Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.

Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

Pleaseeee helppp!! I answered all the other questions but I don't know what to do for this one...

Answer:

16

Step-by-step explanation:

12-(-4)

12+4

16

This is the answer you looking for.

Using the strategy below, we can identify the lightest heart (the pure-hearted person) using the balance only twice, as required by the puzzle.

we can use the following strategy:

Divide the 8 people into 3 groups of 3, and leave 2 people aside.

Weigh any two of the three groups against each other using the balance.

If the two groups weigh the same, then the pure-hearted person must be in the remaining group of two that we left aside. Weigh one of the remaining people against another one from this group.

If they weigh the same, then the remaining person is the pure-hearted one. If one is heavier, then that person is a sinner, and the lighter one is the pure-hearted person.

If the two groups from step 2 are not of the same weight, then the pure-hearted person must be in one of these two groups. Take any two people from the group that weighs more and weigh them against each other.

If they weigh the same, then the pure-hearted person is in the remaining group that was not weighed, and we can find them by weighing one person from that group against another.

If one of the two people weighed in step 5 is lighter, then that person must be the pure-hearted person. If they are the same weight, then the pure-hearted person is in the other group that was not weighed, and we can find them by weighing one person from that group against another.

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

The solution to the system of linear equations y = 2x and y = x - 2 is (2, 0).

The inverse of the function [tex]y=e^{x-4}[/tex] is obtained as y = log (x) + 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function is given as - [tex]y=e^{x-4}[/tex]

A function g is the inverse of the function f if for y = f(x) and x = g(y).

[tex]y=e^{x-4}[/tex]

Replace x with y.

[tex]x=e^{y-4}[/tex]

Now solve for y -

y = log (x) + 4

Therefore, the inverse is y = log (x) + 4.

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Find the inverse of [tex]y=e^{x-4}[/tex].

The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

Answer:

Step-by-step explanation:

Find the sum: 9/10 9/100

A: 18/100

B: 90/100

C: 18/10

D; 99/100

9/10 = 90/100

so

90/100 + 9/100 = 99/100

Answer: D 99/100 I hope this helps

Step-by-step explanation:

9/10+9/100

Write all numerators above the least common denominator 100

90+9/100

Add the numbers 90+9 which would will give you your answer

99/100

Answer:

Step-by-step explanation:

140 cm to inches is 55.1181 or roughly 55 inches.

Over the interval [-3, 1], the local minimum is 0,  Over the interval [-1, 0], the local maximum is 4.39,  Over the interval [0, 3], the local minimum is -32.

By plot the function on a graphing tool and visually identify the local minimum and maximum values over the specified intervals .A function that is continuous for an interval [a,b], a is not equal to b, then there is a local maximum and minimum if:

Local maximum: f(d) > f(x), ∀ x ≠ d, a ≤ d ≤ b

Local minimum: f(c)< f(x), ∀ x ≠ to c, a≤c≤b

we can proceed to solve each question:

Over the interval [-3, 1], the local minimum is 0,

since f(-2) < f(x), ∀ x ≠ -2,-3 ≤ x ≤ -1 .

Over the interval [-1, 0], the local maximum is 4.39,

since f(-0.8) > f(x), ∀ x ≠ -0.8, -1 ≤ x ≤ -1.

Over the interval [0, 3], the local minimum is -32,

since f(-2) < f(x), ∀ x ≠ -2.0 ≤ x ≤3.

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Answer:

0

4.39

-32

Step-by-step explanation:

on edge

The 1.2 meter is 3.93701 feet.

The 1 meter is  3.28084 feet.

1.2 meter = 1.2*3.28084=3.93701

Since 1983, the meter has been internationally defined as the length of the path traveled by light in a vacuum in 1/299,792,

58 seconds. This definition can be applied easily and precisely with modern techniques, and the speed of light is considered a universal constant, making it an ideal  basis for a standard of length.

foot, plural of feet, measured by a number of  ancient, medieval and modern linear measurements (usually 25–3

cm) based on the length of a human foot, used exclusively in English-speaking countries, where it usually consists of 12 inches. , or a third of a yard.

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The optimal amounts of Gatorade and cookies to buy are 4 bottles of Gatorade and 4 boxes of cookies, which gives a total cost of 4(1) + 4(2) = 12, the maximum possible utility for this budget

To find the optimal amounts of Gatorade and cookies to buy in order to maximize utility with a budget of $12, we can use the method of Lagrange multipliers.

