Solve the color puzzle and add the colors

The correct answer is C.

"Labor costs for a repair are less expensive as the number of hours increases."

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The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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The solutions to the equation tan²x - 1 = 0 are x = π/4 and x = 3π/4

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

tan²x - 1 = 0

Add 1 to both sides of the equation

So, we have

tan²x = 1

Take the square root of both sides

tan(x) = ±1

Take the arc tan of both sidesof tan(x) = ±1

So, we have

x = π/4 and x = 3π/4

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Answer:

x=-pie/12

sinxcosx=-1/4

multiply both sides by 2

sin2x = 2sinxcosx we know

now equation will be

sin2x = -1/2

2x=-pie/6

x=-pie/12

Answer:

[tex]\huge\boxed{\sf 44\ boys}[/tex]

Step-by-step explanation:

= Length × Width

Length = 32 m

Width = 11 m

Area of school room:

= Length × Width

= 32 × 11

= 352 m²

= 352 / 8

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

To find the perimeter of a triangle, we need to add the lengths of all three sides. Let's calculate the perimeter using the given side lengths:

Side 1: -2x + 3

Side 2: 9x

Side 3: -2(3x - 2)

Perimeter = Side 1 + Side 2 + Side 3

Substituting the given expressions for each side:

Perimeter = (-2x + 3) + (9x) + [-2(3x - 2)]

Simplifying the expression within the square brackets:

Perimeter = -2x + 3 + 9x - 2(3x - 2)

Using the distributive property:

Perimeter = -2x + 3 + 9x - 6x + 4

Combining like terms:

Perimeter = x + 7

Therefore, the perimeter of the triangle is x + 7.

Answer:

The perimeter is: x + 7

Step-by-step explanation:

A perimeter of a polygon is the sum of all of the sides. For the triangle's perimeter, we must find the sum of the sides.

(-2x+3) + (9x) + -2(3x-2)

-2x+3 + 9x - 6x + 4

9x - 8x + 7

x + 7

The vertex of the graph is a maximum at (-2, 4)

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

The graph

The graph is a quadratic function

From the graph, we can see that the graph has a maximum value

This maximum value represents the vertex of the graph

And it is located at (-2, 4)

So, we have

Maximum = (-2, 4)

Hence, the maximum value of the function is (-2, 4)

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The equation that shows the Pythagorean identity is true for θ = 270° and is in the form sin²θ + cos²θ = 1 is option  B. 0² + (-1)² = 1

The Pythagorean identity is a fundamental trigonometric identity that relates the sine and cosine functions. It states that for any angle θ, the sum of the squares of the sine and cosine of that angle is equal to 1: sin²θ + cos²θ = 1.

We are given θ = 270° and we need to select the equation that satisfies the Pythagorean identity in the given form.

Let's evaluate each option:

A. 0² + 1² = 1

In this case, sin²θ = 0² = 0 and cos²θ = 1² = 1. Adding them together, we get 0 + 1 = 1, which satisfies the Pythagorean identity.

B. 0² + (−1)² = 1

Here, sin²θ = 0² = 0 and cos²θ = (−1)² = 1. Adding them, we have 0 + 1 = 1, which satisfies the Pythagorean identity.

C. (−1)² + 0² - 1

In this equation, sin²θ = (−1)² = 1 and co

s²θ = 0² = 0. However, the equation does not satisfy the Pythagorean identity because 1 + 0 - 1 ≠ 1.

D. 1² + 0² = 1

For this option, sin²θ = 1² = 1 and cos²θ = 0² = 0. Adding them together, we get 1 + 0 = 1, which satisfies the Pythagorean identity.

Based on our evaluation, options A and B both satisfy the Pythagorean identity for θ = 270°. Therefore, either A or B can be selected as the correct equation.The correct answer is  b.

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The Question was Incomplete, Find the full content below :

Which equation shows that the Pythagorean identity is true for θ = 270°?

Select the equation that is in the form sin²θ+ cos²θ = 1.

A. 0² + 1² = 1

B. 0² + (−1)² = 1

C. (-1)² + 0² - 1

D. 1² + 0² = 1

Answer:

x=6-x2-y

Step-by-step explanation:

Swap sides so that all variable terms are on the left hand side.

add x2 to both side

Subtract 6 from both sides.

Divide both sides by −1.

Dividing by −1 undoes the multiplication by −1.

Divide y+x2 −6 by −1.

Answer:

Step-by-step explanation:

You want integers q and r such that 26 = 50q +r, and 0 ≤ r < 50.

Solving for q, we have ...

  (26 -r)/50 = q

For r in the range 0–49, possible values of q are in the range ...

   (26 -0)/50 ≥ q > (26 -49)/50

   0.52 ≥ q > -0.46

The only integer in that range is ...

  q = 0

Then the value of r is ...

