In ΔFGH, f= 67 inches, m∠G=66° and m∠H=30°. Find the length of g to the nearest inch

An equation is considered linear if it is in the form of y=mx+b where m is the slope of the equation and b is the y-intercept.

There are several properties possessed by linear equations, which are as follows:

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Using the Taylor Remainder Theorem, the values of x ≤ 1.2145 for which this approximation is within 0.004458 of the right answer.

The function is f(x) = cos(x) at a=0.

The Taylor Series is:

f(x) = f(a) + f'(a)/1! (x - a) + f''(a)/2! (x - a)^2 + f'''(a)/3! (x - a)^3 + .............

Now, d/dx (cosx) = -sinx at a = 0

d/dx (cosx) = 0

d^2/dx^2 (cosx) = -cosx at a = 0

d^2/dx^2 (cosx) = -1

d^3/dx^3 (cosx) = sinx at a = 0

d^3/dx^3(cosx) = 0

d^4/dx^4 (cosx) = cosx at a = 0

d^4/dx^4 (cosx) = 1

d^5/dx^5 (cosx) = -sinx at a = 0

d^5/dx^5 (cosx) = 0

d^6/dx^6 (cosx) = -cosx at a = 0

d^6/dx^6 (cosx) = -1

Now putting the value

f(x) = 1 + 0/1! (x - 0) + (-1)/2! (x - 0)^2 + 0/3! (x - 0)^3 + 1/4! (x - 0)^4 + 0/5! (x - 0)^5 + (-1)/6! (x - 0)^6 + .............

Simplifying

f(x) = 1 - 1/2! x^2 + 1/4! x^4 - 1/6! x^6 + .............

|1/6! x^6| ≤ 0.004458

Multiply by 6! on both side, we get

x^6 ≤ 0.004458 × 6!

After solving

x ≤ 1.2145

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The complete question is:

Find T5(2): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a=0. Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.004458 of the right answer. Assume for simplicity that we limit ourselves to |x| ≤ 1.

The solution of the system of equations is [tex]$x_1 = \frac{-400}{35}$, \\$x_2 = \frac{-400}{35}$, and $x_3 = -\frac{20}{35}$.[/tex]

The given system of equations can be written in matrix form as follows:

[tex]\begin{bmatrix}1 & -3 & 4 \\ 3 & -7 & 7 \\ -4 & 6 & -1\end{bmatrix}[/tex][tex]\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]

=[tex]\begin{bmatrix}-4 \\ -8 \\ 7\end{bmatrix}[/tex]

We can solve for the unknowns [tex]$x_1$, $x_2$, and $x_3$[/tex]  by using the Gaussian elimination method. The first step is to subtract 3 times the first equation from the second equation, and the result is

[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ -4 & 6 & -1\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]

[tex]=\begin{bmatrix}-4 \\ -20 \\ 7\end{bmatrix}[/tex]

We can then subtract 4 times the first equation from the third equation, and the result is

[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ 0 & 18 & -5\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]

=[tex]\begin{bmatrix}-4 \\ -20 \\ -12\end{bmatrix}[/tex]

We can now add 10 times the second equation to the third equation, and the result is

[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ 0 & 0 & -35\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]

=[tex]\begin{bmatrix}-4 \\ -20 \\ 20\end{bmatrix}[/tex]

We can now solve for [tex]$x_3$[/tex] by dividing the third equation by -35, and the result is = [tex]\frac{20}{-35} = -\frac{20}{35}$.[/tex]

Therefore, the solution of the system of equations is

[tex]$x_1 = \frac{-400}{35}$, $x_2 = \frac{-400}{35}$, and $x_3 = -\frac{20}{35}$.[/tex]

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The curvature of a curve r(t) = 9t i 7t j (2 t2) k is 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2).

Curvature is a measure of the amount by which a curve deviates from being straight. It describes the degree to which a curve bends or twists at any point along its length.

In mathematics, curvature is a property of curves and surfaces that is used to describe their shape and local behavior. For example, the curvature of a circle is constant and is equal to the reciprocal of its radius. The curvature of a straight line is zero.

Curvature is a scalar quantity and is usually measured in units of inverse length, such as 1/meter. There are several ways to mathematically define and calculate curvature, including the concept of the curvature of a curve at a point, which is the rate of change of the direction of the tangent to the curve at that point.

The curvature of a curve is given by:

k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³

where r'(t) is the first derivative of r(t), r''(t) is the second derivative of r(t), and || || is the magnitude or length of a vector.

