2) During a portage, the leader of a scout troop decided to save time by hiking around a
wooded area between the base camp and a lake. The troop reached the lake by walking for
30 minutes on a bearing of N60°E, then for 45 minutes on a bearing of N80°W. The leader
figured that they walked at an average speed of 3km/h. If they could have walked straight
through the forested area at 1km/h, did the troop save any time by going around? If so, how
much?

The diagram that represent the distance and the journeys is added as an attachment

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

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

Next, we create the diagram (see attachment)

The attached figure represents the required diagram

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Answer:

$4.25 for 64 fluid ounces = $0.06640625 per fluid ounce

297 miles on 11 gallons of gas = 27 miles per gallon

124 feet in 10 seconds = 12.4 feet per second

Step-by-step explanation:

The value of measure ∠2 is, 135°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the house,

⇒ m ∠1 = 45°

We know that;

An exterior angle of a triangle is the sum of two opposite angle of a triangle.

Hence, We can formulate;

⇒ m ∠2 = m ∠1 + 90°

⇒ m ∠2 = 45° + 90°

⇒ m ∠2 = 135°

Thus, We get;

⇒ m ∠2 = 135°

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Answer:

1. True

2. False

3. True

4. False

Step-by-step explanation:

Given function:

[tex]f(x)=4(x-2)^3+2[/tex]

The point-of-symmetry of a cubic graph is its point of inflection.

To find the x-value of the point of inflection of a cubic function, differentiate the function twice:

[tex]f'(x)=12(x-2)^2[/tex]

[tex]f''(x)=24(x-2)[/tex]

Set the second differentiated function to zero and solve for x:

[tex]\implies 24(x-2)=0[/tex]

[tex]\implies x-2=0[/tex]

[tex]\implies x=2[/tex]

Substitute the found value of x into the original function to find the y-value of the point of inflection:

[tex]\implies y=4(2-2)^3+2[/tex]

[tex]\implies y=4(0)^3+2[/tex]

[tex]\implies y=0+2[/tex]

[tex]\implies y=2[/tex]

Therefore, the point of symmetry of the cubic function is (2, 2).

The inverse of a cubic function its reflection in the line y = x.

As the point of symmetry is (2, 2), then its reflection in the line y = x is also (2, 2).

So the point of symmetry on f⁻¹(x) is (2, 2).

The given function has an unrestricted domain and range.

The domain of the inverse function is the range of the function.

The range of the inverse function is the domain of the function.

Therefore, as the domain and the range of the original function are unrestricted, so are the domain and range of the inverse function.

The inverse of a cubic function with an unrestricted domain is its reflection across the line y = x.

Therefore, the graphs of f⁻¹(x) and f(x) are reflections across the line y = x.

To find the inverse of the given function, swap x and y:

[tex]\implies x=4(y-2)^3+2[/tex]

Rearrange to make y the subject:

[tex]\implies x-2=4(y-2)^3[/tex]

[tex]\implies \dfrac{x-2}{4}=(y-2)^3[/tex]

[tex]\implies \sqrt[3]{\dfrac{x-2}{4}}=y-2[/tex]

[tex]\implies y=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]

As we have already established, the domain and range of the inverse function are unrestricted.  As each x-value has only one y-value associated with it, f⁻¹(x) is a function.

Answer:

an = - 7n+35

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is constant. To find this difference, we can subtract the first term from the second term and the second term from the third term, etc.

a2 - a1 = 21 - 28 = -7

a3 - a2 = 14 - 21 = -7

Since the difference between consecutive terms is the same, we can conclude that the difference is -7.

The nth term in an arithmetic sequence can be found using the formula: an = a1 + (n-1)d, where d is the common difference.

For this sequence, the nth term can be found as: an = 28 + (n-1)(-7) = 28 - 7(n-1) = 28 - 7n + 7 = 35 - 7n.

So, the formula for the nth term in this arithmetic sequence is an = - 7n+35

Using the formula of area of rectangle and square, the cost of painting is Rs. 1335

The area of a rectangle is equal to the product of its length and width. Mathematically, it can be represented as:

Area = Length × Width

In this problem, we need to substitute the values and calculate the area of the rectangular wall and then subtract the area of the window from it.

Area of rectangle = 15 * 7 = 105m²

The area of the window is calculate by using the formula of area of square.

