Which number completes the Pythagorean Triple of 14, 48, x?

The number of rooms booked to produce maximum revenue is required.

The number of rooms booked to produce the maximum revenue is 250.

The revenue function is

[tex]R(x)=200x-0.4x^2[/tex]

Differentiating with respect to x we get

[tex]R'(x)=200-0.8x[/tex]

Equating with zero

[tex]0=200-0.8x\\\Rightarrow x=\dfrac{-200}{-0.8}\\\Rightarrow x=250[/tex]

Double derivative of the function is

[tex]R''(x)=-0.8x[/tex]

Substituting the value of [tex]x=250[/tex]

[tex]R''(250)=-0.8\times 250=-200[/tex]

Since, it is negative the maximum value of x will be 250.

The number of rooms booked to produce the maximum revenue is 250.

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The number of rooms that produces the maximum revenue for Fred's Estates LLC is 250 rooms, calculated using the formula -b/2a, where a and b are the coefficients of the quadratic revenue function.

To calculate the maximum revenue for Fred's Estates LLC, we need to find the value of x that maximizes the function [tex]R(x)=200*-0.4x2.[/tex]

The maximum value of a quadratic function can be found using the formula -b/2a, where a and b are the coefficients of x² and x in the function. Here, a=-0.4 and b=200.

Using the formula, [tex]x=-b/2a = -200/(2*(-0.4)) = 250[/tex] rooms. Therefore, booking 250 rooms results in the maximum revenue for Fred's Estates LLC.

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Final answer:

After converting their completion fractions to decimal form, Jose finished more of the race than Jenna after 30 minutes, with Jose at 2/3 (approximately 0.6667) and Jenna at 7/12 (approximately 0.5833).

Explanation:

Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race, and Jenna had finished 7/12 of the race. To determine who had finished more of the race, we can compare these two fractions by finding a common denominator or converting them to decimal form.

First, let's convert them to decimal form:

2/3 is approximately 0.6667

7/12 is approximately 0.5833

Comparing the decimal values, we can see that Jose's completion (0.6667) is greater than Jenna's (0.5833). Therefore, Jose had finished more of the race after 30 minutes.

Answer:

The distance from he ball to the goal is 11.85 feet (Approx) .

Step-by-step explanation:

As given

The angle of elevation from a soccer ball on the ground to the top of the goal is 34° .

If the goal is 8 feet tall.

Now by using the trigonometric identity .

[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]

As shown in the diagram given below

[tex]\theta = 34^{\circ}[/tex]

Perpendicular = AB = 8 feet

Base = BC

Put all the values in the identity .

[tex]tan\ 34^{\circ} = \frac{AB}{BC}[/tex]

[tex]tan\ 34^{\circ} = \frac{8}{BC}[/tex]

[tex]tan\ 34^{\circ} = 0.675\ (Approx)[/tex]

[tex]BC = \frac{8}{0.675}[/tex]

BC = 11.85 feet (Approx)

Therefore the distance from he ball to the goal is 11.85 feet (Approx) .

To calculate the distance from the soccer ball to the goal with an angle of elevation of 34 degrees and a goal height of 8 feet, use the tangent trigonometric ratio. The distance is found to be approximately 11.86 feet.

Given the angle of elevation is 34 degrees and the goal's height is 8 feet, we're looking to calculate the adjacent side (distance from the ball to the goal) in a right-angled triangle where the opposite side (goal's height) and the angle are known.

To calculate the distance (let's call it d), we use the tangent function:

So, d = 8/tan(34 degrees).

Calculating this, we find:

Therefore, the distance from the soccer ball to the goal is approximately 11.86 feet.

Answer:

Steplo-by-step explanation:loan is 1200.

The interest rate is 6.50

Pp 46.90

Cumulative payment $53.4

Total payments$1,282.93

Final answer:

Lane will pay a total of $156 in simple interest on the loan of $1200 over 2 years, calculated using the simple interest formula: I = PRT.

Explanation:

Lane borrowed $1200 at a simple interest rate of 6.5% for a period of 2 years. To calculate the total amount of interest that will be paid on the loan, we can use the simple interest formula, which is:

I = PRT

where I is the interest, P is the principal amount borrowed, R is the interest rate per year (expressed as a decimal), and T is the time in years the money is borrowed for.

