what is the angle of depression on top of a 15 foot tall tree to a lake exactly at 30 feet from the top of the tree? what is the angle of elevation for someone on a boat that is 35 feet from shore looking up at the top of the tree?

Answer:

2(1/2)(3)(4) + 12(3) + 12(4) + 12(5)

= 12 + 36 + 48 + 60 = 156 cm^2

C is the correct answer.

Answer: 13 7/8

Step-by-step explanation:

11 + 1/8 + 3/4 + 2 = 13 7/8

Answer:

Let x be the number of bottles of water that Yui buys, and let y be the number of sports drinks she buys.

Since Yui buys a total of 6 bottles of water and sports drinks, we know that:

x + y = 6

We also know that each bottle of water costs $1.50 and each sports drink costs $2.50, and that Yui spends a total of $10. Therefore, we can write another equation based on the total cost:

1.5x + 2.5y = 10

We now have a system of two equations with two variables:

x + y = 6

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Rearranging the first equation, we get:

x = 6 - y

Substituting this expression for x into the second equation, we get:

1.5(6 - y) + 2.5y = 10

Expanding and simplifying, we get:

9 - 1.5y + 2.5y = 10

Combining like terms, we get:

y = 2

Substituting this value of y back into the equation x + y = 6, we get:

x + 2 = 6

Solving for x, we get:

x = 4

Therefore, Yui buys 4 bottles of water and 2 sports drinks.

(7.5, -9) is the final value after reflection and dilation.

To reflect a vector across the line y=x, we switch the x and y coordinates. Therefore, the reflection of (6,-5) across the line y=x is (-5,6).

To dilate a vector by a scale of -1.5, we multiply the vector by -1.5. Therefore, the resulting vector is (-5,6) multiplied by -1.5, which gives us:

(-5,6) * (-1.5) = (7.5, -9)

So the final result after the reflection and dilation is (7.5, -9).

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Answer:

2/6

Step-by-step explanation:

15 isn't a decimal number

11/25=0.44 not recurring (not repeating)

3/20=0.15 not recurring (not repeating)

2/6=0.333333 recurring

so the answer is D

Answer: $1856

Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856

Answer: Reduce the height of the ramp from 1 meter to 0.5 meters

Step-by-step explanation:

A. The amount invested is given as follows: $252.

B. The amount being put in is given as follows: $105.

The amounts are obtained applying the proportions in the context of the problem.

For item a, the amount is of 12% of 2100, hence it is given as follows:

0.12 x 2100 = $252.

For item b, the amount is half of 10% of 2100, hence it is given as follows:

0.5 x 0.1 x 2100 = $105.

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The graph of the line passing through the points (-1, 0) and (-5, 0) is attached.

Given are two points we need to find the equation of line passing through them,

We know that the equation of a line passing through two points, (x₁, y₁) and (x₂, y₂) is,

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here, (x₁, y₁) and (x₂, y₂) are (-1, 0) and (-5, 0).

So,

y-0 = 0-0 / -5+1 (x+1)

y = 0

Hence, the equation of the line is y = 0.

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Car Make and Model that i choose is Toyota RAV4

The Cost of this car as of today is about $27,000

To know the value of car after one year will be:

20% of $27,000

= $5,400.

So the car  value will be:

$27,000 - $5,400

= $21,600 after year 1

3.  Value of car after second year of ownership:

15% of $27,000

= $4,050.

So, the car  value will be:

$21,600 - $4,050

= $17,550 after year 2.

4 The Exponential Function if the car continues to decrease in value by 15% each year will be;

V(x) = 27,000 x (0.85)ˣ

V(5) = 27,000 x (0.85)⁵

= 27,000  x  0.44370

= $11979.9

Therefore, the value of the car after owning it for five years is  $11979.9

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See text below

Car Value: Exponential

1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.

Car Make and Model:

Cost of this car as of today:

2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?

Value of car after one year:

3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?

Value of car after second year of ownership:

4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.

Exponential Function:

Use your exponential function to calculate the predicted value of your car after you own it for five years.

Value after five years of ownership:

Answer:522

Step-by-step explanation:

cut the shape on top to make a triangle and rectangle so then it would be 25x18=450 then for the triangle it would be 18x8=72 450+72=522

1) Brianna's average monthly income is $1,850.

2) Brianna's average monthly expenses are $3,135.

3) Brianna's total monthly cash flow is -$1,295.

The cash flow refers to the cash inflows and cash outflows.

Cash inflows are incomes while cash outflows are expenses.

