Prove that triangle FGH is right-angled at F

Answer:

Sure, here is the solution for the equation G/B=M/n:

```

B = Gn/M

```

Here is the step-by-step solution:

1. Multiply both sides of the equation by B.

```

G/B * B = M/n * B

```

2. Simplify both sides of the equation.

```

G = Gn/n

```

3. Divide both sides of the equation by n.

```

G/n = Gn/n * 1/n

```

4. Simplify both sides of the equation.

```

B = Gn/M

```

Therefore, the solution for B is Gn/M.

Step-by-step explanation:

The triangles ABC and EDF are similar, and x = r × w/u.

As per the question, we have angle A in triangle ABC congruent to angle F in triangle EDF, angle C in triangle ABC congruent to angle D in triangle EDF, and angle B in triangle ABC congruent to angle E in triangle EDF.

Therefore, the triangles are similar by the Angle-Angle (AA) similarity theorem.

To find the expression for x, we can use the fact that the corresponding sides of similar triangles are proportional.

In this case, we have:

x/w = u/r (corresponding sides of similar triangles)

Solving for x, we get:

x = r × w/u

Therefore, x = r × w/u, and it can use this expression to solve for x in triangle ABC and EDF.

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Answer :

Step-by-step explanation:

60 minutes = 1 hour

1 minute = 1/60

1 minute = 0.016666666666667 hours

1.47 minutes = 0.016666666666667 × 1.47

1.47 minute = 0.0245 hours

Therefore, 1.47 Minutes is equal to 0.0245 Hours.

This solution of g(x) has no real solutions, so g⁻¹ (-7) does not exist.

To find g⁻¹ (-7), we need to solve for x in the equation g(x) = -7.

First, we need to determine which part of the piecewise function to use. Since -7 is less than 5, we know that we need to use the first part of the function: g(x) = 5x² if x ≤ -3.

So, we set g(x) = 5x² equal to -7 and solve for x:

5x² = -7

x² = -7/5

This equation has no real solutions since the square of any real number is always nonnegative. Therefore, g⁻¹ (-7) does not exist in the real numbers.

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Answer:

£73.60

Step-by-step explanation:

89198 kWh - 88738 kWh = 460 kWh.

Since each kWh of electricity costs 16p, Fiona’s total cost for electricity in November would be 460 kWh * 16p/kWh = 7360p.

Since there are 100 pence in a pound, this is equivalent to £73.60.

So, Fiona had to pay £73.60 for the electricity she used in November.

The requreid Fiona had to pay £73.60 for the electricity she used in November.

It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.

To find out how much electricity Fiona used in November, we need to subtract the October reading from the November reading:

89,198 kWh - 88,738 kWh = 460 kWh

So, Fiona used 460 kWh of electricity in November.

To find out how much she had to pay, we need to multiply the number of kWh by the cost per kWh:

460 kWh × 16p/kWh = 7360p

We can convert pence to pounds by dividing by 100:

7360p ÷ 100 = £73.60

Therefore, Fiona had to pay £73.60 for the electricity she used in November.

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The independent variable is 't' and the dependent variable is 'd' while the rate of change is '3' and the initial value is '1'.

In the given function d=3t+1:

The independent variable here is 't' which represents time in seconds.

whereas the dependent variable is 'd' and it represent the distance traveled by a car in some unit. The rate of change is 3, and it represents the constant speed of the car in units of distance per unit of time.

While the initial value is 1, which represents the distance traveled by the car when time is 0.

Hence this function can be interpreted as if the car is travelling at a constant speed of 3 units of distance and has already travelled 1 unit of distance at the start of the journey.

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Let's start by assigning variables to the unknowns in the problem:

- Let j be Jim's speed in miles per hour (in other words, the rate at which he walks).

- Let s be Steve's speed in miles per hour (in other words, the rate at which he runs).

- Let m be Matt's speed on his bike in miles per hour.