Let x be the number of bottles of Gatorade to buy, and let y be the number of boxes of cookies to buy. We want to maximize the utility function:

U(x,y) = xy

Subject to the budget constraint:

1x + 2y = 12

To apply the method of Lagrange multipliers, we form the Lagrangian function:

L(x,y,λ) = xy - λ(1x + 2y - 12)

Taking partial derivatives of L with respect to x, y, and λ and setting them equal to zero, we get:

δL/δx = y - λ= 0

δL/δλ  = x - 2λ= 0

δL/δλ = 1x + 2y - 12 = 0

Solving these equations simultaneously, we get:

x = 4

y = 4

λ = 2

Hence, the optimal amounts of Gatorade and cookies to buy are 4 bottles of Gatorade and 4 boxes of cookies.

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The equation for the temperature  with respect to x minutes is

y(x)=  580 - 56x

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The temperature at any  instant of time in minutes( x)  is given by

y(x)=  initial temperature  - (decrement rate * number of minutes)

=>  y(x)=  580 - 56x

The equation for the temperature  with respect to x minutes is

y(x)=  580 - 56x

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The correct statements are (a) and (d). which are the graph is reflected over the x - axis and the the graph is shifted down 1 unit.

a. The graph is reflected over the x-axis.

This statement is true. The negative sign in front of the sine function reflects the graph of the parent function over the x-axis.

b. The frequency decreases by a factor of 1/4.

This statement is false. The coefficient in front of the x in the sine function determines the frequency of the wave. Since there is no coefficient in front of x in this case, the frequency of the wave remains the same.

c. The phase shift is 1/4 unit to the right.

This statement is false. The phase shift determines how the graph is horizontally shifted left or right. However, there is no horizontal shift in this case, so the phase shift is 0.

d. The graph is shifted down 1 unit.

This statement is true. The negative sign in front of the sine function also shifts the graph down by 1 unit.

e. The graph is reflected over the y-axis.

This statement is false. A reflection over the y-axis would require a negative sign in front of x, not in front of the sine function.

f. The frequency increases by a factor of 4.

This statement is false. As mentioned in (b), there is no change in frequency in this case.

Therefore, the correct statements are (a) and (d).

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

The value of 1 dollar is 0.94 Euro

The United States dollar (symbol: $; code: USD; also abbreviated US dollar or US dollar to distinguish it from other dollar-denominated currencies; called dollar, US dollar, American dollar or colloquially alone) is the  currency of the United States dollar. United States and several other countries. The Coinage Act of 1792 established the American dollar along with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of dollar and cent coins. US banknotes are issued as Federal Reserve notes, often called greenbacks because they are predominantly green.

US monetary policy  is managed by the Federal Reserve System, which serves as the nation's central bank.

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The volume of the empty portion of Container B is approximately 47.1 cubic feet, to the nearest tenth of a cubic foot.

The formula V = r2h, where r is the cylinder's radius and h is its height, can be used to determine a cylinder's volume.

Water in Container A has a volume of:

V A is equal to (3 ft)2(5 ft) 141.37 ft3.

This amount of water will be moved to Container B, which has a 15-foot height and a 2-foot radius. Container B contains a total of:

V B = (1.5 x 2 x 15) x 188.5 ft 3

The volume of the empty space in Container B after the water has been pumped from Container A to Container B can be estimated by deducting the volume of the water from the overall volume of Container B:

47.1 ft3 = V empty = V B - V A

As a result, to the nearest tenth of a cubic foot, the volume of Container B's empty space is roughly 47.1 cubic feet.

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The area of the shaded part in the circle will be 10840.99 ft².

The circumference = 2 * pi * r = 221.056

Use this fact to find r

2*pi*r =  221.056

Divide by pi

2*r =  221.056 / 3.141

2*r =  70.378      

Divide by 2

r = 35.19

Now that you have the radius of the inner circle, use it to find the area.

Area = pi * r^2

Area = 3888.37

Now we need the radius of the outer circle

r = 35.19 + 33.3

r = 68.49

Find the area of the other circle

Area = pi * 68.49^2

Area = 14729.36

Finally the area of the shaded region is the area of the large circle - the area of the small circle

Area of the shaded area = 14729.36- 3888.37

Area of the shaded area = 10840.99 to the nearest hundredth.