Monthly Rent = $700

Gas = $120

Car Insurance = $75

Health Insurance = $140

Renter's Insurance = $25

Cell phone = $110

Utilities = $100

Groceries = $300

Entertainment/eating out = $250

Total monthly expenses = $1,820

= $21,840 ($1,820 x 12)

College = $12,000

Gifts = $1,000

Vacations = $1,500

Clothes = $800

Charity =$600

Total monthly expenses = $21,840

Total annual expenses = $37,740

Average monthly expenses = $3,135 ($37,740 ÷ 12)

Monthly Income = $1,600

Yearly Income = $ 19,200 ($1,600 x 12)

Annual Scholarship = $3,000

Total annual income = $22,200

Average monthly income = $1,850 ($22,200 ÷ 12)

Average monthly income = $1,850

Average monthly expenses = $3,135

Cash flows = -$1,295 ($1,850 - $3,135)

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Using the defined iterative process, xₙ ₊ ₁ = 4xₙ(3 - xₙ) with x₀ = 5,

The value of x₁ is -40

The value of x₂ is -6880

From the question, we are to compute the values of x₁ and x₂ from the given iterative process

The definition of the iterative process is:

xₙ ₊ ₁ = 4xₙ(3 - xₙ)

From the given information,

x₀ = 5

To determine the value of x₁, we will substitute n = 0

xₙ ₊ ₁ = 4xₙ(3 - xₙ)

x₀ ₊ ₁ = 4x₀(3 - x₀)

x₁  = 4x₀(3 - x₀)

Substitute x₀ = 5

x₁  = 4(5)(3 - 5)

x₁  = 20(-2)

x₁  = -40

To determine the value of x₂, we will substitute n = 1

xₙ ₊ ₁ = 4xₙ(3 - xₙ)

x₁ ₊ ₁ = 4x₁(3 - x₁)

x₂ = 4x₁(3 - x₁)

Substitute x₁  = -40

x₂ = 4(-40)(3 - (-40))

x₂ = -160(43)

x₂ = -6880

Hence,

The value of x₁ is -40

The value of x₂ is -6880

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Answer:

=997

Step-by-step explanation:

46-15=31

31×32=992

992+5=997

Answer:  997

Step-by-step explanation:

Answer:

12 packages of water

5 packages of cheese sticks

Step-by-step explanation:

The LCM (least common multiple) of 5 and 12 is 60.

w = # of pkgs of water

c = # of pkgs of cheese sticks

5w = 12c = 60

w = 60/5 = 12

c = 60/12 = 5

The fraction model we are given can be represented by the expression: 7/1 ÷ 1/2

From the fraction model given, we can see that each of the shaded parts represents a half of the model parts.

Thus, we have in total:

(1/2) * 7 = 3¹/₂

This means the 7 parts shaded is being divided by 1/2

Therefore, we can easily conclude that the equation to represent a fraction model is expressed by the algebra form:

7/1 ÷ 1/2

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The required, experimental probability that a team will consist of two girls and a boy is 0.33. Option A is correct.

To find the experimental probability that a team will consist of two girls and a boy, we need to count the number of times that Kayla got a team with two girls and one boy and divide that by the total number of trials.

So, out of 50 trials, there were 17 trials where the team had two girls and one boy. Therefore, the experimental probability is:

17/50 = 0.34

Therefore, it is 0.34, which is closest to option (A) 0.33.

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The total cost paid on the condominium is $468,046.80.

The total cost means total expenditure incurred to produce some type of output.  The total cost is calculated as follows:

The total number of monthly payments is:

= 30 years x 12 months/year

= 360 months

The total amount paid towards mortgage is:

= 360 x $1175.13

= $423,046.80

The total cost of the condominium will be:

= Down payment + Total amount paid towards mortgage

= $45,000  + $423,046.80

= $468,046.80.

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The graph that represents the function f(x) = -2sin(x) +37 is graph D

The graph of the function f(x) = -2sin(x) +37 is a sinusoidal wave with an amplitude of 2 and a vertical shift of 37. The negative sign in front of the sine function indicates that the wave is inverted or reflected about the x-axis.

In this graph, the maximum value of the function is 39 (when x = 0) and the minimum value is 35 (when x = π).

In conclusion, the graph that represents the function f(x) = -2sin(x) +37 is graph D

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If company's marginal cost function is c(x)= 14 / √x, the total cost of producing the first 25 units is $10.67.

The marginal cost function is given as c(x) = 14 / √x, where x is the number of units produced.