First, we convert R to a decimal by dividing it by 100:

R = 6.5% / 100 = 0.065

Next, we substitute the values into the formula:

I = $1200 × 0.065 × 2

I = $1200 × 0.13

I = $156

Therefore, the total amount of interest that Lane will be paying on the loan over the next 2 years is $156.

Answer:

2^(8/9) in²

Step-by-step explanation:

Make use of the identity ...

... (a^b)^c = a^(bc)

Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity

... (ab)^c = a^c·b^c

In this case a = 2^(4/9), b = in, c = 2.

So, the working of your problem is ...

... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2

... = 2^(4/9·2) in^2 = 2^(8/9) in^2

Answer:

A = 4200 ft^2

Step-by-step explanation:

We know the formula for area is

A = l*w

We need to have the same units

convert yd to ft

1 yd = 3ft

Multiply each by 70

70 yds = 210 ft

A = 210 *20

A = 4200 ft^2

The area of the pavement section is 4200 square feet, computed by converting the length to the same unit as the width and multiplying width by length.

The subject of this question is the calculation of the area of a rectangle. The rectangle in question is a section of pavement with a width of 20 ft and a length of 70 yd. Before calculating, it's important to have the measurements in the same units. Converting 70 yards to feet (since 1 yard equals 3 feet) we get 210 feet. The formula to calculate the area of a rectangle is Area = Width x Length. Substituting the given values into the formula, we get: Area = 20 ft x 210 ft which equals 4200 square feet. Therefore, the pavement section's area is 4200 square feet.

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9.9 years

A = P(1 + rt) . . . . account balance after time t at rate r starting with principal P

... 3000 = 2500(1 + 0.0202t) . . . . filling in the given numbers

... 1.2 = 1 + 0.0202t . . . . divide by 2500

... 0.2 = 0.0202t . . . . . . subtract 1

... 0.2/0.0202 = t ≈ 9.901

It will take about 9.9 years for the account balance to reach $3000.

Answer:

56 = (0.85)w

Step-by-step explanation:

"is" translates to "=".

"of" translates to "×".

We can let "what number" translate to "w".

Then ...

56 is 85% of what number . . . . translates to ...

56 = 0.85×w

_____

Of course, you know that 85% = 85/100 = 0.85.

1/3, 1/4, 1/5

40% = 40/100 = 2/5

Any fraction with a numerator of 2 and a denominator larger than 5 will be less than 40%, for example.

So, we can choose 2/6 = 1/3, 2/8 = 1/4, and 2/10 = 1/5 as some such values.

_____

We could also choose something like 39.99% = 3999/10000, or 1% = 1/100.

Answer:

The cost of the wristband for 8 rides is $35.

Step-by-step explanation:

The expression for the cost, C, for r rides is

C = 2.5r + 15

Since she wants to go on 8 rides, r is 8.

Substitute r with 8 in the cost equation and evaluate it.

C = 2.5r + 15

C = 2.5 * 8 + 15

C = 20 + 15

C = 35

The cost of the wristband for 8 rides is $35.

Answer:

‪0.155922‬

Step-by-step explanation:

Answer: 0.1562 kilograms

Step-by-step explanation: To convert 5.5 ounces into kilograms, we first convert 5.5 ounces into grams using the conversion factor 1 oz = 28.4 g.

Since we are going from a larger unit "ounces" to a smaller unit "grams" we multiply 5.5 by the conversion factor which is 28.4 to get 156.2.

This means that 5.5 ounces is equal to 156.2 grams.

Next, we convert 156.2 grams into kilograms using the conversion factor

1 kilogram = 1,000 grams. Since we are going from a smaller unit "grams" to a

larger unit "kilograms" we divide 156.2 by the conversion factor which is 1,000

and we get 0.1562 kilograms.

Therefore, 5.5 ounces is equal to approximately 0.1562 kilograms.

Using the smallest number she has, 9 daisies..

18/9 = 2

45/9 = 5

She can make 9 bouquets with 2 roses, 1 daisy and 5 tulips in each.

That means each bouquet would have 8 total flowers.