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The word "ml" stands for millilitre, a unit of measurement used to gauge a liquid's capacity.

One millilitre, or 0.001 litres, is equal to one thousandth of a litre. In scientific and medical settings, the volume of drugs, syrups, or even other liquids is frequently measured in millilitres.

On either hand, "milligrammes" (mg) is a weight or mass unit which is used to determine how much of a substance is present. One milligramme, or 0.001 grammes, is equivalent to one thousandth of a gramme. Milligrams are frequently used to express the percentage of a drug in a solution or to quantify the dosage of pharmaceuticals.

The conversion of ml to milligrams depends on the density of the substance being measured. Density is the measure of how much mass is contained in a given volume. Therefore, if you know the density of the substance, you can use it to convert ml to milligrams.

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The mode would remain the same because 24 is already a part of the set.

Mode is a measure of central tendency, or an average, in a set of numerical data. It is the most frequently occurring value in a set of data.

For example, consider the following set of numbers: 1, 2, 2, 3, 3, 3, 4, 4, 5. In this set, 3 is the mode since it appears most often. It occurs three times, while the other numbers occur fewer times.

Mode can be used with both continuous and discrete data. Continuous data can be divided into classes, and the mode is the most frequent class. For example, if the numbers above were in the following classes: 1-2, 3-4, 5-6, then 3-4 would be the mode since it occurs the most often.

Mode can also be used with categorical data. In this case, the mode is the most frequent category.

For example, if the data set consists of the categories blue, green, and red, and blue occurs most often, then blue is the mode.

24 is the most frequently occurring number in the set of 24, 58, 24, 24 53. So it is the mode. It appears 3 times, which is more than any other number.

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The least common denominator is 4x^2.

Answer:

Step-by-step explanation:

the least common denominator is 4 x^2

(x+1)/4x

3(x+1)/2x^2

To find the common denominator, find the prime factors of each denominator

4x =2*2*x

2x^2 = 2*x*x

We need to take the greatest number of each term

2:  We have two 2's in the first term and one 2 in the second term so we will take two 2's

x: we have one x in the first term and two x's in the second term so we take two x's

common denominator; 2*2*x*x

                                     4x^2

The factored form of the polynomial 7x³ + 14x² + 3x + 6​ is ( x + 2 )( 7x² + 3 ).

Given the polynomial in the question;

7x³ + 14x² + 3x + 6​

To completely factor, we factor out the greatest common factor from each group.

First, group the first two terms and the last two terms.

( 7x³ + 14x² ) + ( 3x + 6 ​)

Now, factor out the greatest common factor from each group.

( 7x³ + 14x² ) + ( 3x + 6 ​)

7x²( x + 2 ) + ( 3x + 6 )​

7x²( x + 2 ) + 3(x + 2 )

Hence, we have;

( x + 2 )( 7x² + 3 )

Therefore, the factored form is ( x + 2 )( 7x² + 3 ).

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The measurement of the LM will be 42.0

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b² = h² -p²

given KM = 52, NL = 33

So the triangle MLN

LM = √(33²+26²) = 42.0

Hence The measurement of the LM will be 42.0

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well, we know the points are all colinear, so the slope from the 1st to the 2nd, will be the same as from the 2nd to the 3rd, same exact slope, hell let's check what's up

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ 3 }{ 1 } \implies 3[/tex]

ahaaa! that means that the slope of (3 , 8) and (-1 , y) is 3, hmmmm

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{y}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{3}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 3 }\implies \cfrac{y-8}{-4}=3 \\\\\\ y-8=-12\implies \boxed{y=-4}[/tex]

Answer:

The solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 1.76 and x ≈ 7.85.

Step-by-step explanation:

f(x) = 0.15x³ - 2x² + 7x - 3.3

g(x) = 1.5|x - 7.3|

To solve the equation, we can set the two functions equal to each other and then solve for x:

0.15x³ - 2x² + 7x - 3.3 = 1.5|x - 7.3|

We can split this equation into two cases, depending on the sign of x - 7.3:

Case 1: x - 7.3 ≥ 0

In this case, we have:

0.15x³ - 2x² + 7x - 3.3 = 1.5(x - 7.3)

0.15x³ - 2x² + 7x - 3.3 = 1.5x - 10.95

0.15x³ - 2x² + 5.5x + 7.65 = 0

We can solve this cubic equation by using numerical methods, such as the Newton-Raphson method or the bisection method. One solution to this equation is x ≈ 1.76.

