(6) An observer sits 60 feet from a hot air balloon resting on the ground. The balloon lifts off and climbs straight up at a constant rate. After 10 seconds, the angle of elevation from the observer to the balloon is 6 = 49'. a. Find the line-of-sight distance from the observer to the balloon. b. At what rate is the angle of elevation changing (degrees per second)?

Answer:

x=   \(\frac{9}{2} y\) or  y=  \(\frac{2}{9} x\)

Step-by-step explanation:

Solving for (x)

Step 1: Add -3y to both sides.

2x+3y+−3y=12y+−3y

2x=9y

Step 2: Divide both sides by 2.

\(\frac{2x}{2} = \frac{9y}{2}\)

Solving for (y)

Step 1: Add -12y to both sides.

2x+3y+−12y=12y+−12y

2x−9y=0

Step 2: Add -2x to both sides.

2x−9y+−2x=0+−2x

−9y=−2x

Step 3: Divide both sides by -9.

\(\frac{-9y}{9} = \frac{-2x}{9}\)

Answer:

$37.20

Step-by-step explanation:

The total amount earned will be:

= $24.50 + $12.70

= $37.20

A situation in which he has zero dollars is when he spends the whole $37.20

This is a difficult decision that you have to make. On the one hand, you really want to see the play and have come all this way to do so.

On the other hand, you have lost a $100 bill and may not be able to afford a ticket. Ultimately, it is your decision to make. If you have the financial means, you could consider buying a ticket and seeing the play. Alternatively, you could look for discounted tickets if available or wait until you have the funds available before buying a ticket.

The cost of a ticket to watch a play depends on the venue, seating arrangements, and other factors. Generally speaking, tickets for a play can range from around $10 to upwards of $100, depending on the show and its popularity.

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Answer: \(167\dfrac15\text{ miles}\).

Step-by-step explanation:

Since

\(64\dfrac45\text{miles}=\dfrac{64\times5+4}{5}\text{ miles}\\\\=\dfrac{324}{5}\text{ miles}\)

\(18\dfrac45\text{ miles}=\dfrac{18\times5+4}{5}\text{ miles}\\\\=\dfrac{94}{5}\text{ miles}\)

Total distance traveled during the trip = \(\dfrac{324}{5}+\dfrac{94}{5}+\dfrac{324}{5}+\dfrac{94}{5}\)

\(= \dfrac{836}{5}\\\\=167\dfrac15\text{ miles}\)

Hence, the distance traveled during their trip was \(167\dfrac15\text{ miles}\).

Answer:

20%

Step-by-step explanation:

Basically Belle did 8 + 32 = 40 problems total. If she got 8 right then she got 8/40. 8/40 = 1/5 = 20%. :)

Answer:

88

Step-by-step explanation:

Given

x = 4y² - 12 ← substitute y = 5

x = 4(5)² - 12 = 4(25) - 12 = 100 - 12 = 88

Answer:

2^-4*2^5= 2

Step-by-step explanation:

Answer:

The expression below, 4x=20 when x=5.

Step-by-step explanation:

4(5)=20

Answer:

102 inches squared

Step-by-step explanation

A = (b x h) / 2

A = (12 x 17) / 2

= 102

Cₙ = C₀ * Cₙ₋₁ + C₁ * Cₙ₋₂ + C₂ * Cₙ₋₃ + ... + Cₙ₋₂ * C₁ + Cₙ₋₁ * C₀. This recurrence relation represents the number of ways to parenthesize the product of n + 1 numbers based on the parenthesization of smaller products.

The total number of ways to parenthesize x₀ · x₁ · x₂ · ... · xₙ, denoted as Cn, can be calculated by summing the products of \(C_k\) and C_{(n - k)} for all possible values of k:

Cₙ = C₀ * Cₙ₋₁ + C₁ * Cₙ₋₂ + C₂ * Cₙ₋₃ + ... + Cₙ₋₂ * C₁ + Cₙ₋₁ * C₀

To find a recurrence relation for Cₙ, let's consider the base cases first:

C_0: There is only one number, x₀ , so no parenthesization is needed.

Therefore, \(C_0\) = 1.

