The table shows a hot air balloon's height h , in feet, during a descent at various times t , in seconds.
Part A: Use the table's first two ordered pairs to find the hot air balloon's rate of change.

Part B: Is the rate of change constant? Explain.

Part C: What was the hot air balloon's height at the time the descent began?

Part D: Write , as a linear function of
.

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:

[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]

[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]

tan θ ≈ 77.173°

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

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The length of a square with diagonal of 10 cm is 5√2 cm.

Each angle in a square is 90 degrees.

Therefore, the diagonal form a right triangle with the length of the square.

The length of the square are equal.

Hence, using Pythagoras theorem,

let

x = length of square

x² + x² = 10²

2x² = 100

x² = 50

x = √50

x = 5√2

Therefore, the length of a square with diagonal of 10 cm is 5√2 cm.

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Answer:

The value of g(-2) and g(4) cannot be compared because they are two different functions with two completely different values.

Step-by-step explanation:

So, you plug in -2 in the function of the x in g(x) = 8x - 2

Then, you multiply 8 by -2 in g(-2) = 8x - 2

8 × -2 would be -16

Afterwards you subtract -16 by 2 in g(-2) = -16 - 2

The function of g(-2) is -14 in g (x) = -14

You plug in 4 in the function of x in g(4) = 8x - 2

g(4) = 8 (4) - 2

Then, You multiply 8 by 4 which will give you 32 in

g(4) = 32 - 2

Lastly, you subtract the 32 by 2 and the function of the answer would be 30 in g(x) = 30

Answer:

3x + y = 9.5

Step-by-step explanation:

1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.

y = -3x + c

2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.

-3 = 8 - k / k - 3

-3(k - 3) = 8 - k

-3k + 9 = 8 - k

-3k + k = 8 - 9

-2k = -1

k = -1/-2

k = 1/2

3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.

y = -3x + c

1/2 = -3(3) + c

1/2 = -9 + c

1/2 + 9 = c

9.5 = c

Completed equation of the line: y = -3x + 9.5

4) Write it in the form of ax + by = c.

3x + y = 9.5

The center of mass is mathematically given as

[tex]\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

[tex]\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end[/tex]

We calculate the total mass of the system.

[tex]\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}[/tex]

Step 03: Calculate the moment of the system.

[tex]\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}[/tex]

we calculate the center of mass.

[tex]\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}[/tex]

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Based on the given parameters about old cone, the height of the new cone is 12 inches

Old cone:

New cone:

equate ratio of radius to height in old and new cone

2 : 6 = 4 : h

2/6 = 4/h

cross product

2 × h = 6 × 4

2h = 24

h = 24/2

h = 12 inches

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The radius of the base is 8.245 cm

Given, a vase with a circular base exerts

Pressure = 700 N/m²

Force = 15 N

Area = ?

∴ area = πr²

By finding out the area of the vase we can calculate the radius.

We know that Pressure = Force/Area

According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.

therefore apply the above the formula to find out the area and radius.

700 = 15/πr²

 πr² = 15/700

 πr² = 3/140

  r² = 3/140 × 3.14

since π value is 3.14

  r² = 0.0068

   r = √0.0068

   r = 0.0824 m

   r = 0.0824 × 100

   r = 8.245 cm

we get radius as 8.245 .

Hence we get the radius of the base of the vase as 8.245 cm.

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The amount paid in tax based on the information is Rs 13500.

From the information given, the monthly salary is 45000. Therefore, the yearly salary will be:

= 45000 × 12

= 540000

Also, it's stated that the tax rate for first 450000 is 1% and next 100000 is 10%. Therefore, the amount that will be paid in tax will be:

= (450000 × 1%) + (90000 × 10%)

= 4500 + 9000

= 13500

Therefore, the amount paid in tax will be Rs 13500.

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The additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ

The six basic properties of parallelograms are primarily;

Now, looking at the parallelogram properties above and comparing with the given image of the quadrilateral attached, we can say that the additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ

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Answer:

5

Step-by-step explanation:

2x + 15 = 3x + 10

3x + 10 = 2x + 15

3x - 2x = 15 - 10

x = 5

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

[tex]2x + 15 = 3x + 10[/tex]

• Group like terms together:

  • Subtract 5 from both sides:

     [tex]2x = 3x - 5[/tex]

  • Subtract 3x from both sides:

      [tex]-x = -5[/tex]

• Multiply both sides by -1:

[tex]x = 5[/tex]  

Answer: A

Step-by-step explanation:

[tex]C=2\pi r=2(\pi)(17) \approx 106.8[/tex]

By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.