From the first sentence of the problem, we know that:

s = m + 4   (Steve runs 4 miles per hour slower than Matt rides his bike)

And from the second sentence, we know that:

j = s - 3   (Jim walks 3 miles per hour slower than Steve runs)

We want to find out how long it takes Jim to walk 25 miles and how long it takes Matt to ride his bike x miles. We can use the formula:

time = distance / rate

For Jim, we have:

time = 25 / j

For Matt, we have:

time = x / m

We also know that Steve runs 16 miles in the same time that Matt rides his bike 24 miles, so we can write:

16 / s = 24 / m

Substituting s = m + 4 and solving for m, we get:

16 / (m + 4) = 24 / m

16m = 24(m + 4)

16m = 24m + 96

8m = 96

m = 12

So Matt rides his bike at a speed of 12 miles per hour.

Now we can use the equations we set up earlier to solve for j and x:

j = s - 3

s = m + 4

j = (m + 4) - 3

j = m + 1

j = 13

x / m = 25 / j

x / 12 = 25 / 13

x = (25 * 12) / 13

x = 300 / 13

x ≈ 23.08

So it takes Jim 25 / 13 ≈ 1.92 hours to walk 25 miles, and it takes Matt 23.08 hours to ride his bike x = 300 / 13 ≈ 23.08 miles.

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The directions of motion for this calculation are:

i) Right, right, left

ii) Undetermined

The first operation is subtraction of y from x, which moves to the right on the number line. The second operation is addition of the opposite of z, which is subtraction of z from the result of the first operation. This also moves to the right on the number line. The final operation is addition of the opposite of z, which is subtraction of z from the result of the second operation. This moves to the left on the number line. Therefore, the directions of motion are right, right, left.

Since we don't know the values of x, y, and z, we cannot determine the sign of the final answer. Therefore, the answer is undetermined.

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The area of the largest outside circle in square centimeters is closest to e)1,017.36 cm².

The area of the largest circle is equal to the sum of the areas of the three inner circles and the area of the white region between them. Since the three inner circles are congruent, we can divide the white region into three equal parts. Let the radius of each inner circle be 'r'. Then, the radius of the largest circle is '3r'.

The area of the white region is the difference between the area of the square and the sum of the areas of the three congruent sectors. The area of each sector is (1/6)πr².

Therefore, the area of the white region is (9/4) r². Finally, we can use the formula for the area of a circle to find the area of the largest circle: A = π(3r)² + 3(1/6)πr² - (9/4) r² = (63/4)πr². If we substitute the value of r as 6 cm (since the diameter of the inner circle is 12 cm), we get the area of the largest circle as (63/4)π(6)² ≈ 1,017.36 cm²(e).

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To solve the triangle, we have;

Angle Q = [tex]112^{o}[/tex]

QR = 30.0

PR = 40.2

A sine rule is a trigonometric function that can be applied to determined the unknown side, or angle of a none right triangle.

From the information given in the question, to solve the triangle;

P + R + Q = 180

42 + 26 + Q = 180

Q = 180 - 68

   = 112

Q = [tex]112^{o}[/tex]

Applying the sine rule,

QR/Sin P = PR/Sin Q = PQ/Sin R

PR/Sin Q = PQ/Sin R

PR/Sin 112 = 19/ Sin 26

PRSin 26 = 19*Sin 112

             = 17.6165

PR = 17.6165/ 0.4384

  = 40.1836

PR = 40.2

Also,

QR/Sin P = PQ/Sin R

QR/Sin 42 = 19/ Sin 26

QRSin 26 = 19*Sin 42

                = 12.7135

QR = 12.7135/ 0.4384

     = 28.9998

QR = 30

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The testimonies of Nazi officials at the Nuremberg Trials were incredibly important because they provided valuable insight into the atrocities committed by the Nazi regime.

Their testimonies helped to dispel any claims of denial that the events of the Holocaust had occurred. The confessions given by the Nazi officials gave detailed accounts of the crimes committed by the regime, and helped to hold those responsible accountable for their actions. It is important to note that while some Nazis did receive lighter sentences because of their confessions, the vast majority of those involved were held fully responsible for their crimes. Overall, the testimonies of Nazi officials played a crucial role in bringing justice to the victims of the Holocaust and shedding light on the horrific actions of the Nazi regime.

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Based on the information given in the table, we can see that there is a linear relationship between the total amount Mrs. Jacobs will be charged for a skating party and the number of children attending. This means that we can use a linear equation to represent this relationship.