Area of square = 4 * 4 = 16m²

Area of wall painted = 105 - 16 = 89m²

The cost of painting one square meter = Rs. 15

1m² = Rs. 15

89m² = x

x = 15 * 89

x = Rs. 1335

The cost is Rs. 1335

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Step-by-step explanation:

this is the process and figure is cointerior

The solution to the monomial in standard form is  0.04b^19.

The term "polynomials in standard form" can also refer to a polynomial written in the decreasing order of the degree of the variable.

The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.

Given that:

= (-0.2b^6)^3*5b

Rewrite using the commutative property of multiplication

= 5(-0.2b^6)^3b

Apply the product rule to −0.2b^6

= 5(-0.2^3)(b^6)^3b

= 5(-0.008b^18)b

= 5(-0.008^19)

= 0.04b^19

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$2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned amount for the first year was $475.

The financial planner invested $5,750 of the couple's money. Let x be the amount of money invested in the savings account paying 2% annual simple interest and y be the amount of money invested in the riskier mini-mall development plan paying 12% annual simple interest. Since the combined interest earned for the first year was $475, we can write the equation 2x + 12y = 475. Since the total amount of money invested was $5,750, we can add the equation x + y = 5,750 to our system of equations. Solving the system of equations yields x = 2,250 and y = 3,500. Thus, $2,250 was invested at 2% and the remaining $3,500 was invested at 12%. The combined interest earned for the first year was $475.

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Answer:

Can 3. $2.40, Red Kidney Beans, 500g, Can. This can costs $0.0048 per gram.

Answer:

Aled's mother paid £220.

Aled paid £44.

Gareth paid £396.

Step-by-step explanation:

1-(1/3)= 2/3 [fraction of amt. Aled and Gareth paid]

£660×(2/3)= £440 [amt. Aled and Gareth paid]

total units= 1+9

= 10

10 units= £440

1 unit= £440÷10

= £44

9 units= £44×9

= £396

£660×(1/3)= £220

Answer: If 20% of the 60 students in the Geneva Middle School marching band play the trombone, then 60 * 20% = 12 students play the trombone. To shade the grid to show the percent, you can shade 20 out of 100 squares on the grid, or 1/5 of the total number of squares.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Simply substitute for y in the equation if y = 12.

2 + y + 1  ->  2 + (12) + 1 = 15

Answer:

see below

Step-by-step explanation:

(x+ 2 4/5) * 2 = perimeter

so perimeter = 2x + 5.6

The ratio of used books to all books is 7 : 13 and  the ratio of new books to used books is 6 : 7

If there are 13 books on a shelf. 6 of these books are new.

(a) The ratio of used books to all books

Number of all books = 13

Number of used books = total no. of books - no. of new books

                                       =  13 - 6

                                       = 7

So, ratio of used books to all books

= no. of all books : no. of total books

= 7 : 13

Thus, the ratio of used books to all books = 7 : 13

(b) The ratio of new books to used books

Number of new books = 6

Number of used books = 7

So, the ratio of new books to used books

= no. of new books : no. of used books

= 6 : 7

Thus, the ratio of new books to used books = 6 : 7

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Answer: In a parallelogram, opposite sides are equal in length and parallel, so if we subtract the vectors AB and BC from each other, we will get the vector for CD.

Given A = (4,0), B = (1.5,0), and C = (-3,-5), we can calculate the vectors AB and BC as follows:

AB = B - A = (1.5, 0) - (4, 0) = (-2.5, 0)

BC = C - B = (-3, -5) - (1.5, 0) = (-4.5, -5)

Next, we subtract these vectors to find the vector for CD:

CD = BC - AB = (-4.5, -5) - (-2.5, 0) = (-2, -5)

Finally, we add the vector CD to vertex C to find vertex D:

D = C + CD = (-3, -5) + (-2, -5) = (-5, -10)

So, the ordered pair for vertex D is (-5, -10).

Step-by-step explanation:

Answer:

  (d)  C'(-1, 14)

Step-by-step explanation:

You want the coordinates of C' after the point C(-1, -6) is reflected across the line y = 4.

Reflection across the horizontal line y=4 will not change the x-coordinate of the point, so C' has an x-coordinate of -1.

The point (-1, 4) on the line of reflection will be the midpoint of C and C', so we have ...

