Find the solution of the exponential equation
5^-x/16=5
in terms of logarithms, or correct to four decimal places.

x= ------------

here is the picture if you need it.

The solution is: the values of x and y is 32° and 51° respectively.

Using the triangle theorem, the values of x and y is 32° and 51° respectively

From △MNP

∠M + ∠N + ∠P = 180° (Sum of interior angles in a triangle)

N = 180 - (142 + 24)

N = 180 - 168

N = 14°

Equate the expression :

2x - 50 = 14

2x = 14 + 50

2x = 64

x = 64 / 2

x = 32°

From ; 2x - y = 13 _____(1)

Substitute x = 32 into the expression ;

2(32) - y = 13

64 - y = 13

64 - 13 = y

51° = y

Therefore, the values of x and y is 32° and 51° respectively.

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complete question:

Find the value of x and y. Triangle MNP = triangle TUS

Answer:

Step-by-step explanation:

4x/3 + x/6 =6

get a common denominator first

8x/6 + x/6 =6

then add

9x/6 = 6

multiply by six

9x = 36

divide by 9

x= 4

Part A: After 15 days will have 32,768 magical beans.

Part B: As the value of the magical beans is less than the value of the car the trade does not make sense at least not from a financial perspective. B NO.

Part C: We would need at least 17 days for the number of magical beans to exceed the value of the car. C MAYBE?.

Based on the given information can observe that the number of beans doubles every day.

So, after 15 days will have 2¹⁵ = 32,768 magical beans.

The value of the 32,768 magical beans would be:

32,768 beans × $0.50/bean

= $16,384

Part C:

Let us assume that after 'n' days, the number of beans would be equal to or greater than the value of the car.

Value of the car in terms of magical beans = $65,000/$0.5 per bean

= 130,000 beans

Now, we can set up an equation based on the doubling of beans:

2ⁿ >= 130,000

Taking the logarithm base 2 on both sides, we get:

n × log2(2) >= log2(130,000)

n >= log2(130,000)

n >= 16.98

We would need at least 17 days for the number of magical beans to exceed the value of the car.

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The sentence given in the question does not include a participial phrase. Hence, correct option is False

The sentence "The picture frame held a picture of our family on vacation" does not include a participial phrase.

A participial phrase is a phrase that acts as an adjective. In this sentence, the phrase "on vacation" is an adjective phrase that describes the noun "family." However, it is not a participial phrase because it is not formed from a verb.

A participle is a verb form that can be used as an adjective. In this sentence, the verb "hold" is not used as an adjective.

Therefore, the phrase "on vacation" is not a participial phrase.

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Answer:

By substituting the values of A, C, and D the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

Step-by-step explanation:

From the given information, we have;The vertical stretch of the sine function = 3 × The parent function∴ A = 3Given that the horizontal shift left = π/2 units, (from an online source with similar question)The vertical shift down = 4 unitsThe given function, g is g(x) = A·sin(x + C) + DWhere;A = The amplitude = The maximum displacement from the rest or equilibrium position = 3C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)Therefore, the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

answer

(z+2)(z-2)

steps

its a rule

a²-b²= (a+b) (a-b)

vedantu

The given image is a parallelogram, because the two lines are Parallel to each other implying that they will never cross each other

Based on the question above,  the coordinates of the figure are:

O = (0,0)

P = (a, b)

S = (a + c, b)

T = (c,0)

Note that the vertices O and T and they can be seen on the same horizontal level, due to the fact that they have the same y-coordinate and can be used also for vertices P and S

The length of the sides by distance formula will be:

PS = c

OT = c

So this implies that the opposite sides are parallel and congruent. Therefore, the image is a parallelogram

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The distance between point A (2, 4) and point B (-2, 1) is equal to 5 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-2 - 2)² + (1 - 4)²]

Distance = √[(-4)² + (-3)²]

Distance = √[16 + 9]

Distance = √25

Distance = 5 units.

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Complete Question:

3. Find the distance from point A to B.

A (2, 4) B (-2, 1) C(2, -1)​ D (0, 0)

The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C

Selection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.

In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.

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The correct option number that is NOT a good method for solving the problem is: Option C: 20.48.[c-0.08.6-c0] (45000. ((0.08)(6)=0.08. t)at 45000-(00:48) Il 6 -0.08- 1) at -562500- 20.48.[c-0.08.6-c0]

The problem requires finding the Accumulated Total Value of the income stream generated by Hank's Auto Wash over six years, assuming the income is reinvested at an interest rate of 8% per year, compounded continuously. To solve the problem, we need to use the formula for continuous compounding:

A = P[tex]e^{(rt)[/tex]

Where A is the accumulated total value, P is the initial principal (in this case, the annual revenue of $45,000), e is the mathematical constant e (approximately 2.71828), r is the interest rate (0.08), and t is the time period (6 years).