In this question we must apply algebraic rules to find the roots of a quadratic equation, the roots are the values of the equation such that is equal to zero. Now we present the complete procedure:

6 · x² + 18 · x = 0

6 · x · (x + 3) = 0

x = 0 ∨ x = - 3

By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.

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Answer:

-100/3,0

Step-by-step explanation:

substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

if that makes sense Hope this helps pls brainliest have a nice day :>

Answer:

100- 3X

Step-by-step explanation:

SLAY

Using proportions, the ratios are given as follows:

a) 9:196.

b) 27:2744.

c) 3:14.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the standard ratio of 3:14 units, we have that:

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Answer: 10

Step-by-step explanation:

The first term is 3 and the common ratio is 1/2.

Using the sum of a geometric series formula,

[tex]\frac{3069}{512}=\frac{3(1-(1/2)^{n}}{1-(1/2)}\\\\\frac{3069}{1024}=3(1-(1/2)^{n})\\\\\frac{1023}{1024}=1-(1/2)^{n}\\\\-(1/2)^{n}=-\frac{1}{1024}\\\\(1/2)^n=\frac{1}[1024}\\\\2^{-n}=2^{-10}\\\\n=10[/tex]

Answer: 44.2

Step-by-step explanation:

108.29*2/4.9=44.2

Answer:

Vertex form: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]

Standard Form: [tex]y=0.50x^2-2x-1[/tex]

Step-by-step explanation:

Well the vertex form of an equation is given in the form: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex, and by looking at the graph, you'll see the vertex is at (2, -3). So plugging this into the equation gives you: [tex]y=a(x-2)^2-3[/tex]. Now to find a which will determine the stretch/compression, you can substitute any point in (besides the vertex, because that'll result in (x-2) being 0). So I'll use the point (0, -1) which is the only point I think I can accurately determine by looking at the graph (besides (4, -1) since it's symmetric). Anyways I'll plug this in

Plug in (0, -1) as (x, y)

[tex]-1 = a(0-2)^2-3[/tex]

calculate inside the parenthesis

[tex]-1 = a(-2)^2-3[/tex]

square the -2

[tex]-1 = 4a-3[/tex]

Add 3 to both 3 to both sides

[tex]2 = 4a[/tex]

divide both sides by 4

[tex]a=\frac{1}{2}[/tex]

This gives you the equation: [tex]y=\frac{1}{2}(x-2)^2-3[/tex]

To convert this into standard form you simply expand the square binomial, you can use the foil method to achieve this, but it generally expands to: [tex](a+b)^2=a^2+2ab+b^2[/tex].

Original equation:

[tex]y=\frac{1}{2}(x-2)^2-3[/tex]

expand square binomial:

[tex]y=\frac{1}{2}(x^2-4x+4)^2-3[/tex]

Distribute the 1/2

[tex]y=0.50x^2-2x+2-3[/tex]

Combine like terms:

[tex]y=0.50x^2-2x-1[/tex]

Answer:

First Question: 1. 60 hours 2. Wednesday 6:00 PM

Step-by-step explanation:

Sorry but I couldn't figure out the answer to the second question :(

Hope this helped :D

The input and output table that works for both rules is input = 20 and output = 10.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the output and x represent the input.

From the first rule:

y = x/2

From the second rule:

y = x - 10

To work for both rules:

x/2 = x - 10

x = 2x - 20

x = 20

y = 20 - 10 = 10

The input and output table that works for both rules is input = 20 and output = 10.

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Answer:

Distance on the map (in centimeters) represents an actual distance of 4 kilometers is 3,2 cm.

Step-by-step explanation:

The scale of a map = 4 cm : 5 km

The scale of a map = 4 : 500.000

So, 0,000008 times the actual distance is the distance on the map.

0,000008 × 400.000 = 3,2 cm

Answer:

1) 150 mph

2) 90 mph

3) 3 mph

Explanation:

1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150

2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.

3) We know that both trains combined travel 150 mph. 450/150=3.

Based on the data given, the speeds and time taken are as follows:

Speed is the ratio of distance covered and time taken.

1)The distance covered by the two trains in 5 hours = 750 miles.

The trains move at a constant speed and their combined speed will be:

Combined speed = 750/5

Combined speed = 150 mph

2) The train heading south has a speed 1.5 times faster than the other train heading north.

Ratio of speeds = 3 : 2

Speed of faster train 150 x 3/5 = 90 mph

3) The combined speed of the trains = 150 mph

Distance to be covered = 450 miles

Time taken = 450/150

Time taken = 3 hours

In conclusion, the speed of the two trains are determined from the distance travelled and time taken.