Case 2: x - 7.3 < 0

In this case, we have:

0.15x³ - 2x² + 7x - 3.3 = -1.5(x - 7.3)

0.15x³ - 2x² + 7x - 3.3 = -1.5x + 10.95

0.15x³ - 2x² + 8.5x - 14.25 = 0

Again, we can solve this cubic equation by using numerical methods. One solution to this equation is x ≈ 7.85. Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 1.76 and x ≈ 7.85.

Answer:

x = -4.05, x = 2.15, and x = 4.96.

Step-by-step explanation:

To find the solutions to the equation f(x) = g(x), we need to substitute the expressions for f(x) and g(x) and solve for x.

0.15x³ - 2x² + 7x - 3.3 = 1.5x - 7.3

0.15x³ - 2x² + 5.5x + 3 = 0

We can solve this equation using numerical methods, such as graphing or using a calculator, to find the solutions to two decimal places. One possible method is to use a graphing calculator and graph the function y = 0.15x³ - 2x² + 5.5x + 3, and then use the intersect function to find the x-values where the function intersects the line y = 1.5x - 7.3.

Using this method, we find that there are three solutions to the equation, to the nearest hundredth: x = -4.05, x = 2.15, and x = 4.96.

Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x = -4.05, x = 2.15, and x = 4.96.

The value of x is 20 using the extension of Triangle Proportionality Theorem.

Transversal lines are lines that passes intersects the two lines on a plane in two different points.

Here given three parallel lines and two transversal lines cutting these parallel lines.

By the extension of Triangle Proportionality Theorem, we have "When two or more lines which are parallel to each other are cut by two transversals, then the parallel lines divide the transversals proportionally."

Applying the theorem here,

4x / 5x = (6x - 8) / (8x - 20)

4 / 5 = (6x - 8) / (8x - 20)

Cross multiplying,

4 (8x - 20) = 5 (6x - 8)

Using the distributive property,

32x - 80 = 30x - 40

2x = 40

x = 20

Hence the value of x is 20.

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Therefore , the solution of the given problem of expression comes out to be the numbers we need to drag to complete this exercise are -25, since -5 multiplied by 5 gives us -25.

Addition, multiplication, and variables  mathematics are required. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

Given :

To factor the expression -5g + 15h using a negative factor, we can rewrite it as:

-5(g - 3h)

Now, we can see that the expression has been factored using a negative factor (-5). We can check this by distributing the factor back and verifying that it gives the original expression:

-5(g - 3h) = -5g + 15h

So the numbers we need to drag to complete this exercise are -25, since -5 multiplied by 5 gives us -25.

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Answer: 96

Step-by-step explanation:

Answer:

You are correct! The actual distance, in miles, between Zionsville and Lafayette is 96 miles. This is calculated by multiplying 8 inches (the distance on the map) by 12 miles (the scale of the map), which results in 96 miles.

$25 hourly is $52,000 per year.

To convert an hourly rate to an annual salary, we need to multiply the hourly rate by the number of hours worked per week, then by the number of weeks worked per year.

Assuming a standard work week of 40 hours and 52 weeks in a year, we can calculate the annual salary for an hourly rate of $25 as:

Annual salary = Hourly rate x Hours per week x Weeks per year

Annual salary = $25/hour x 40 hours/week x 52 weeks/year

Annual salary = $52,000

Therefore, an hourly rate of $25 is equivalent to an annual salary of $52,000.

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The factorial of a number n is the product of all positive integers up to and including n

The factorial function is typically represented using the "!" symbol, such that n! represents the product of all positive integers up to and including n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To represent the factorial function using product notation, we can write:

n! = ∏_{i=1}^n i

This means that we take the product of all positive integers from 1 to n, which is equivalent to computing n!. For example, using this notation, we can write:

5! = ∏_{i=1}^5 i = 1 x 2 x 3 x 4 x 5 = 120

Note that the product starts at i=1 and goes up to n, which includes all the positive integers we want to multiply together.

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Answer:

1) What are your options?

2) 847,200

3) 6.7 × 10^5

Step-by-step explanation: You always move the decimal until you get to the first digit after zeroes and then x 10 and the power is how many times it took to place the decimal in front of the number.