Given the curve r(t) = 9t i + 7t j + (2 t²) k, we can find its first and second derivatives:

r'(t) = 9 i + 7 j + 4t k

r''(t) = 4 k

So, the curvature of the curve r(t) is:

k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³ = ||9 i + 7 j|| × ||4 k|| / ||9 i + 7 j + 4t k||³ = 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2)

Since this expression depends on t, the curvature is a function of t, not a constant.

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Marginal Revenue is negative, the firm should consider reducing its output to increase its total revenue.

Therefore, correct answer will be a. increase.

Marginal Revenue (MR) is a crucial concept in economics that measures the change in a firm's total revenue as a result of selling one additional unit of output. MR is used by firms to make decisions about how much output to produce and what price to charge.

In a linear (inverse) demand function, MR is negative when the elasticity of demand is less than one, meaning that the demand for a product is relatively inelastic. In other words, as the firm increases output, the price will decrease, causing total revenue to decline.

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Answer:

No solution, because the slopes are the same and the y-intercepts are different.

Step-by-step explanation:

The two equations are:

y = 1/4x + 1 and y= 1/4x - 1

Since the left sides are equal we can equate the right sides:
1/4x + 1 = /4x - 1

1/4x cancels out of the equation and we get the absurdity:

1 = -1

This indicates no solution to the system of equations

Answer:
No solution, because the slopes are the same and the y-intercepts are different.

We can see that the slopes are the same (1/4) and the y-intercepts are different (1 and -1)

Answer: -7

Step-by-step explanation: multiply first then you have 2x+8= -6.

subtract 8 from both sides. you now have 2x= -14. divide by 2. X = -7 ( look at attached image if confused)

Answer:

Step-by-step explanation:

The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line. Plugging in the given points, we get:

slope = (8 - 6) / (-5 - (-10)) = 2 / 5 = 0.4

So the slope of the line through the points (-10, 6) and (-5, 8) is 0.4

The one which not the benefit of being a member of a professional organization is providing certificate examinations at discounted rate. The correct option is D.

Professional associations provide the better networking opportunities with people who are specifically in our industry. Whether we are looking to pursue employment opportunities, link with other industry professionals, or even looking for a mentor in our profession, the networking opportunities are invaluable.

Another benefits of joining in a professional organization is that it helps build the career portfolio of a professional. Organizations which can provide opportunities for speaking engagements, career specialization, publication and even scholarship and training programs abroad.

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Although part of your question is missing, you might be referring to this full question: All of the following are benefits of being a member of a professional organization, except:

A. providing a wide range of continuing education units.

B. publishing newsletters and magazines dealing with current issues and trends in healthcare.

C. providing tuition reimbursement.

D. providing certificate examinations at discounted rate.

The  equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).

We need to solve for x,

6+0.6x - 24=0.25x

After rearranging the equation we get,

0.35x=18

Divide both side by 0.35x

x=18/0.35

x = 51.43

The  equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).

Inconclusion the equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation is described as having one or more variables in French.

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Complete question: Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.

Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?

Answer:

Step-by-step explanation:

Since the numerator is missing, you want to multiply the denominator onto the other side.

5 x 7 =35

x=35

Answer:

x=35

Step-by-step explanation:

Easy way to solve is making x/5 an improper fraction (fraction whose numerator is equal to or greater than its denominator.)

How I solved it was by multiplying 7×5=35, then I plugged the value into x making it (35/5)=7.

Now just make it a proper fraction, 35÷5=7, now we have 7=7.

The domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.

The domain of a function is the set of all possible input values for which the function is defined. For the function f(x) = 10x + 8, the domain will be all real numbers greater than or equal to 0. This can be seen by examining the equation: if x = 0, then f(x) = 8. Therefore, the domain of the function will be all x values such that x ≥ 0. To calculate the upper bound for the domain, we can solve for x by subtracting 8 from both sides of the equation, resulting in 10x = -8. Dividing both sides by 10 gives us x = -0.8. Therefore, the domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.

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The number of miles he can travel on 44.2 gallons of gas would be = 1697.28 miles

The table shows that there is direct proportional relationship between the number of miles traveled and the number of gallons used by Parker. That is increase in the number of mile = increase in the number of gallons.

If 34 gallons = 1305.6 miles

44.2 gallons = X miles

Make X miles the subject of formula;

X miles = 44.2 × 1305.6/34

= 57707.52/34

= 1697.28 miles

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Each decimal number has a unique bit structure that starts at 1 bit, that's why it is impossible to convert a decimal number to binary digit-by-digit as is achievable with hexadecimal.