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Rewriting the equation of the given line in slope-intercept form,

[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]

This means the slope of the given line is -1/2.

As perpendicular lines have slopes that are negative reciprocals, the answer is 2.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Determine the slope of the line perpendicular to 3x+6y=18

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form

[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x

[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].

[tex]\cline{1-2}[/tex]

Now, perpendicular lines' slopes are opposite inverses of each other.

The opposite inverse of -1/2 is

                  = 2

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=2}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]

Answer:

B

Step-by-step explanation:

y² - 12y + 32

consider the product of  factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)

the factors are - 4 and - 8 , since

- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then

y² - 12y + 32 = (y - 4)(y - 8)

Answer:

B. (y-4)(y-8)

Step-by-step explanation:

Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.

1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.

They are: -8 and -4.

2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.

y² - 8y - 4y +32

y(y - 8) - 4(y - 8)

(y - 4)(y -8)

The brackets or error bars shown at the top of each bar extend one standard error above and below each of the group means. For group 1, the error bar extends 3.9 units above and below the mean for group 1.

A researcher is investigating whether a reading intervention program improves reading comprehension for second graders. He collects a random sample of second graders
Group 1 consists of n₁ = 52 second graders who did not participate in the program. Their mean reading comprehension score is M₁ = 36.8.
Group 2 consists of n₂ = 56 second graders who did participate in the program. Their mean reading comprehension score is M₂ = 52.4.

Error bar, are the line through a point on a graph,axes, which emphasizes  the uncertainty or variation of the corresponding coordinate of the point.

We have the data,
σ = 25.24, n₁ = 52 M₁ = 36.8.

n₂ = 56  M₂ = 52.4.

Error bar  = M2-M1/n2-n1
      =  (52.4-36.8)/(56-52)
      =  3.9

Thus, the required value that will be put in black space is 3.9

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The given expression is equivalent to the number 147.

We have given that,

[tex](3\times4)^2+\frac{6}{2}[/tex]

We have to determine the value of the given expression.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

[tex]=(12)^2+\frac{6}{2} \\=144+3\\=147[/tex]

Therefore the given expression is equivalent to the number 147.

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Answer:

the distance between both points is 10

Step-by-step explanation:

Distance (d) = √(-14 - -8)2 + (-16 - -8)2

= √(-6)2 + (-8)2

= √100

= 10

The distance between the two points (-8, -8) and (-14, -16) is 10 units.

We have,

To find the distance between two points in a coordinate plane, you can use the distance formula:

Distance = [tex]\sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

In this case, the two points are (-8, -8) and (-14, -16).

Let's plug the values into the distance formula:

Distance = √[(-14 - (-8))² + (-16 - (-8))²]

Distance = √[(-14 + 8)² + (-16 + 8)²]

Distance = √[(-6)² + (-8)²]

Distance = √[36 + 64]

Distance = √100

Distance = 10

Thus,

The distance between the two points (-8, -8) and (-14, -16) is 10 units.

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By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.

Herein we must simplify an expression that uses logarithms by applying any of the following three laws:

[tex]\log_{a} (b \cdot c) = \log_{a} b + \log_{a} c[/tex]      (1)

[tex]\log_{a} \left(\frac{b}{c} \right) = \log_{a} b - \log_{a} c[/tex]     (2)

[tex]\log_{a}{b^{c}} = c \cdot \log_{a} b[/tex]     (3)

Now we proceed to simplify the expression:

[tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex]

[tex]\log_{2} 2\cdot y = \log_{2} 8\cdot x^{3} - \log_{2} \frac{8\cdot x^{3}}{2}[/tex]

[tex]\log_{2} 2 \cdot y = \log_{2} \frac{\frac{8\cdot x^{3}}{1} }{\frac{8\cdot x^{3}}{2} }[/tex]

[tex]\log_{2} 2\cdot y = \log_{2} 2[/tex]

By the relationship between logarithms and powers of same base:

2 · y = 2

y = 1

By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.

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Answer:

$3820 total, $32 per alumnus.

Step-by-step explanation:

The total cost will be [tex]12\times120+650+730+1000=3820[/tex]

Each alumnus pays [tex]\frac{3820}{120} =31\frac{5}{6}[/tex]

Rounding to nearest whole number = $32 per alumnus.

Answer: 18 feet

Step-by-step explanation:

The area of a rectangle is given by [tex]A=lw[/tex], which means that the length of the unknown side is [tex]\frac{216}{12}=18[/tex] feet.

A is zero

B) D

C) x= - 1 & x= 4

Hope this helps!