Plugging in the values, we get:

A = 45000[tex]e^{(0.086)[/tex]

A = 45000[tex]e^{0.48[/tex]

A = 450001.6186

A = $72,838.50

Therefore, the accumulated total value of the income stream at the end of 6 years is $72,838.50.

The method that is NOT a good method for solving the problem is "45000.20.48.[c-0.08.6-c0]." This is not a valid formula for calculating the accumulated total value of an income stream under continuous compounding.

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Answer: 2(x − 6)(x − 3) is the answer

Step-by-step explanation:

The calculated value of the period of the function is 6

From the question, we have the following parameters that can be used in our computation:

The equation, f(x) = 2cos(2π/6(x + 4)) +3

A sinusoidal function is represented as

f(x) = acos(2π/b(x + c)) + d

Where the period is B

When the equations are compared, we have

2π/b = 2π/6

This gives

b = 6

Hence, the period of the function is 6

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Complete question

Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?

After considering all the given data we come to the conclusion that the gross income of the given individual is = $2640.

The individual's gross income per month can be evaluated as follows
Gross Income = Hourly rate × Hours worked per week × Weeks per month
Staging the values given in the problem statement:
Gross Income = 16.50 × 40 × 4 = $2640
The FICA tax is a mixture of Social Security and Medicare taxes, here it involves the total 15.3% of earnings. The individual is  responsible for half of the total bill (7.65%), which involves a 6.2% Social Security tax and 1.45% Medicare tax on the individual's earnings.
The Federal Tax withholding is 10% of the individual's gross income per month.
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Answer: Obtuse triangle? The line marked with O and E is more than 90 degrees

Step-by-step explanation:

Answer:

The answer is 49

Step-by-step explanation:

We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.

We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:

14/42 = 0.3333

We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:

0.3333 * 147 = 49

Therefore, the best estimate for the number of dogs that suffer from the disease is 49.

Answer: 15/38 or 0.39473684210526315789473684210526

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)

To answer these questions, I would need more information about the population being referred to. Specifically, I would need to know the number of residents who have only completed high school and are under age 50, as well as the total number of residents who have only completed high school. I would also need to know the number of residents aged 20-29 who have completed only high school or just some college, as well as the total number of residents aged 20-29.

Do you have this information available?

Answer:

D=2, 3, 5, 6, 7, 8, 9,

Step-by-step explanation:

btw can i js get 1  brainly?

{2,3,5,6,7,8,9}

The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.

Answer:

(-1,1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

equation form:
x=-1, y=1

have a great day and thx for your inquiry :)

By substituting each of the provided options into the given system of linear equations, it is revealed that the ordered pair (-1, 1) is a valid solution for both the equations.

The correct answer is (-1, 1)

In mathematics, a system of linear equations consists of multiple linear equations with the same variables. These equations describe various relationships among these variables, typically representing lines in a multi-dimensional space. Solving such systems involves finding values for the variables that satisfy all equations simultaneously. Methods like substitution, elimination, or matrix algebra can be used to solve these systems. These systems are fundamental in fields like physics, engineering, economics, and computer science for modeling and solving real-world problems involving multiple interconnected variables.

We can solve this problem by substituting values from the given options into the equations and checking for which option both equations are valid. The system of linear equations is: x + 4y = 3 and y = -4x - 3.

Therefore, the ordered pair that is a solution to the system of linear equations is (-1, 1).

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Factoring in the dimensions , Design 1 would be the best recommendation because it requires less material and can hold a slightly larger volume of sand in comparison to Design 2.  

For Design 1:

Dimensions: 3 m x 3 m x 30 cm

We find the total area:

Two faces measures 3 m x 3 m = 9 m² each for the bottom and top

Two faces measures 3 m x 30 cm = 0.9 m² each for back and front

Two faces measures 3 m x 30 cm = 0.9 m² each

Therefore the total area of materials needed for Design 1 is found as

= 9 m² + 9 m² + 0.9 m² + 0.9 m² + 0.9 m² + 0.9 m² = 21.6 m²

Design 2:

Dimensions: 3.25 m x 3.25 m x 25 cm

In the same way, we find  the area of materials needed for Design 2:

Total area of materials needed for Design 2 = 10.5625 m² + 10.5625 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² = 24.375 m²

Design 1 volume is :

Volume = Length x Width x Height

Volume of sand for Design 1 = 3 m x 3 m x 0.3 m = 2.7 m³

Design 2 volume is :

Volume of sand for Design 2 = 3.25 m x 3.25 m x 0.25 m = 2.40625 m³

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Answer:

Median, because Sunny Town is symmetric.