It impossible to convert a decimal number to binary on a digit-by-digit basis as can be done for hexadecimal because each decimal number has a separate bit structure that starts at 1 bit and goes quickly, it is difficult to convert a decimal number to binary string of 4 bits digit by digit.

However, since each hexadecimal number has a width of 4 bits, this is achievable. It is relatively easy to go back and forth between binary and hexadecimal. The comparable 4-bit binary string is used to replace each hexadecimal digit in the original number.

Hexadecimal Number FD13.

1111 1101 00010011 each hexadecimal digit with its corresponding 4-bit binary value.

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The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)

The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"

The disk method is predominantly used when we rotate any particular curve around the x or y-axis.

Suppose a function x = f(y), which is rotated about the y-axis.

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫dc [tex][f(y)]^{2}[/tex]dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)

Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)

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The volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)

The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"

The disk method is predominantly used when we rotate any particular curve around the x or y-axis.

Suppose a function x = f(y), which is rotated about the y-axis.

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π∫dc [f(y)]² dy

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)

Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy.  Option (A)

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The value of x is 15

The value of y is 7.

The unknown sides:

x = 15

5y - 3 = 33

y + 9 = 16

x - 2 = 13

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Similar triangles mean the ratios of the corresponding sides are equal.

Now,

(5y - 3)/(y + 9) = 30/x = 26/(x - 2)

Taking two ratios.

(5y - 3)/(y + 9) = 30/x

5xy - 3x = 30y + 270

Taking two ratios.

30/x = 26/(x - 2)

30x - 60 = 26x

30x - 26x = 60

4x = 60

x = 15

Now,

Substituting x = 15

5xy - 3x = 30y + 270

5 x 15 x y - 3 x 15 = 30y + 270

75y - 45 = 30y + 270

75y - 30y = 270 + 45

45y = 315

y = 7

Now,

x = 15

5y - 3 = 35 - 3 = 33

y + 9 = 7 + 9 = 16

x - 2 = 15 - 2 = 13

Thus,

x is 15 and y is 7.

The unknown sides are 15, 33, 16, and 13.

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No, it's not possible for Trevor to use 1/2 of the poster for his pictures, 3/8 for his hypothesis, and 1/4 for the experiment process.

This is discovered by addition of fraction

= 1/2 + 3/8 + 7/8

= 7/8

The fractions 1/2, 3/8, and 1/4 add up to 7/8, which is greater than 1.

Since the fractions represent parts of a whole poster, the total must be less than or equal to 1.

Therefore, Trevor needs to adjust the fractions so that their sum is less than or equal to 1.

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The required dimensions in the figure are

DG = FG = EG incenters

solving for angle FXD using SOH CAH  TOA

The side XG is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

sin 22 = FG / XG

XG = 14 / sin 22

XG = 37.37

sin x = DG / XG = 14 / 37.37 hence x = 22

therefore angle FXD is 44 degrees

EG = DG = 14

angle FZG

< DYE + < FXD + < FZE = 180 sum of angles of a triangle

94 + 44 + < FZE = 180

< FZE = 180 - 94 - 44

< FZE = 42

< FZE = 2 * < FZG

< FZG = 42 / 2

< FZG = 21

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Answer:

4 is there answer I think

Step-by-step explanation:

You need to work 84 hours per month at your second job to meet your monthly savings goal.

Fixed expenses = 2,034.24 x 30% = $610.72

Discretionary income = 2,034.24 - 610.72 = $1,423.52

Savings goal per month = $1,423.52 x 20% = $284.70

Net pay per hour = $9.50 - ($9.50 x 7.65%) - ($9.50 x 11.5%) - ($9.50 x 7.75%) = $7.33

Hours per month = $284.70 ÷ $7.33 = 84 hours.

To calculate, first find the number of your fixed expenses by multiplying your primary job income by 30%. This is $610.72. Then subtract your fixed expenses from your primary job income to find your discretionary income, which is $1,423.52. Multiply that by 20% to find the amount you want to save each month, which is $284.70.

Finally, divide that amount by your net pay per hour after taxes from your second job, which is $7.33, to find the number of hours you need to work, which is 84 hours.

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If two line segments are parallel to each other and the first line segment has endpoints at (2, 3) and (1,9) while the second line segment has endpoints at (5, 4) and (3,Y), the value of y is:

16

Two lines are parallel if and only if they have the same slope. So, to find the value of y, we need to find the slope of the first line segment and use it to find the equation of the second line segment.