To find the equation, we need to determine the slope (m) and y-intercept (b) of the line. We can do this by using two points from the table: (10, 100) and (20, 180).

The slope (m) can be calculated using the formula:

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

Plugging in the values, we get:

m = (180 - 100) / (20 - 10) = 8

The y-intercept (b) can be found by plugging in one of the points and the slope into the equation:

y = mx + b

Using the point (10, 100) and the slope we just calculated, we get:

100 = 8(10) + b

Solving for b, we get:

b = 20

Therefore, the equation that best represents y, the total amount in dollars Mrs. Jacobs will be charged for x number of children attending the skating party, is:

y = 8x + 20

This equation shows that for every additional child that attends the skating party, Mrs. Jacobs will be charged an additional $8, and the initial cost of the party is $20.

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For a function f(x) = e^x, we can find its Taylor series expansion Tn centered at x = 23 using the formula:

Tn(x) = Σ (f^(k)(23) * (x - 23)^k) / k!, for k = 0 to n

Since the derivative of e^x is always e^x, the k-th derivative evaluated at 23 is f^(k)(23) = e^23 for all k. Therefore, the Taylor series expansion becomes:

Tn(x) = Σ (e^23 * (x - 23)^k) / k!, for k = 0 to n

This is the Tn centered at x = 23 for all n for the function f(x) = e^x, with symbolic notation and fractions as requested.

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The evaluation of the triple integral ∫∫∫E 4[tex]x^{2}[/tex] + 3dV is  (38/15)ππ

To evaluate the triple integral ∫∫∫E 4x^2 + 3dV in spherical coordinates, we need to express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.

The volume element dV in spherical coordinates is given by:
dV =  sin φ dρ dθ dφ
where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.
The region E in which we are integrating can be defined in spherical coordinates as follows:
0 ≤ ρ ≤ 2
0 ≤ θ ≤ 2π
0 ≤ φ ≤ π/2
Substituting these expressions into the volume element, we have:
dV =  sin φ dρ dθ dφ
= (sin φ) dρ dθ dφ
Now, we need to express the integrand 4[tex]x^2[/tex] + 3 in terms of the spherical coordinates.

The variable x can be expressed in terms of the spherical coordinates as:
x = ρ sin φ cos θ
Therefore, 4[tex]x^2[/tex] + 3 can be expressed as:
4[tex]x^2[/tex] + 3 = 4 [tex]sin^2[/tex] φ [tex]cos^2[/tex] θ + 3
Substituting this expression into the triple integral, we have:
∫∫∫E 4[tex]x^2[/tex] + 3dV
Now, we can evaluate the integral by performing the integration in the order φ, θ, ρ.
= (8/15)π + 2π
= (38/15)ππ

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Step-by-step explanation:

If u want to find the volume

V= width × length × height

V= 8.5 cm × 12 cm × 29 cm

V= 2958 cm3

If a person places $81200 in an investment account earning an annual rate of 3. 6%, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.

To solve this problem using the formula V = Pent, we need to plug in the given values.

P = $81200 (the principal initially invested)
r = 0.036 (the annual interest rate, expressed as a decimal)
t = 13 years

Using the formula V = Pent, we get:

V = $81200e^(0.036*13)

Using a calculator, we can evaluate e^(0.036*13) to be approximately 1.5498.

So V = $81200*1.5498 = $125689.60

Therefore, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.

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After considering all the given data provided by the question we conclude that the number 18 present in the given equation  is  constant .

The equation for the sunflower's height is h = 18 + 2.5w.
Here, the number 18 shows the height of the sunflower during the time it was planted, so it is the constant term present in the equation and hence it does not relie on the duration of weeks that have passed.
The coefficient of w is 2.5, which represents the rate at which the sunflower grows in height per week.
Therefore, after one week, the sunflower would be 20.5 inches tall (18 + 2.5 x 1), after two weeks it would be 23 inches tall (18 + 2.5 x 2), after four weeks it would be 28 inches tall (18 + 2.5 x 4), and after six weeks it would be 33 inches tall (18 + 2.5 x 6).

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Carla's right rectangular prism could have either a 3x4 or a 2x6 rectangle as the bottom layer, with a height of 2 units, to achieve the given volume of 24 cubic units.