C1: There are two numbers, x₀ and x₁. We can only multiply them in one way, so \(C_1\) = 1.

Now, let's consider the case for n ≥ 2:

To parenthesize the product x₀ · x₁ · x₂ · ... · xₙ, we can split it at each position k, where 1 ≤ k ≤ n.

If we split at position k, the left side will have k + 1 numbers (x₀ · x₁ · x₂ · ... · x\(_k\)) and the right side will have (n - k) + 1 numbers (\(x_{k+1}, x_{k+2}, ..., x_n\)).

The number of ways to parenthesize the left side is C_k, and the number of ways to parenthesize the right side is \(C_{(n - k)}\).

Therefore, the total number of ways to parenthesize x₀ · x₁ · x₂ · ... · xₙ, denoted as Cn, can be calculated by summing the products of \(C_k\) and \(C_{(n - k)\) for all possible values of k:

Cₙ = C₀ * Cₙ₋₁ + C₁ * Cₙ₋₂ + C₂ * Cₙ₋₃ + ... + Cₙ₋₂ * C₁ + Cₙ₋₁ * C₀

This recurrence relation represents the number of ways to parenthesize the product of n + 1 numbers based on the parenthesization of smaller products.

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Answer:

y + 2 = 5(x - 5)

Step-by-step explanation:

You must provide a value for the slope, m.

supposing that the slope, m, were 5, then the desired equation in point-slope form would be:

y + 2 = 5(x - 5)

On solving the question, unit rate by using the given graph could be 2.4 potatoes/pound

Graph can be defined as the visual representation which is used to represent the data.

The unit rate is the slope of the line.

The slope of the line =  (change in y-value)/(change in x-value)

= (36 potatoes - 12 potatoes)/(15 pounds - 5 pounds)

= (24potatoes)/(10 pounds)

= 2.4 potatoes/pound

The relationship here is proportional, so the line goes through the point (0, 0) and the unit rate can be figured from any point:

(12 potates)/(5 pounds)

= (24 potatoes)/(10 pounds)

= (36 potatoes)/(15 pounds) = 2.4 potatoes/pound

Hence, The unit rate by using the given graph could be 2.4 potatoes/pound .

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The correct question is -

Identify the unit rate in the graph.

A. 40mph

B. 75mph

C. 50mph

D. 25mph

Answer:

Step-by-step explanation:

outer area=

first need to find the circumference of outer diameter

= π×4.8

= 15.079644.... cm

to find the outer curved area you would then do

= 77×15.079644

(ii) =1161.13264 cm²

inner curve area

circumference= π×4

=12.5663706.... cm

77×12.5663706

(i) =967.610537 cm²

total surface area=

as the outer and inner curved areas are already found only the top and bottom surfaces need to be

= area of larger circle

=π×4.8²

=72.382294.... cm²

smaller circle

=π×4²

=50.2654824.... cm²

72.382...-50.265

=22.1168116 x 2

=44.2336232 cm²

total surface area

(iii)= 2172.9768 cm²

(round this to however many decimals you need)

I hope this is understandable and useful!

also how many marks is this for?

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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The approximate cost per square inch of the apple pie is $0.22. Therefore, option D is the correct answer.

The term "approximate cost" refers to the price of the plot for residential, commercial, and non-residential uses based on the land's value and the expense of carrying out development work.

Given that, a bakery sells apple pies for $11.05.

The pie has a diameter of 8 inches

Then radius =8/2 =4 inches

Now, area of a pie = 3.14×4²

= 3.14×4×4

= 50.24 square inches

The cost per square inch

= 11.05/50.24

= 0.219

≈ $0.22

Therefore, option D is the correct answer.

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Answer:cost per square inch of the apple pie is $0.22. Therefore, option D is the correct answer.

Answer:

GPH

Step-by-step explanation:

Technically that's correct, but I think the problem wants you to orient the angle so that M corresponds with G and O corresponds with H.