  26 = 50·0 +r

  r = 26

<95141404393>

To find an equation for the temperature, D, in terms of t, we can use the properties of a sinusoidal function to model the temperature variation over the day.

Given:

High temperature: 80 degrees

Low temperature occurs at 5 AM (t = 5)

t is the number of hours since midnight

Let's assume a sinusoidal function of the form:

D = A * sin(B * t + C) + Dc

where:

A represents the amplitude (half the difference between the high and low temperatures)

B represents the frequency (how many cycles occur over a 24-hour period)

C represents the phase shift (how much the function is shifted horizontally)

Dc represents the vertical shift (the average temperature throughout the day)

We can determine the values of A, B, C, and Dc based on the given information.

Amplitude (A):

The amplitude is half the difference between the high and low temperatures:

A = (80 - 50) / 2

= 30 / 2

= 15 degrees

Frequency (B):

Since we want the temperature to complete one cycle over a 24-hour period, the frequency can be calculated as:

B = 2π / 24

Phase Shift (C):

Since the low temperature occurs at 5 AM (t = 5), the function should be shifted horizontally by 5 hours. To convert this to radians, we multiply by (2π / 24):

C = 5 * (2π / 24)

Vertical Shift (Dc):

The average temperature throughout the day is the midpoint between the high and low temperatures:

Dc = (80 + 50) / 2

= 130 / 2

= 65 degrees

Now we can put all the values together to obtain the equation for the temperature, D, in terms of t:

D = 15 * sin((2π / 24) * t + (5 * 2π / 24)) + 65

Simplifying further:

D = 15 * sin((π / 12) * t + (π / 12)) + 65

Therefore, the equation for the temperature, D, in terms of t is:

D = 15 * sin((π / 12) * t + (π / 12)) + 65.

Answer:

54 m²

Step-by-step explanation:

i.

xy = 24

y = 24/x

ii.

A = (x + 2)(y + 3)

A = xy + 3x + 2y + 6

A = x(24/x) + 3x + 2(24/x) + 6

A = 24 + 3x + 48/x + 6

A = 3x + 48/x + 30

iii.

A = 3x + 48x^-1 + 30

dA/dx = 3 + (-1)(48)x^-2

dA/dx = 3 - 48/x²

3 - 48/x² = 0

48/x² = 3

x² = 16

x = 4 or x = -4

We discard the negative answer.

x = 4

y = 24/x

y = 24/4

y = 6

A = xy

A = (x + 2)(y + 3)

A = (4 + 2)(6 + 3)

A = 6(9)

A = 54

The balance in the Inventory account at January 31 was $158,000.The correct answer is option C.

To determine the balance in the Inventory account at January 31, we need to consider the purchases and sales made during the period.

At the end of last year, the company had merchandise costing $140,000 in inventory. In January of the current year, they purchased merchandise costing $102,000. This means the total cost of available inventory at the beginning of January was $140,000 + $102,000 = $242,000.

During January, the company sold merchandise that it had purchased at a total cost of $84,000. Since Games-2-Use uses a perpetual inventory system, the cost of goods sold is immediately recorded, and the inventory balance is adjusted accordingly.

Therefore, to find the balance in the Inventory account at January 31, we subtract the cost of goods sold from the available inventory at the beginning of January: $242,000 - $84,000 = $158,000.

Hence, the correct answer is option c. $158,000. This represents the balance in the Inventory account at January 31, considering the purchases and sales made during the month.

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The probable question may be:

At the end of last year, Games-2-Use had merchandise costing $140,000 in inventory. During January of the current year, the company purchased merchandise costing $102,000, and sold merchandise that it had purchased at a total cost of $84,000. Games-2-Use uses a perpetual inventory system.

The balance in the Inventory account at January 31 was:

Select one:

a. $84,000.

b. $140,000.

c. $158,000.

d. $242,000

Answer:

5 is the tens, 6 is the hundred

Answer:

Step-by-step explanation:

10s - 9

100ths - 6

Answer:

  3902.2 ft

Step-by-step explanation:

You want the length of cable required to span the distance from the top of a mountain 3400 ft above the plain from a location 940 ft from the base of the mountain, which rises at an angle of 74°.

The edge of the base of the mountain will be at a horizontal distance from the point below the peak given by ...

  Tan = Opposite/Adjacent

  Adjacent = Opposite/Tan

  width to center = (3400 ft)/tan(74°) ≈ 974.93 . . . . feet

The cable is the hypotenuse of a right triangle with one leg 3400 ft and the other (974.93 +940) = 1941.93 ft. The length of that is ...

  c = √(3400² +1914.93²) ≈ 3902.2 . . . . feet

The shortest length of cable needed is about 3902.2 feet.

