find the value of x and the mesasurement of angle axc

The equations of the other line are:

BC: y = 2x

AD: y = 2x + 2

CD = -¹/₂x + 5.5

The formula for the equation of a line between two coordinates is expressed as:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Thus, for the lines we have:

BC has B(-2, 4) and C(-1, 6)

Thus:

BC: (y - 4)/(x - 2) = (6 - 4)/(-1 + 2)

BC: (y - 4)/(x - 2) =2

BC: y - 4 = 2x - 4

BC: y = 2x

AD has  A(2,2) and D(3, 4)

Thus:

AD: (y - 2)/(x - 2) = (4 - 2)/(3 - 2)

AD: y - 2 = 2x - 4

AD: y = 2x + 2

CD has C(-1, 6) and D(3, 4)

CD: (y - 6)/(x + 1) = (4 - 6)/4

CD: y - 6 = -¹/₂(x + 1)

CD = -¹/₂x + 5.5

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The average rate of change over the interval from -3 to 1 is 2.000

To find the average rate of change over the interval from -3 to 1, we need to calculate the change in y divided by the change in x.

Δy = y₂ - y₁ = (-10) - (-18) = 8

Δx = x₂ - x₁ = 1 - (-3) = 4

Now, we can calculate the average rate of change using the formula:

Average Rate of Change = Δy / Δx

Average Rate of Change = 8 / 4 = 2

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Is not possible to define a radius  nor a diameter in a trapezium.

Radius and diameter are two measures defined for circles.

Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).

At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.

To get the area use the formula:

Area = (base1 + base2)*height / 2

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Answer: True

Step-by-step explanation:

The lateral faces are the triangular faces that connect the apex of the pyramid to the edges of the base. The area of each lateral face can be calculated using the formula for the area of a triangle, which is [tex]\frac{1}{2} \times b \times h[/tex]. The area of the base is simply the area of the polygon that forms the base of the pyramid.

__________________________________________________________

The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. (True or False)

The correct answer is True.

The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. This can be represented by the formula:

[tex]\qquad\qquad\Large\boxed{\rm{\:SA = B + LA\:}}[/tex]

The lateral faces are the faces that are not the base, so their areas are calculated using the formula for the area of a triangle. The area of the base is calculated using the appropriate formula depending on the shape of the base.

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a)  the value of the tractor after two years is $10,400.

b)  the value of the tractor after six years is $5,200.

To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.

a) After two years:

Substituting t = 2 into the equation, we get:

v = -1,300(2) + 13,000

v = -2,600 + 13,000

v = 10,400

Therefore, the value of the tractor after two years is $10,400.

b) After six years:

Substituting t = 6 into the equation, we get:

v = -1,300(6) + 13,000

v = -7,800 + 13,000

v = 5,200

Therefore, the value of the tractor after six years is $5,200.

To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:

-1,300t + 13,000 = 0

-1,300t = -13,000

t = -13,000 / -1,300

t = 10

Therefore, the tractor will have no value after 10 years.

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If sinθ = 5/13 and θ is in Quadrant II, then sin (θ/2) will be equal to  [tex]\frac{5}{\sqrt{26}}[/tex]

To find sin(θ/2), we can use the half-angle identity for sine, which states that:

sin(θ/2) = ±[tex]\sqrt{\frac{(1 - cos\theta)}{2}}[/tex]

Given that sinθ = 5/13 and θ is in Quadrant II, we can determine the value of cosθ using the Pythagorean identity

sin²θ + cos²θ = 1

sinθ = 5/13

sin²θ = (5/13)² = 25/169

cos²θ = 1 - sin²θ = 1 - 25/169 = 144/169

cosθ = ±√(144/169) = ±12/13

Since θ is in Quadrant II, the cosine is negative. Therefore, cosθ = -12/13.

Now, we can calculate sin(θ/2):

sin(θ/2) = ±√((1 - cosθ) / 2) = ±√((1 - (-12/13)) / 2) = ±√((1 + 12/13) / 2) = ±√(25/26) = ±5/√26

Since θ is in Quadrant II, sin(θ/2) will be positive.

Therefore, sin(θ/2) = 5/√26.