The sizes of the angles marked are:

a = 90 degrees;    b = 45°;   c = 100°;    d = 80°

To find the measure of a, note that the sum of the angles on a straight line is equal to 180 degrees, therefore, since a right angle is 90 degrees, we have:

a + 90 = 180

a = 180 - 90

a = 90 degrees.

a + b + 45 = 180° [angles on a straight line = 180 degrees]

Substitute:

90 + b + 45 = 180

b = 180 - 90 - 45

b = 45°

d = 180 - 100 [supplementary angles]

d = 80°

c = 180 - d [linear pair]

c = 180 - 80

c = 100°

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Answer:

The correct options are;

3 Congruent sides

Corresponding congruent Angle-Side-Angle

Corresponding congruent Side-Angle-Side

Corresponding congruent Side-Side-Angle

Step-by-step explanation:

The conditions for congruency are;

Two triangles are congruent when

AAS which is the acronym for corresponding Angle-Angle-Side are congruent

SAS  which is the acronym for corresponding Side-Angle-Side are congruent

SSS which is the acronym for corresponding Side-Side-Side are congruent

ASA which is the acronym for corresponding Angle-Side-Angle are congruent.

The criteria that always proves triangles

are congruent are;

Option A; Corresponding congruent Angle-Side-Angle

Option A; Corresponding congruent Angle-Side-AngleOption B; Corresponding congruent Side-Angle-Side

Option A; Corresponding congruent Angle-Side-AngleOption B; Corresponding congruent Side-Angle-SideOption D: 3 congruent sides

There are some congruence theorems that prove that two triangles are congruent and they are;

1) SSS; This means Side - Side - Side and it denotes that the 3 corresponding sides of both triangles are congruent.

2) SAS; This denotes Side - Angle - Side and it denotes that the 2 corresponding sides and the included corresponding angle are congruent.

3) ASA; This denotes Angle - Side - Angle and it means that the 2 corresponding angles and the included corresponding side are congruent.

4) AAS; This denotes Angle - Angle - Side and it denotes that the 2 corresponding angles and corresponding non-included side are congruent.

In conclusion, from the options, options A, B & D.

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Answer:

an infinite number of solutions

Step-by-step explanation:

−3x −17 = −17 −3x

left side = right side  TRUE because -3x-17 is the same as -17-3x

we can rearrange  the the equation

−3x −17 +17 = −17 +17−3x, add 17 on both sides of the equations

            -3x = -3x, divide both sides by (-3)

               x = x

Since this equation is always true ( for any number ) we have an infinite number of solutions (since there are is an infinity of numbers.)

Answer:

144

Step-by-step explanation:

2(3x+4)+2(2x_1)=64

x=4

2x_1=9

3x+4=16

9×16=144

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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1) 2 3÷4 = 11÷4

hence, 11÷8 = 1.37 .

2)  4 2÷9 =38÷9 .

hence, 38÷18 = 2.11 .

simplify  2 3÷4  = 11÷4

and

4 2÷9 = 38÷9.

now 1/2 of 11/4 = 11/8 = 1.37.

1/2 of 38/9 = 38/18 = 2.11 .

Answer:

1/12

Step-by-step explanation:

Landing on the 5 is a 1/6 chance, landing on tails is a 1/2 chance, multiply, and you get 1/12

Answer:

see below

Step-by-step explanation:

We can just add up all of these fractions:

2 1/8 + 7/8 = 2 8/8 = 3

8 5/8 + 4/8 = 8 9/8 = 9 1/8

3 + 9 1/8 = \(12\frac{1}{8}\)

The rate of change of the area of the triangle is not constant and will depend on the angle between the ladder and the ground.

The area of the triangle formed by the ladder wall and ground is dependent on the angle between the ladder and the ground. The area of a triangle is equal to half the product of the length of the base and the corresponding height. Therefore, if the angle between the ladder and the ground changes, the corresponding height of the triangle will also change, resulting in a change of the area of the triangle. As the angle between the ladder and the ground changes, the rate of change of the area of the triangle will also change.

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Answer:

The shaded segment  = The arc area - The triangle

The arc area = pi x radius^2 x angle/360

                     = pi x 9^2 x (360-270)/360 = 63.61 (m2)

The triangle area = 9 x 9/2 = 41.5 (m2)

(because this is right triangle)

=> The shaded segment = 63.61 - 41.5 = 22.11 (m2)