The slope of the first line segment can be found using the formula:

Since the two lines are parallel, they have the same slope, so we can use the slope to find the equation of the second line segment.

Expanding the equation and solving for y, we get:

Now that we have the equation of the second line segment, we can use the x-coordinate of one of its endpoints (3) to find the corresponding y-coordinate.

So, the value of y is 16.

Complete Question:

"Two line segments are parallel to each other. The first line segment has endpoints at (2, 3) and (1,9). The second line segment has endpoints at (5, 4) and (3,Y).

What is the value of y?

A. 34

В. 16

C. 10

D. 6"

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Answer:

Below

Step-by-step explanation:

A =   qty 2  at 12.50 each =   25.00

B =   33.90 / 2 = 16.95 unit price

C  =   31.00 / 6.20 = quantity 5

VAT is value added tax ...take the total  108.28   and multiply by 15% = 16.24

a) The length of the base is 10 units and the height is 7 units. The area is 35 square units.

B) The length of the base is 10 units and the height is 6 units. The area is 30 square units.

C) The length of the base is 10 units and the height is 3 units. The area is 15 square units.

D) The length of the base is 4 units and the height is 11 units. The area is 22 square units.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The base and height are highlighted in each triangle.

A)

The length of the base is 10 units.

The length of height is 7 units.

The area of the triangle is 1/2 × 10 × 7 = 35 square units.

B)

The length of the base is 10 units.

The length of height is 6 units.

The area of the triangle is 1/2 × 10 × 6 = 30 square units.

C)

The length of the base is 10 units.

The length of height is 3 units.

The area of the triangle is 1/2 × 10 × 3 = 15 square units.

D)

The length of the base is 11 units.

The length of height is 4 units.

The area of the triangle is 1/2 × 11 × 4 = 22 square units.

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There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.

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The common chord has a length equal to 6 centimeters.

In this problem we find the case of two circles of different radii (r₁ = 5 cm, r₂ = 3 cm), whose distance between centres is equal to 4 centimeters. We are required to determine the length of the chord common to the two circles.

First, determine one angle of a triangle by law of cosine:

cos θ = [(5 in)² - (3 in)² - (4 in)²] / [- 2 · (3 in) · (4 in)]

θ ≈ 90°

Second, determine the length of the common chord:

x = 2 · (3 cm)

x = 6 cm

The length of the common chord is equal to 6 centimeters.

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The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.

Caffeine is a natural chemical with stimulant effects.

Let's call the new half-life time for an individual with extended half-life as t. The function for the amount of caffeine (C) in the bloodstream after time t can be expressed as:

C(t) = 80 * (1/2)^(t/8)

Using this formula, we can determine the amount of caffeine in the bloodstream after different times:

1 hour:

C(1) = 80 * (1/2)^(1/8) = 80 * (1/2)^0.125 ≈ 79.28 mg

5 hours:

C(5) = 80 * (1/2)^(5/8) ≈ 64.51 mg

10 hours:

C(10) = 80 * (1/2)^(10/8) ≈ 51.37 mg

20 hours:

C(20) = 80 * (1/2)^(20/8) ≈ 25.68 mg

Therefore, The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.

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The legs' lengths are 7 and 24 respectively. As a result, choice C is the right answer.

Completed question ;

The hypotenuse of a right triangle measures 25. Which could be the lengths of the legs?

A. 3 and 4

B. 5 and 5

C. 7 and 24

D. 10 and 15

Given data :

The hypotenuse of a right triangle measures 25.

A) 3²+4²= Square of the hypotenuse

25=Square of the hypotenuse

Hypotenuse=5 units

B) 5²+5²= Square of the hypotenuse

50=Square of the hypotenuse

Hypotenuse=5√2 units

C) 7²+24²= Square of the hypotenuse

625=Square of the hypotenuse

Hypotenuse=25 units

D) 10²+15²= Square of the hypotenuse

325=Square of the hypotenuse

Hypotenuse=√325 units

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The volume of this prism = 2 × 3 × 9 units³.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given figure we get,

A rectangular prism made up of unit cubes.

There are 3 layers, and each layer is 9 units long and 2 units wide.

i.e. l = 9

w = 2

h = 3

so, the volume = V

we know, V= l.w.h

so, V = 9.2.3

Hence, The volume of this prism = 2 × 3 × 9 units³.

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