quadratic transformation

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

12

Step-by-step explanation:

Brandon's car can go in one gallon gas= 18 miles

In the United States, the gallon is a unit of measurement for liquids such as gasoline, water, and milk. If your car's tank is nearly empty, you should stop and purchase at least a few additional gallons of gas. A gallon of liquid is equal to 4 quarts or 3.785 liters.

Brandon's car used 3/4 of a gallon to travel 13 1/2 miles.

3/4 of a gallon(G)= 13 1/2 miles

3/4*G=27/2

G=18 miles

Hence, Brandon's car can go in one gallon gas= 18 miles.

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Answer:

first option

Step-by-step explanation:

integers are like whole numbers but can also be negative

Answer:

A

Step-by-step explanation:

Answer:Step-by-step explanation:

x+46=90

x=90-46

x=44°

The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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Answer:

The measure is 68

Step-by-step explanation:

180-112 = 68

side alternate exterior (supplementary)

The measure of angle 1 will be equal to 68.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet. The supplementary angle is defined as the angle having the sum of 180 degrees.

Given that there are two parallel lines intersecting one line at an angle of 112. The angle 1 will be calculated as:-

The angle will be calculated as follows:-

∠1 + 112 = 180

∠1 = 180 - 112 = 68

Therefore, the measure of angle 1 will be equal to 68.

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Answer:

Third quadrant

Step-by-step explanation:

To count quadrants, you do it counter-clockwise, so, since the point is in the (negative, negative) quadrant, it is the third one

The 8th term of the given geometric sequence is -163840;

Given sequence 10, -40, 160,..... is a geometric progression;

Here, a = 10; r = -4;

The nth term of a geometric progression is given by aₙ = a(rⁿ⁻¹);

Therefore;

a₈ = 10(-4)⁸⁻¹ = 10(-4)⁷ = -163840;

A sort of sequence known as geometric progression (GP) is one in which each following phrase is created by multiplying each preceding term by a fixed number, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers.

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Part a.

In this case, we need to substitute the given point values into the expression x-2y. Then for point (7,3), we have

Now, for point (7,5) we have

Part b.

As we can note, in the first case we got 1 which is 2 units from 3. In the second case, we got -3, which is 6 units from 3. Therefore, point (7,3) gives the closest value to 3

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer: With $17.50 you can buy 7 packs of grape tomatoes.

Step-by-step explanation: For this question you can find the answer by taking 52.50 ÷ 21 which is 2.5 so that packs are $2.50 a pack and then you can either plug in numbers or take 17.50 ÷ 2.5.

Hope this helps.

Answer:

You can only buy 7 packages. Each package cost $2.50

Step-by-step explanation:

Alright so the cost of 21 packages of grapes cost $52.50 dollars.

So to get how much 1 package cost you divide 21 into 52.50

so 52.50 divided by 21= 2.5

So each package cost $2.50

So you have $17.50 to spend

so take 2.50 and divided that by 17.50

17.50 divided by 2.5= 7 so you can only by 7 packages for $17.50

Answer:

W21221

Step-by-step explanation:

The blue line and area represents the fist inequality

The green line and area represent the second inequality

The area of intersection of both colors is the solution to the system of equations

The point (2,6) is part of the solution and it is in the shaded region, we know because that point is part of the green line.

y = (1/2)x + 5 ==> when x = 2, y = 6 ==> Point(2,6) is part of the green line (second inequality)

Second answer:

The point (2,6) is part of the is in the shaded region, we know because that point is part of the second inequality.

At approximately 16c a cup, Folgers Coffee is better value than Seaftle's Best which costs 18c a cup.

A word problem is a mathematical problem written as one sentence or more that requires  application of mathematical knowledge to a 'real-life' scenario.

To determine the brand of coffee with the best value, we have to find the respective value per cup

To find the respective value per cup, we divide the prices given by the number of cups they represent.

For Folgers coffee

=12.88÷80

=$0.16

Hence, Folgers Coffee is approximately 16c per cup

For Seaftle's Best

=9.00÷50

=$0.18

Hence, Seattle's Best is 18c per cup.

Folgers Coffee which cost 16c per coffee is a better value than Seaftle's Best which costs 18c a cup

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the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The given function is:

f(x) = -(x + 3) - 1

To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.