  (C +C')/2 = (-1, 4)

  C +C' = 2(-1, 4) = (-2, 8) . . . .  .multiply by 2

  C' = (-2, 8) -C

  C' = (-2, 8) -(-1, -6) = (-1, 8+6)

  C' = (-1, 14)

__

Additional comment

Effectively, the reflection across the line y=4 is the transformation ...

 (x, y) ⇒ (x, 8 -y)

Answer:

C'(-1, -6).

Step-by-step explanation:

the reflection across y = 4 for point C(-1, -6).

When reflecting a point across a horizontal line like y = 4, the y-coordinate remains the same, and the x-coordinate is inverted with respect to the line of reflection.

For point C(-1, -6), the y-coordinate remains -6, and the x-coordinate is inverted across y = 4:

New x-coordinate = -1

So, the reflected image of point C across y = 4 is C'(-1, -6).

None of the provided options match this reflection, so it seems there might be an error in the given answer choices. The correct reflection of point C(-1, -6) across y = 4 is C'(-1, -6).

The measure of the side of the partial rectangle is 7 cm

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangular figure be represented as P

Now , the equation will be

The length of the rectangle 1 = 12 cm

The width of the rectangle 1 = 6 cm

The length of the rectangle 2 = 15 cm

The width of the rectangle 2 = 5 cm

Now , let the unknown length be represented as A

And , A = length of the rectangle 1 - width of the rectangle 2

Substituting the values in the equation , we get

The unknown length A = 12 cm - 5 cm

On simplifying the equation , we get

The unknown length A = 7 cm

Hence , the unknown length of the rectangle is A = 7 cm

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=22\\ r=4 \end{cases}\implies 22=\cfrac{\theta \pi (4)}{180}\implies 22=\cfrac{\theta \pi}{45} \\\\\\ (22)(45)=\theta \pi \implies \cfrac{(22)(45)}{\pi }=\theta \implies 315.13\approx \theta[/tex]

Based on the information in the graph, the length of DF is 3.87 cm, the length of XF is 4.89 cm. The point 2cm from E is 5cm from X and the angle of D is 60°.

To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:

To find the length of the side DF we must apply the Pythagorean theorem substituting the values that we know as shown below:

The point 2cm from E would lie on the line EX at 2cm from E and 5cm from X.

To calculate the angle of D we can use a compass, in this case, we know that the angle of X is 90°, so the other 90° that make up the triangle are distributed between point F and D. However, we know that F has a angle less than D so we can infer that F has an angle of 30° and D has an angle of 60° which we can check with a compass.

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A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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By the 1/3 ratio, the value of x for the given figure is 33 units.

A ratio is an ordered pair of integers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls). A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Here,

4/12=3/x1=5/x2

1/3=3/x1

x1=9 units

1/3=5/x2

x2=15 units

12+15+9=33 units

The value of x for the given figure is 33 units by the ratio of 1/3.

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1800 + 150x = y

150x is the money she makes a month

Y is the total

enjoy :D

Solving the provided question, we can say that by Pythagoras theorem VT² = 18² + 24² = 900  => VT =  [tex]\sqrt{1900} = 30[/tex]

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Pythagoras theorem

VT² = 18² + 24² = 900  

VT =  [tex]\sqrt{1900} = 30[/tex]

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Answer:

Step-by-step explanation:

If Boden's account has a principal of $600 and a simple interest rate of 3.9%, then the interest he earns each year can be calculated as follows:

Simple Interest = Principal * Rate * Time = $600 * 3.9% * 1 = $23.40

So, after one year, the amount of money in the account will be $600 + $23.40 = $623.40

This process can be repeated for multiple years to find the amount of money in the account for a specific time period.

The slope of the points in this table is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (-1 + 3)/(-1 + 2)

Slope, m = 2/1

Slope, m = 2.

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Answer:

£481.02

Step-by-step explanation:

To calculate, you can multiply the original cost by the increase percentage (expressed as a decimal) and add that to the original cost:

£466.98 * 1.032 = £480.9936

£480.9936 + £466.98 = £481.02

Rounding to 2 decimal places, the answer is £481.02.

Nice work on getting part (a) correct.

The 261% falls in the "250-300%" range, so they pay 8.5% of their yearly income toward health insurance.

8.5% of $65,500 = 0.085*65500 = 5567.50

That represents the yearly contribution. Divide that by 12 to find the monthly contribution.

5567.50/12 = 463.95833 = 463.96 approximately

Then round to the nearest dollar to get 464