The correct option is the last:

[tex] a_n = -2a_{n-1}+1 [/tex]

In fact, every term in the sequence is one more than twice the opposite of the previous one:

We start with 3. Twice its opposite is -6. Plus one, we get -5.

We start with -5. Twice its opposite is 10. Plus one, we get 11.

We start with 11. Twice its opposite is -22. Plus one, we get -21.

The recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

To find a recursive formula for the given sequence, we need to determine the relation between consecutive terms.

Let's denote the sequence as an, where:

[tex]a_1 = 3\\a_2 = -5\\a_3 = 11\\a_4 = -21\\[/tex]

First, let's calculate the differences between consecutive terms:

[tex]a_2 - a_1 = -5 - 3 = -8\\a_3 - a_2 = 11 - (-5) = 16\\a_4 - a_3 = -21 - 11 = -32[/tex]

We observe that each difference is a multiple of 8 and that each difference is twice the previous difference but with alternating signs.

The recursive formula can be defined as:

[tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Thus the recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Answer:

x=0

Step-by-step explanation:

-0.2(x-20)=4-x

The first step is to distribute the -.2

-.2 x -.2 * -20 = 4-x

-.2x +4 = 4-x

Add x to each side

x-.2x +4 = 4-x+x

.8x +4 = 4

Subtract 4 from each side

.8x +4-4 = 4-4

.8x=0

Divide by .8

.8x/.8 = 0/.8

x =0

Answer:

1: Simplify 15/20 to 3/4

y/4=3/4

Multiply both sides by 4

y=3/4×4

Simplify 3/4×4 to 12/4

y=12/4

Simplify 12/4 to 3

y=3

2: Multiply both sides by z-3

6=8/5(z-3)

Simplify 8/5(z-3) to 8(z-3)/5

8(z-3)/5

Multiply both sides by 5

6×5=8(z-3)

Simplify 6×5 to 30

30=8(z-3)

Divide both sides by 8

30/8=z-3

Simplify 30/8 to 15/4

15/4=z-3

Add 3 to both sides

15/4+3=z

Simplify 15/4+3 to 27/4

27/4=z Switch sides z=27/4

x = 8.5

The other two sides are given in the diagram.

The Pythagorean theorem tells you ...

... 19² = 17² +x²

Subtracting 17², we have ...

... x² = 361 -289 = 72

Taking the square root gives x.

... x = √72 = 6√2

... x ≈ 8.5

Answer:

So the value of x=3  and y =3

Step-by-step explanation:

5x + 3i = 15 + yi

To find out x   , set the constant terms  equal to each other and solve for x

5x= 15

Divide by 5 on both sides

x= 3

To find out y   , set the ';i' terms  equal to each other and solve for y

3= y

So the value of x=3  and y =3

Answer:  The required value of x is 3 and that of y is 3.

Step-by-step explanation:  We are given to find the values of x and y that satisfies the following equation :

[tex]5x+3i=15+yi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

[tex]a+bi=c+di~~~~~~~~~\Rightarrow a=c,~b=d.[/tex]

That is, the real and parts on both sides of the equation are equal.

From equation (i), we have

[tex]5x+3i=15+yi.[/tex]

Equating the real and imaginary parts on both sides of the above equation, we get

[tex]5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3[/tex]

and

[tex]3=y\\\\\Rightarrow y=3.[/tex]

Thus, the required value of x is 3 and that of y is 3.

Answer:

it will grow 30 ft in 20 years

Step-by-step explanation:

the height will equal the growth rate times the time

height = 1.5 ft/year * 20 year

height = 30 ft

2

Solve the second equation for y.

... 8x -12 = 4y . . . . add 4y -12

... 2x -3 = y . . . . . . divide by the coefficient of y

The coefficient of x is 2, so a parallel line will have an x-coefficient of 2. The line ...

... y = 2x -6 . . . . . . . . m = 2

will be parallel to the given line, so will not intersect it.

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

The definition of a line segment is the set of points on a line between two given end points, including those end points. The best description is the one that matches the definition.

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

3 ft

The statue's height is 1.5 times the length of its shadow, so we expect the same relationship for the globe.