Carla built a right rectangular prism using unit cubes, with a volume of 24 cubic units and a height of 2 units. To determine the possible figure for the bottom layer of the prism, we need to understand the relationship between the volume, height, and the base area.

The volume of a rectangular prism can be calculated using the formula: Volume = Base Area × Height. In Carla's case, the volume is 24 cubic units, and the height is 2 units. By rearranging the formula, we can find the base area: Base Area = Volume ÷ Height. Substituting the given values, Base Area = 24 ÷ 2, which equals 12 square units.

Now, we need to find a possible figure for the bottom layer with an area of 12 square units. Since the bottom layer is made of unit cubes, it must have whole-number dimensions. There are two possible rectangular figures that meet this requirement: 1) a 3x4 rectangle, and 2) a 2x6 rectangle. Both of these figures have an area of 12 square units (3x4 = 12 and 2x6 = 12) and can be formed using unit cubes.

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Answer:  640

Step-by-step explanation:

The claim of cooking duck legs at given temperature with mean , standard deviation represents reject the null hypothesis, accept the alternative hypothesis.

Confidence level = 90%

Sample mean maximum temperature x = 182 degrees

Hypothesized population mean μ =175 degrees

Sample standard deviation s = 5 degrees)

Sample size n =12

To test the claim that employee is capable of cooking the duck legs within the required temperature range.

Set up the following hypotheses,

Null hypothesis,

The mean maximum temperature of the duck legs is equal to or greater than 175 degrees (μ ≥ 175).

Alternative hypothesis,

The mean maximum temperature of the duck legs is less than 175 degrees (μ < 175).

Testing whether the mean is less than a specific value (175 degrees), this is a one-tailed test.

To reject or fail to reject the null hypothesis,

Use a one-sample t-test with a significance level of 0.1 .

T-test statistic is ,

t = (x - μ) / (s / √n)

Plugging in the values, we get,

t = (182 - 175) / (5 / √(12))

 = 4.85

The degrees of freedom for this test is n-1 = 11.

Using a t-distribution table ( attached table) ,

Critical value for a one-tailed test with 11 degrees of freedom and a significance level of 0.1.

The critical value is 1.363.

Since the calculated t-value 4.85 is greater than the critical value (1.363).

Reject the null hypothesis at the 90% confidence level.

⇒Sufficient evidence to conclude that the mean maximum temperature of the duck legs cooked by your cook is less than 175 degrees.

Employee is not capable of cooking the duck legs within the required temperature range.

Therefore, for the given situation of confidence level of 90% reject the null hypothesis, accept the alternative hypothesis.

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The estimate increase for $120 by 160% is 192. The calculated increase for $120 by 160% is 192.

Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin phrase "per centum", which means "per hundred". Percentages are often used to describe a part of a whole.  Percentages are used in many areas of life, such as finance, business, and statistics. They are used to calculate interest rates, taxes, discounts, and many other important figures.

Here,

Estimate: To estimate 160% of 120, we can first find 10% of 120, which is 12. Then, we can find 100% of 120 by multiplying 12 by 10, which is 120. Finally, we can add 60% of 120, which is 72 (since 60% is 6 times 10%), to get an estimate of 192.

Calculate: To calculate 160% of 120, we can first convert the percentage to a decimal by dividing it by 100, which gives us 1.6. Then, we can multiply 120 by 1.6 to get:

120 x 1.6 = 192

So the total increase is 192.

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Thus, the percentage raise received on the family's $88,000 yearly income is 9.4%.

The difference in between final value and the starting value, stated as a percentage, is known as a percentage increase.

The base amount still determines whether a percentage rise or drop by a given percentage occurs. The absolute value change also changes if the basic amount does.

Hence, although the percentage rise or reduction is the same in this instance, the absolute increase is different.

Given data:

From the table, compound interest for the yearly inflation rate of 3% is 1.09417024.

Thus,

amount after compounding:

A = $88,000  * 1.09417024.

A = 96286.98112

A = $96286.98

percentage raise = (96286.98 - 88,000 )/ 88,000

percentage raise = 0.094 * 100

percentage raise = 9.4%

Thus, the percentage raise received on the family's $88,000 yearly income is 9.4%.