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The polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

We shall divide the polynomial x³ + 3x² - 8x + 140 by x + 7 as follows;

x³ divided by x equals x²

x + 7 multiplied by x² equals x³ + 7x²

subtract x³ - x² from x³ + 3x² - 8x + 140 will result to -4x² - 8x + 140

-4x² divided by x equals -4x

x + 7 multiplied by -4x equals -4x² - 28x

subtract -4x² - 28x from -4x² - 8x + 140 will result to 20x + 140

20x divided by x equals 20

x + 7 multiplied by 20 equals 20x + 140

subtract 20x + 140 from 20x + 140 will result to a remainder 0

Therefore, the polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0

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An output value for (fog)(x) is 55/(x² + 2x).

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(fog)(x) = 5/(x + 2) × 11/x

(fog)(x) = 55/x(x + 2)

(fog)(x) = 55/(x² + 2x)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x² + 2x ≠ 0

x² ≠ -2x

x ≠ -2

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.

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Answer:

False

Step-by-step explanation:

When calculating volume, units of measurement are cubed. When calculating surface area, units of measurement are squared.

Further explanation:

Let's say you are finding the area of a rectangle. The length is 5in and the width is 7 in.

since you know l*w is area, you need to multiply 5in and 7in. 5*7=35 and then the two units of measurement, in*in=in^2 so 5in*7in=35in^2. the unit is squared not cubed.

The units of measurement for surface area are always SQUARED. Hence the correct answer is FALSE.

In 2-D, the total space covered by any two-dimensional figure is called Area while if we talk about 3-D, the total area of all the outer surfaces when added, sums up to form the Surface Area. Hence, the surface area is the multiplication of any two of the physical quantities.

For example,

Area of a square=(side x side)

                           =(metre x metre) or (cm x cm) [in terms of units]

                           = [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex]

Similarly,

Surface Area of cube=6x(side x side)  [summation of the area of 6 faces of cube]

                                   =(metre x metre) or (cm x cm) [in terms of units]

                                    = [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex]  (again)

Therefore, The units of measurement for the surface area are always SQUARED. Hence the correct answer is FALSE.

When talking of volume, since volume is the amount of space taken by any object or any 3-Dimensional body, the units of measurement of Volume are always cubed. For example, [tex]metre^{3}[/tex] or [tex]cm^{3}[/tex].

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Answer:

-1 - 6x = x - 15

Add 15 to both sides using the addition property of equality.

14 - 6x = x

14 = 7x

2 = x

D) -1 - 6x + 15 = x - 15 + 15

Answer and Step-by-step explanation:

Please refer to the photo for the solution!

The value of a and b in the given complex expression is  1/10 and -1/10 respectively.

This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.

(2i/2+i) - 3i/(3+i) = a + bi

{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi

6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi

(-2 + 3) / (6 + 5i - 1) = s+bi

1 / (5 + 5i) = a+bi

Now we multiply top and bottom by 5 - 5i :

5 - 5i / (5 + 5i)(5 - 5i) = a+bi

5 - 5i / 25 -25i² = a+bi

5 - 5i / 50 = a+bi

1/10 - 1/10i = a+bi

On comparing the real and imaginary part on the both sides:

a= 1/10 , b= -1/10.

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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The correct answer is each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.

To find the total area of the garden beds, we can use the expression:

Total area = (length of one side)^2 * number of garden beds

Given that each garden bed has a length of 4 feet, we substitute 4 for the length of one side in the expression:

Total area = (4)^2 * 3

Simplifying:

Total area = 16 * 3

Total area = 48 square feet

Therefore, if each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.

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Answer:

B. 0.593

Step-by-step explanation:

The calculated period of the function is 12

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

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Using the above as a guide, we have the following:

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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Answer:

The answer is 2400 cm^3

Step-by-step explanation:

You just need to multiply the dimensions

Answer:

2400 cm³

Step-by-step explanation:

Volume of cuboid = length × width × height

Volume = 8 cm × 15 cm × 20 cm

Volume = 2400 cm³

So, the volume of the cuboid is 2400 cm³

So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.

Step-by-step explanation:

To find the value(s) for x such that f(x) = 23, we can set up the equation:

x^2 - 4x + 2 = 23

To solve this quadratic equation, we need to rearrange it into the standard quadratic form:

x^2 - 4x - 21 = 0

Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 4x - 21 = 0, the coefficients are: a = 1, b = -4, and c = -21.

Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))

x = (4 ± √(16 + 84)) / 2

x = (4 ± √100) / 2

x = (4 ± 10) / 2

Now, we have two solutions:

x = (4 + 10) / 2 = 14 / 2 = 7

x = (4 - 10) / 2 = -6 / 2 = -3

Therefore, the values for x such that f(x) = 23 are x = 7 and x = -3.

Explanation:

Plug x = -2 into h(x)

h(x) = x+4

h(-2) = -2+4

h(-2) = 2

This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.

g(x) = 5x

g(2) = 5*2

g(2) = 10

Therefore, g[ h(-2) ] = 10

The length of AB = CD and CD = AB based on the proof that :

Looking at the segments CD and AB, both segments are of equal length, hence they would be equal

Similarly , both segments are parallel and have the same end points. Hence, they are equal.

Therefore, AB = CD

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Rounding to the nearest whole number, the membership of the Network Club in 2020 will be approximately 5,564.

Therefore, the correct answer is: E. 5,564.

To calculate the membership of the Network Club in 2020, we can use the continuous growth formula:

[tex]A = P \times e^{(rt)[/tex]

Where:

A is the final amount or membership in 2020,

P is the initial amount or membership in 2010,

e is the mathematical constant approximately equal to 2.71828,

r is the annual growth rate as a decimal,

t is the number of years.

Given:

P = 2,500 (membership in 2010),

r = 8% = 0.08 (annual growth rate),

t = 2020 - 2010 = 10 years (number of years).

Plugging in the values into the formula, we have:

[tex]A = 2,500 \times e^{(0.08 \times 10)}[/tex]

Calculating the exponent:

[tex]A = 2,500 \times e^{(0.8)[/tex]

Using a calculator, we find that[tex]e^{(0.8)[/tex]  is approximately 2.22554.

Now, we can calculate the final amount A:

A ≈ 2,500 [tex]\times[/tex] 2.22554 ≈ 5,563.85  

Therefore, the correct answer is: E. 5,564.

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Answer: The answer is 5564

Step-by-step explanation: P=I[tex]e^rt[/tex]=2500e^(0.08)(10)=5563.85

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

A line segment is a fundamental concept in geometry, representing a portion of a line that has a definite beginning and end. It consists of an infinite number of points situated between two endpoints.

The endpoints themselves are distinct points on a line, and they are included as part of the line segment. Unlike a line, which extends indefinitely in both directions, a line segment is confined to a specific length.

This length is often referred to as the 'measure' of the line segment. Additionally, line segments serve as building blocks for various geometrical shapes and figures by connecting multiple points in space.

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The Question in English

What is the definition of a line segment?

Answer:

∠ ADE = 55° , ∠ ACE = 32.5° , ∠ BAD = 22.5°

Step-by-step explanation:

the measure of the inscribed angle ADE is half the measure of its intercepted arc AE , then

∠ ADE = [tex]\frac{1}{2}[/tex] × 110° = 55°

---------------------------------

the measure of the secant- secant angle ACE is half the difference of the measures of the intercepted arcs , that is

∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD) = [tex]\frac{1}{2}[/tex] (110 - 45)° = [tex]\frac{1}{2}[/tex] × 65° = 32.5°

-----------------------------------------

the measure of the inscribed angle BAD is half the measure of its intercepted arc BD , that is

∠ BAD = [tex]\frac{1}{2}[/tex] × 45° = 22.5°

The correct range for the piecewise graph is [-4, 2].

We need to find the minimum and maximum values of the y-coordinates.

The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.

The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.

We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.

Therefore, the correct range for the piecewise graph is [-4, 2].

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Answer: 2×2×5×7 or, in exponent form, [tex]2^2[/tex]×[tex]5^1[/tex]×[tex]7^1[/tex]

Step-by-step explanation:

We can use a factor tree to determine the prime factorization of 140. You may notice that there are several factors to choose from that will give us 140, but you can choose any because in the end it will give you the same answer!

                                                         140

                                                     14   ×  10

                                                   2×7      2×5

That is all, because the final numbers listed are prime and we cannot perform any further actions.

Hope this helps!

Answer:

the distance from Maria's desk to Monique's desk is approximately 8.94 feet.