... 1.5 × 2 ft = 3 ft

_____

Comment on the problem

As a practical matter, with the sun high enough in the sky to cast a shadow shorter than the object's height, it will be quite difficult to measure the length of the shadow of the point at the top of the globe. The shadow of other parts of the globe will interfere.

Answer:

-16 sqrt(3) +16i

Step-by-step explanation:

z = 2 cis (pi/6)

z^5 = 2^5 cis (5*pi/6)

z^5 = 32 cis (5pi/6)

 z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)

        = 32 * (-sqrt(3)/2) + 32i (1/2)

        = -16 sqrt(3) +16i

2/5

There are 2 units of green and 5 units of "pink," so the ratio is ...

... green/pink = 2/5

Answer:

A = 10w

Step-by-step explanation:

In the area formula, the coefficient of width is length. Here, that is ...

... A = 7w

7 is the coefficient of the width. Increasing it by 3 makes it be 10, so we have ...

... A' = 10w

_____

Comment on the problem statement

The problem does not make it clear whether area stays the same as the coefficient increases. We have assumed that it does not.

Also, the coefficient of width in the area formula has units of inches. "Increases by 3" makes no sense in this context. It would make sense for it to increase by 3 inches. The result is very different if the increase is 3 microns, for example.

9 students did not study in either the cafeteria or the student lounge.

How to find the number

To find the number of students who did not study in either the cafeteria or the student lounge, we solve as follows

Let

C = 92

L = 86

C ∩ L = 40

We find the number in either C, L or C ∩ L

= (92 - 40) + (86 - 40) + 40

= 52 + 46 + 40

= 138

The number  did not study in either the cafeteria or the student lounge

= 147 - 138

= 9

Answer:

AE

Step-by-step explanation:

Pairs of letters identify line segments:

... AE, EG, AG

... AD, DE, AE

Segment AE is common to both lists.

Answer :

The proof is as follows :

Step-by-step explanation:

Let NC = x

⇒ AB = 3x and AN = 2x

In Δ ABN, By using Pythagoras theorem,

AB² = BN² + AN²

⇒ BN² = AB² - AN²

⇒ BN² = (3x)² - (2x)²

⇒ BN² = 5x²

⇒ BN = x√5  .......................(1)

Now in ΔANC , Using Pythagoras theorem We have,

AC² = NC² + AN²

⇒ AC² = x² + (2x)²

⇒ AC² = 5x²

⇒ AC = x√5   ....................(2)

From equations (1) and (2) We get,

AC = BN , which is our required result

Answer:

BN=AC=√5 x.

The proof is explained in step-by-step explaination.

Step-by-step explanation:

Let NC=x. It is given that AB=3NC & AN=2NC

⇒ AB=3x & AN=2x

By applying Pythagoras theorem

In triangle ANC,

[tex]AC^{2}=AN^{2}+NC^{2}[/tex]

⇒ [tex]AC^{2} = (2x)^{2}+x^{2}[/tex]

⇒ [tex]AC^{2}=4x^{2}+x^{2} =5x^{2}[/tex]

⇒ [tex]AC=\sqrt{5}x[/tex]   →    (1)

Similarly, In triangle ABN,

[tex]AB^{2}=AN^{2}+BN^{2}[/tex]

⇒ [tex](3x)^{2}=BN^{2}+x^{2}[/tex]

⇒ [tex]9x^{2} = (BN)^{2}+4x^{2}[/tex]

⇒ [tex]BN^{2}=5x^{2}[/tex]

⇒ [tex]BN=\sqrt{5}x[/tex]   →   (2)

From eq (1) & (2),    AC=BN

Answer:

2

Step-by-step explanation:

1/2 cup = 2/4 cups = 2 × 1/4 cup

Alonzo can make 2 batches that each require 1/4 cup.

Answer:

x + y = 60

Step-by-step explanation:

In the given figure, we have two lines that intersect each other at one point.

Therefore, the opposite angles are equal to each other and we can write them in the form of an equation as:

2y - 5 = 95 --- (1)

3x + 55 = 85 --- (2)

Now solving each of the equations to find the value of x and y.

For y:

2y - 5 = 95

2y = 95 + 5

2y = 100

y = 50

For x:

3x + 55 = 85

3x = 85 -55

3x = 30

x = 10

Therefore, x + y = 10 + 50 = 60.