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To make 132 cookies 3.14 pounds of butter would be used.

It is given that a bakery make 7 dozen cookies using 2 lbs of butter.

We know that 1 lb=1 pound

We know that 1 dozen = 12

7 dozen =7 × 12

= 84 cookies

We have to find how many pounds of butter would be used to make 132 cookies.

Let x be the number of pounds butter would be used to make 132 cookies

84/2 = 132/x

Apply cross multiplication

84x = 264

Divide both side by 84

x = 264/84

Hence, to make 132 cookies 3.14 pounds of butter would be used .

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The triangle above has the following measures. The length of sider is 13.3 inches.

q = 8 inches

m ∠Q = 37°

sin (Q) = q/r

r = q / sin(Q)

= 8 / sin (37°)

= 13.3 inches

In Math, a triangle is a three-sided polygon that comprises of three edges and three vertices. The main property of a triangle is that the amount of the inward points of a triangle is equivalent to 180 degrees. This property is called point total property of triangle.

There are three points in a triangle. These points are framed by different sides of the triangle, which meets at a typical point, known as the vertex. The amount of every one of the three inside points is equivalent to 180 degrees.

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The cost of the stock, including the broker's fee, is $50,454.30.

The cost of the stock can be found by multiplying the number of shares purchased by the price per share. In this case, the investor purchased 500 shares of Exxon-mobil stock at $98.93 per share, so the cost of the stock can be calculated as follows:

Cost of stock = Number of shares × Price per share

Cost of stock = 500 × $98.93

Cost of stock = $49,465

However, the broker charges 2% of the cost of the stock, which is an additional fee that needs to be added to the total cost. To find the broker's fee, we can simply multiply the cost of the stock by 2%:

Broker's fee = 2% × Cost of stock

Broker's fee = 2% × $49,465

Broker's fee = $989.30

Therefore, the total cost of the stock, including the broker's fee, is:

Total cost of stock = Cost of stock + Broker's fee

Total cost of stock = $49,465 + $989.30

Total cost of stock = $50,454.30

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The art room at Johnson Elementary School has a storage room with the are of 165 square feet. The length of one wall is 15 feet. The width of the storage room 11 feet. The perimeter of the room is 52 feet.

Find the width of the storage room, we need to use the formula for area:
Area = Length x Width
We know that the area is 165 square feet and the length is 15 feet, so we can plug those values in and solve for the width:
165 = 15 x Width
Width = 11
So the width of the storage room is 11 feet.
Find the perimeter of the room, we need to add up the lengths of all four walls. We know that one wall is 15 feet, and since the opposite wall must also be 15 feet to maintain the same area, we can add up the remaining two walls:
Perimeter = 2 x (15 + Width)
Perimeter = 2 x (15 + 11)
Perimeter = 2 x 26
Perimeter = 52
So the perimeter of the storage room is 52 feet.

The width of the storage room 11 feet. The perimeter of the room is 52 feet.

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Answer:

y=x+8

Step-by-step explanation:

since you are starting with the linear function y=x+7

a translation one unit to the left would be y=x+7(+1)

which gives us the answer y=x+8

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. If the circumference of the circular table is 816.4 centimeters, then we can use this formula to find the radius of the table. Solving for r, we get r = C / (2π) = 816.4 / (2π) ≈ 129.9 centimeters (rounded to one decimal place).

Answer:

[tex] \sqrt{20n} = \sqrt{4} \sqrt{5n} = 2 \sqrt{5n} [/tex]

C is the correct answer.

Using the Pythagorean theorem, the value of x, rounded to the nearest tenth, is 11.5 units.

In the given right triangle ABC with right angle B, you are given the lengths of sides BC (8 units) and AC (14 units). You are asked to find the length of side AB (x units). To do this, you can use the Pythagorean theorem, which states that the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC).

So, the equation for this triangle is:

AC² = AB² + BC²

Plug in the given values:

14² = x² + 8²

196 = x² + 64

Subtract 64 from both sides:

132 = x²

Now, find the square root of 132:

x ≈ 11.5

So, the value of x, rounded to the nearest tenth, is 11.5 units.

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