Answer:

  302 m²

Step-by-step explanation:

You want the area of the figure composed of a triangle and rectangle.

The formulas for the areas of the parts are given in the problem statement.

The base length of the triangle is (18 m - 5m - 5 m) = 8 m. Then its area is ...

  A = 1/2bh

  A = 1/2(8 m)(8 m) = 32 m²

The area of the rectangle is ...

  A = LW

  A = (18 m)(15 m) = 270 m²

The area of the figure is the sum of the areas of its parts:

  A = (triangle area) + (rectangle area)

  A = 32 m² +270 m² = 302 m²

The area of the figure is 302 m².

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The interest Pedro will have to pay is $5200

From the question, we have the following parameters that can be used in our computation:

Principal = $32.500

Rate = 4% simple interest

Time = 4 years

The formula of simple iinterest is

I = Principal * Rate * Time

substitute the known values in the above equation, so, we have the following representation

I = 32500 * 4% * 4

Evaluate

I = 5200

Hence, Pedro have to pay $5200 as interest

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The measures of the marked angles in the figure are:

x = 0.8°

6x + 8° = 12.8°

x + 12° = 12.8°

We have that:

x + 12° and 6x + 8°.

We equate the expression: 6x + 8° = x + 12°

We then  solve for x:

6x - x = 12° - 8°

5x = 4°

We then divide  both sides by 5:

x = 4° / 5

x = 0.8°

We get the  measure of the marked angle for

6x + 8°:

6(0.8°) + 8° = 4.8° + 8° = 12.8°

We also get the measure of the marked angle as:

x + 12°:

0.8° + 12° = 12.8°

In conclusion, an  angle is formed when two straight lines or rays meet at a common endpoint.

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Rational square roots: √225, √81, √576, √36, √441, √324

Irrational square roots: √300, √120, √12, √50, √200

Let's determine whether each square root is rational or irrational:

√225 = 15. This is a rational number since it can be expressed as a fraction of two integers (15 = 15/1).

√300 ≈ 17.32050808. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√120 ≈ 10.95445115. This is also an irrational number for the same reasons as above.

√81 = 9. This is a rational number since it can be expressed as a fraction of two integers (9 = 9/1).

√576 = 24. This is a rational number since it can be expressed as a fraction of two integers (24 = 24/1).

√36 = 6. This is a rational number since it can be expressed as a fraction of two integers (6 = 6/1).

√12 ≈ 3.464101615. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√441 = 21. This is a rational number since it can be expressed as a fraction of two integers (21 = 21/1).

√50 ≈ 7.071067812. This is an irrational number for the same reasons as above.

√324 = 18. This is a rational number since it can be expressed as a fraction of two integers (18 = 18/1).

√200 ≈ 14.14213562. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

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Answer:

Step-by-step explanation:

The sum of three angles in a triangle is equal to 180°.

(1) 40°, 90°, 60°

40 + 90 + 60 = 190. Therefore, it could not be the measures of the three angles if a triangle.

(3) 120°, 30°, 20°

120 + 30 + 20 = 170. Therefore, it could not be the measures of the three angles if a triangle.

(2) 50°, 100°, 30°

50 + 100 + 30 = 180. Therefore, it could be the measures of the three angles if a triangle.

(4) 70°, 70°, 60°

70 + 70 + 60 = 200. Therefore, it could not be the measures of the three angles if a triangle.

Answer:

Dependent and Independent could be used like a ride on a bike, or even traveling to a friend's house. The dependent variable depends on the independent variable, so let's say I biked at a speed of 7 min per hour and I traveled 42 miles. The independent variable is minutes, because distance depends on time.

Step-by-step explanation:

A cylinder has two types of edges: the curved edges and the top and bottom edges.

A cylinder is a three-dimensional geometric shape that consists of two circular bases and a curved surface connecting the bases. The circular bases have a certain number of edges, depending on the number of sides each base has.

Since a circle has no straight edges, the circular bases of a cylinder do not contribute any edges.

The curved surface of a cylinder has no straight edges either, as it consists of a smooth, continuous surface.

Therefore, the curved surface does not contribute any edges to the cylinder.

The only remaining edges are the top and bottom edges of the cylinder. Each base of the cylinder has a single edge that runs along the circumference of the circular base.

Hence, the cylinder has two edges from its top and bottom bases.

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The blue rectangular prism have a greater volume of 36 cubic units which makes the option C correct.

The volume of a rectangular prism is calculated by multiplication of its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.

volume of red rectangular prism = 4 units × 3 units × 2 units

volume of red rectangular prism = 24 cubic units

volume of blue rectangular prism = 4 units × 3 units × 3 units

volume of blue rectangular prism = 36 cubic units

Therefore, the blue rectangular prism have a greater volume of 36 cubic units

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