<95141404393>

Answer:

C) More than 1 solution

Step-by-step explanation:

[tex]3y-12x=18\\2y-8x=12\\\\3(y-4x)=18\\2(y-4x)=12\\\\y-4x=6\\y-4x=6\\\\6=6[/tex]

Therefore, since both sides will always be equal to each other, then there are infinitely many solutions (so C is the best choice)

The slope of line e is -8/7, which represents a proper fraction

The slope of line e, which is perpendicular to line d, can be determined using the concept that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's find the slope of line d using the given points (10, 8) and (2, 1). The slope (m) is calculated using the formula:

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

Plugging in the values, we have:

m = (1 - 8) / (2 - 10)

= (-7) / (-8)

= 7/8

Since line e is perpendicular to line d, its slope will be the negative reciprocal of 7/8. The negative reciprocal is obtained by flipping the fraction and changing its sign. Therefore, the slope of line e is -8/7.

Hence, the slope of line e is -8/7, which represents a proper fraction.

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Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.

Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:

Total economic cost:

Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144

Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131

Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135

Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).

Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.  

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The total amount due at maturity is $23,495.73.Given:Principal amount (P) = $24,000 Rate of interest (R) = 2.75% Time (n) = 4 years First partial payment (A) = $4,210 Time after first partial payment (t) = 4/12 years = 1/3 year Second partial payment (B) = $3,240 Time after second partial payment (t) = 6/12 years = 1/2 year.

We need to find the amount due at maturity.Amount due at maturity can be calculated by the formula given below;A = P [ i ( 1 + i )n ] / [ ( 1 + i )n – 1 ] Where,A = amount due at maturity P = principal amount R = rate of interest in decimal n = time in yearsi = rate of interest per period For yearly interest, i = R / 100.For monthly interest, i = R / (12 × 100)For quarterly interest, i = R / (4 × 100)For half-yearly interest, i = R / (2 × 100)

Now, we will find the value of i first, which can be calculated by dividing the yearly interest rate by 100. Here, the interest is compounded half-yearly.i = R / (2 × 100)i = 2.75% / (2 × 100)i = 0.01375

Let's substitute the values of P, R, n, i, A in the formula and calculate the amount due at maturity.P = $24,000R = 2.75%n = 4 yearsi = 0.01375A = $4,210t = 1/3 yearsA = P [ i ( 1 + i )n ] / [ ( 1 + i )n – 1 ]4,210 = 24,000 [ 0.01375 ( 1 + 0.01375 )16 ] / [ ( 1 + 0.01375 )16 – 1 ]On solving the above equation, we get;Amount of loan due after 4 months is $23,188.45.

Now, we will calculate the second amount due at maturity after the second partial payment.B = $3,240t = 1/2 year.Let's find the balance due at the end of 6 months using the following formula;B = C ( 1 + i )n

Where,B = balance due at the end of 6 monthsC = amount due at the end of 4 monthsi = 0.01375n = (6 - 4) / 12 yearsB = C ( 1 + i )nB = $23,188.45 ( 1 + 0.01375 )1/2

On solving the above equation, we get;Amount due at maturity after the second partial payment is $22,201.98

Now, we will calculate the amount due at maturity.Amount due at maturity = balance due after second payment + interest for remaining periodAmount due at maturity = $22,201.98 + interest for 3.5 years.Let's calculate the interest for 3.5 years;Interest = P × i × nInterest = $24,000 × 0.01375 × 3.5 Interest = $1,293.75 Amount due at maturity = $22,201.98 + $1,293.75Amount due at maturity = $23,495.73.

Therefore, the total amount due at maturity is $23,495.73.

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Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

Answer:

CD: 8.5

m<D: 20.6°

m<C: 69.4°

Step-by-step explanation:

CD:

The first thing it wants us to do is find the length of CD. Since the triangle shown is a right triangle, we can use Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex])  to solve for the missing length. It's important to remember that when using the Pythagorean theorem, c is the hypotenuse.

[tex]a^{2}+b^{2}=c^{2}\\3^{2}+8^{2}=c^{2}\\9 + 64 = c^{2}\\73 = c^{2}\\\sqrt{73} =c[/tex]

Since our answer is no an integer, we must turn it into a decimal.

[tex]\sqrt{73}[/tex] ≈ 8.544003745 ≈ 8.5

m<D:

Now, they want us to find the measure of <D. To do this, we will need to use trig functions (sine, cosine, tangent). To help us determine which trig function to use, we can remember the acronym SOH CAH TOA. This acronym tells us that sine is equal to opposite divided by hypotenuse, cosine is equal to adjacent divided by hypotenuse, and tangent is equal to opposite divided by adjacent. Since we do the hypotenuse and sides adjacent and opposite of <D, we can choose whichever trig function we want. For this problem, we will use tangent, so we can avoid using a rounded number, 8.5, as one of our sides.

