoted by 1/x or x^(-1).

For example, to find the reciprocal of 8, you would divide 1 by 8, like this:

1/8 = 0.125

To find the reciprocal of a fraction, you can also turn the fraction upside down to get its reciprocal. For instance, 4/3 is 3/4's inverse.

To find the inverse of a matrix, you can use the following formula:

A^(-1) = (1/det(A)) * adj(A)

where A is the matrix, det(A) is the determinant of the matrix, and adj(A) is the adjugate of the matrix. The transposition of a matrix's cofactor matrix is adjugate. The cofactor matrix is a matrix of the determinants of the minors of the original matrix, each of which is multiplied by a cofactor (-1)^(i+j). The minors of a matrix are the determinants of the square submatrices formed by deleting one row and one column from the matrix. The determinant of a matrix is a scalar value that can be computed from its elements.

For example, consider the matrix A:

[a b]

[c d]

The determinant of A is:

det(A) equals (a * d) - (b * c).

The cofactor matrix of A is:

[d -b]

[-c a]

The adjugate of A is the transpose of the cofactor matrix, so it is:

[d -c]

[-b a]

The inverse of A is then:

A^(-1) = (1/det(A)) * adj(A)

= (1/((a * d) - (b * c))) * [d -c]

[−b a]

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The number of maple trees that were in the woodlot is 72.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

At the end of the year, maple:oak has a ratio of 3:11 and there were 132 oak so 132 = 11 units.

In this case, 132/11=12 so there were 3 times 12 maple trees at the end or 36 so 36:132.

Assuming the units stay the same (1 unit = 12), at the beginning of the year there were 108 maple trees . The more trees will be:

= 108-36

= 72

There were 72 more trees.

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The simplified trigonometric expression is cos(z). We did not get any of the answer choices provided, as they were all incorrect.

Use the trigonometric identities for sine and cosine of negative angles.

Recall that sin(-x) = -sin(x) and cos(-x) = cos(x).

Using these identities, we can simplify the given expression:
sin(z) + cos(-z) + sin(-z)
= sin(z) + cos(z) + (-sin(z))
= sin(z) - sin(z) + cos(z)
= cos(z)

Therefore, the simplified trigonometric expression is cos(z). We did not get any of the answer choices provided, as they were all incorrect.

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