The derivative of the function is:

f'(x) = -1

The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.

Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

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i can't see the photo.

9514 1404 393

Answer:

  1/2

Step-by-step explanation:

The base of the exponent tells us the common ratio of this geometric series is 1/2. The start value of n=7 tells us the first term in the series we're evaluating is ...

  a1 = 2(1/2)^(7-4) = 2·(1/2)^3 = 2/8 = 1/4

The formula for the infinite sum of a geometric series is ...

  S = a1(1/(1-r))

Filling in the values we know, this is ...

  S = (1/4)(1/(1 -1/2)) = (1/4)(2) = 1/2

The infinite sum is 1/2.

Answer:

5

Step-by-step explanation:

o+5=y=5

1+5=y=6

2+5=y=7

.:y=x+5

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer: 42

Step by step:

42 is divisible by both 7 and 2

Answer:

44

Step-by-step explanation:

4 x 11 = 44

2 x 22 = 44

Answer:  15 + |−6| = 21 steps

Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.

Answer:

The number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.

Step-by-step explanation:

You know that the temperature of liquid at 16.9°C is decreasing at a rate of 2.3°C per minute. Then, the temperature of the liquid after t minutes, as its value decreases, will be the difference between the initial temperature of 16.9 ° C and the temperature after t minutes. So:

temperature of the liquid= 16.9°C - 2.3 °C/minute * t

On  the other  side, you know that the temperature of a solid at 30.7°C is decreasing at a rate of 6.9°C per minute. Then, the temperature of the solid after t minutes, as its value decreases, will be the difference between the initial temperature of 30.7°C and the temperature after t minutes. So:

temperature of the solid= 30.7°C - 6.9 °C/minute * t

You want to calculate the number of minutes it will take for a liquid and a solid to reach the same temperature. This is:

temperature of the liquid= temperature of the solid

16.9°C - 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t

Solving:

- 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t - 16.9°C

- 2.3 °C/minute * t + 6.9 °C/minute *t= 30.7°C - 16.9°C

4.6 °C/minute * t = 13.8 °C

t=3 minutes

So the number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.

The meaning of \(\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\) is that the set of natural numbers is the intersection of all inductive sets.

The set of natural numbers is inductive because it satisfies both of these conditions. The set is non-empty because it contains the number 1. And if x is a natural number, then x+1 is also a natural number.

In other words, a set is inductive if it satisfies the following two conditions:

The concept of an inductive set is important in mathematics because it allows us to define the set of natural numbers.

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Answer: C

Step-by-step explanation:

For this problem, you want to find (FoG)(x). Then, you want to find the inverse of that.

(FoG)=5(x-4)-6               [distribute]

(FoG)=5x-20-6               [combine like terms]

(FoG)=5x-26

Now, we want to find the inverse. To find the inverse, you switch the x with y and y with x, then solve for y.

y=5x-26                          [switch x with y and y with x]

x=5y-26                          [add both sides by 26]

x+26=5y                         [divide both sides by 5]

y=(x+26)/5

Now, we know that y=(x+26)/5 is the answer.

Substitute [ x - 4 ] for x in the function of "R"

R(x) = 5(x - 4) - 6

R(x) = 5x - 20 - 6

R(x) = 5x - 26

Switch variables to find the inverse and solve for y

y = 5x - 26

x = 5y - 26

x + 26 = 5y

(x+26)/5 = y

Therefore, the answer is D.

Best of Luck!

Answer:

n=4 Now im The Brainliest

Step-by-step explanation:

Answer:

Uh i think 3?

Step-by-step explanation:

well 2 x 3 is 6, so if i had to assume i think 3, the whole number is 2 though

Answer:

9

Step-by-step explanation:

6/(2/3)= 6*3/2=18/2=9

Answer:

7.) 135%, 13.5, 8⅗

from least to greatest= 1.35, 8.6, 13.5.

= 135%, 8⅗, 13.5.

8.) ⅙, 16.7%, 0.16

from least to greatest= 0.16, 0.17, 0.17

= 0.16, 1/6, 16.7%

**sorry if it's late ...

you could also check it too

Answer:

This is not an equation. It is an expression, you can't solve for x in an expression

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16