Tan(D) = opposite / adjacent

Tan(D) = 3 / 8     [Take the tan inverse of both sides}

[tex]Tan^{-1}(Tan(D))=Tan^{-1}(3/8)[/tex]     [Simplify]

[tex]D=Tan^{-1}(3/8)[/tex]     [Solve]

D ≈ 20.55604522

D ≈ 20.6°

m<C:

Lastly, we must find the last unknown angle on the triangle. Since all angles on a triangle total 180°, if know that <C+<D+<E=180°. Let's solve this equation.

<C+<D+<E=180°

<C + 20.6 + 90 = 180     [Add]

<C + 110.6 = 180     [Subtract]

<C = 180 - 110.6     [Solve]

<C = 69.4°

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

The total amount of Japanese Yen exchanged for the 5 days of use is approximately 758,476.44 (¥).

To calculate the total Japanese Yen exchanged for the 5 days of use, we need to consider the average amount spent per day and convert it to Japanese Yen using the exchange rate provided.

The average amount spent per day is given as R 4,042.19.

To calculate the total amount spent for 5 days, we multiply this amount by 5, which gives us R 20,210.95.

To convert this amount to Japanese Yen, we need to use the exchange rate of 1 South African Rand (ZAR) to Japanese Yen (¥) provided in the table, which is 37.51715.

Multiplying the total amount spent in Rand (R 20,210.95) by the exchange rate (37.51715), we get:

20,210.95 (R) [tex]\times[/tex] 37.51715 (¥/R) = 758,476.44 (¥)

Therefore, the total amount of Japanese Yen exchanged for the 5 days of use is approximately 758,476.44 (¥).

Note: The given exchange rate and currency data are based on the specified date and are subject to change.

It is advisable to refer to the most recent exchange rates for accurate calculations.

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There are approximately 43.36 days on hand in inventory.

To calculate the number of days on hand in inventory, we need to divide the number of staplers in stock by the average number of staplers sold per day.

First, let's calculate the average number of staplers sold per day:

Average staplers sold per year = 1624

Number of days per year = 350

Average staplers sold per day = Average staplers sold per year / Number of days per year

= 1624 / 350

≈ 4.64 (rounded to two decimal places)

Now, we can determine the number of days on hand in inventory:

Number of staplers in stock = 201

Number of days on hand in inventory = Number of staplers in stock / Average staplers sold per day

= 201 / 4.64

≈ 43.36 (rounded to two decimal places)

Therefore, there are approximately 43.36 days on hand in inventory.

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Answer: the answer is 1:16

The coordinate of points on the graph indicates that the n-shaped graph which is below the x-axis, has no zeros, the correct option is therefore;

A. The graph has no zeros.

The zeros of a graph are the points at which the graph intersects the x-axis.

The graph in the question is n shaped and the peak point (the point with the highest y-value), which is a max point on the graph is located 2 units below the x-axis, therefore, the graph does not intersect the x-axis, and the graph therefore has no zeros. The correct option is therefore option A; The graph has no zeros

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The correct total weight of the bags of granola is 8 1/4 pounds.

One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.

In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.

To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:

2 + 2 + 3 = 7 (sum of whole numbers)

1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)

Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.

By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.

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The probable question may be:

Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.

what is one thing that you could do to Roberto's Reasoning

Answer:

Step-by-step explanation: ong

The equation 4x² - 2y² = 9 is the equation of a hyperbola x²/(3/2)² - y²/(3/√2)² = 1 with vertices are (0, ±3/2) and co vertices (±3/√2, 0)

The equation of a hyperbola with vertices (0, ±a) and co vertices (±b, 0)and transverse axis x - axis is given by

x²/a² - y²/b² = 1 where

Given the equation 4x² - 2y² = 9,we want to determine which type of equation it is. We proceed as follows.

Since 4x² - 2y² = 9,

Dividing through by 9, we have that

4x²/9 - 2y²/9 = 9/9

4x²/9 - 2y²/9 = 9/9

x²/9/4 - y²/9/2 = 1

Comparing this equation with the equation of a hyperbola above we have that

So,

So, x²/(3/2)² - y²/(3/√2)² = 1

So, its vertices are (0, ±3/2) and co vertices (±3/√2, 0)

So, the equation is the equation of a hyperbola

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Answer:

180 houses

Step-by-step explanation:

For every 10 flats, there are 30 bungalows. So, if there are 30 bungalows then there will be 100 flats in the village.

For every 5 flats there are in the village, there are 9 houses. There are 100 flats in the village. So, we can divide 100 by 5.

[tex]\frac{100}{5}[/tex]=20

20(9)=180

Therefore, there are 180 houses in the village.

Good luck on your homework!