To find the total cost of producing the first 25 units, we need to integrate the marginal cost function from x=0 to x=25, as follows:

Total cost = ∫₀²⁵ 14 / √x dx

We can use integration by substitution to solve this integral. Let u = √x, then du/dx = 1/(2√x), and dx = 2u du. Substituting these into the integral, we get:

Total cost = ∫₀⁵ √14/u du

This can be integrated using the power rule of integration. We have:

Total cost = 2√14 [[tex]u^{(3/2)[/tex]/3]₀⁵

Substituting back u = √x, we get:

Total cost = 2√14 [[tex](\sqrt{x})^{(3/2)[/tex]/3]₀²⁵

= 2√14 [[tex](\sqrt{25})^{(3/2)[/tex]/3 - [tex](\sqrt{0})^{(3/2)[/tex]/3]

= 2√14 (5/3)

= 10.67

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Answer:

C. complementary

Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.

The measure of the angle of the triangle ∠BCD = 13°

Given data ,

Let the triangle be represented as ΔBCD

Now , in triangle BCD, we are given the following angle measurements:

angle CDE = (9x - 12)°

angle BCD = (2x + 3)°

angle DBC = (3x + 5)°

From the exterior angle theorem , we get

∠CDE = ∠BCD + ∠DBC

On simplifying , we get

9x - 12 = 2x + 3 + 3x + 5

9x - 12 = 5x + 8

Subtracting 5x on both sides and adding 12 , we get

4x = 20

Divide by 4 on both sides , we get

x = 5

So , the measure of angle ∠BCD = 2(5) + 3

m∠BCD = 13°

Hence , the angle is m∠BCD = 13°

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The complete question is attached below :

In triangle BCD , BD is extended through point D to point E , ∠CDE = ( 9x - 12 )° , ∠BCD = ( 2x + 3 )°, and ∠DBC = ( 3x + 5 )°, find ∠BCD

Answer:

y = 1

Step-by-step explanation:

the absolute value function always gives a positive result , that is

| - a | = | a | = a

then

y = | 3 - x | ← substitute x = 4

y = | 3 - 4 | = | - 1 | = | 1 | = 1

The expression (7√98 + 3√242) divided by 6√50 simplifies to the fraction of 4/3.

To simplify the expression (7√98 + 3√242) ÷ 6√50, we need to rationalize the denominator. This means we need to simplify the expression in such a way that there are no radical signs in the denominator. To do this, we can use the fact that the product of a radical and its conjugate is a rational number.

First, let's simplify the terms under the radicals by factoring out the perfect squares:

√98 = √(49*2) = 7√2

√242 = √(121*2) = 11√2

Now the expression becomes:

(7√2 + 311√2) ÷ (6√(252))

= (7√2 + 33√2) ÷ (6*5√2)

= 40√2 ÷ 30√2

= 4/3

In conclusion, to simplify expressions involving radicals, we need to factor out perfect squares and use the property of the conjugate to rationalize the denominator.

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Based on this excerpt, the results that Ford helped achieve by implementing the described process was the development of an assembly line, capable of increasing productivity and production efficiency.

He was the founder of the Ford Company and the theory of Fordism, which consists of mass production, reducing costs, increasing efficiency through specialization of work.

Therefore, as we see in the excerpt, mass production generated the greatest speed and precision in each step of the work, increasing productivity and reducing losses and costs associated with production.

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The best answer to the given question is B.

When a variable "varies inversely as y," it means that as y increases, the variable decreases, and vice versa. This relationship is expressed mathematically as:

variable = k/y

where k is a constant.

When a variable "varies directly as y," it means that as y increases, the variable also increases, and vice versa. This relationship is expressed mathematically as:

variable = k*y

where k is a constant.

Option (a) does not provide any information about the relationship between variables. Option (c) and (d) provide incomplete information as they do not specify the variable that varies with y. Option (b) correctly explains the two types of relationships between variables and their mathematical expressions.

Option B is the best answer.

Kathy worked 9.14 hours for Job A and 18.86 hours for job B to make 186.10

Assuming hours of work for job A is x while that of job B is y

According to the given information, Kathy works a total of 28 hours per week

x + y = 28

Job A pays $6.10 per hour, and Job B pays $6.80 per hour, to make $184.10, we have the equation below

6.10x + 6.80y = 184

x + y = 28

6.10x + 6.80y = 184

solving simultaneously using calculator

x = job A = 9.143 = 9.14 (to 2 decimal places)

y = job B = 18.857 = 18.86 to 2 decimal places))

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1. intrest earned per year $116.25

2. total after 20 years $3,825

116x20= $2325

$1500+ 2325=3825

Answer:

Step-by-step explanation:

5 is greater than 0.004

Answer: 5 is greater

Step-by-step explanation:

Answer: Themba needs a total of 7.5  cups of yogurt to make 5 bowls of fruit dip, so 0.75 cup(s) will be needed

Step-by-step explanation:

your welcome.