Find the length and width of the actual room, shown in the scale drawing. Then find the area of the actual room. Round the final answer, if necessary, to the nearest tenth.

The length c of the right angle triangle is 9 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.

The sides of a right angle triangle can be found using trigonometric ratios as follows:

Therefore,

sin 60° = opposite / hypotenuse

where

opposite side = c

hypotenuse side = 6√3 ft

Hence,

sin 60° = c / 6 √3

cross multiply

c = 6√3 × sin 60

c  = 6√3 × √3 / 2

c = 6 × 3 / 2

c = 18 / 2

Therefore,

c = 9 units

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Answer:

  2m⁴ +0m³ -3m² +0m +7

Step-by-step explanation:

You want the index form of 2m⁴-3m²+7.

The index form of a polynomial has terms with all indices present in decreasing order, using 0 coefficients where necessary.

The given polynomial is missing indices 3 and 1, so we add those with coefficients of 0:

  2m⁴ +0m³ -3m² +0m +7

Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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The actual time is 6:30.

Since Sri's car clock is not accurate, it is gaining time at a constant rate. By knowing that at 12:00 noon the car clock and the watch were in sync, we can estimate that the car clock is gaining 5 minutes per hour.

Therefore, when Sri looks at his car clock at 7:00 and his watch is missing, we can calculate that the actual time is 6:30. This is done by subtracting the 5-minute difference in time between the car clock and the watch at 12:30 (12:35 car clock, 12:30 watch) from the 7:00 car clock. The result is 6:30.

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In a reaction the amount f a substance which react with another substance is known as it's equivalent.

The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."

It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.

The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.

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The expression (x - 8) is not the factor of the polynomial x⁶ - 64x⁴ + x² - 7x - 51.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ x⁶ - 64x⁴ + x² - 7x - 51

If the value of the polynomial is zero at x = 8. Then (x - 8) will be the factor of the polynomial.

At x = 8, the value of the polynomial is given as,

⇒ (8)⁶ - 64(8)⁴ + (8)² - 7(8) - 51

⇒ 262,144 - 262,141 + 64 - 56 - 51

⇒ - 43

The expression (x - 8) is not the factor of the polynomial x⁶ - 64x⁴ + x² - 7x - 51.

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The estimated solution of the system 3x + y = 10 and y = 6x + 1 is (1, 7)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the linear equation:

3x + y = 10

y = -3x + 10   (1)

y = 6x + 1     (2)

Subtracting equation 2 from 1 to solve using elimination method gives:

0 = -9x + 9

9x = 9

x = 1

put  x = 1 in eqn 2:

y = 6(1) + 1

y = 7  

The solution is (1, 7)

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No, horizontal asymptote is not represented by y- axis it is represented by the x -axis.

Therefore, the horizontal asymptote is not represented by the y-axis, it is represented by the x-axis.

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Answer:

alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25

Step-by-step explanation:

Answer:

-4 + 6x.

Step-by-step explanation:

8 - 3(4 - 2x)

= 8 - 12 + 6x

= -4 + 6x.

The correct answer is 6x - 4

Simplify :

8 - 3(4 - 2x)

8 - (12 - 6x)               (using BODMAS rule)

8 - 12 - (-6x)            

( 8 -12) + 6x        

-4 + 6x

= 6x - 4

Approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

In the given question, a wheel having a diameter of 50 cm.

If the elf travels a distance of 25 meters then we have to find how many revolutions did the wheel go through.

Since we have the wheel's diameter, we can determine the radius of the wheel. As we already know, the length of a wheel's revolution is equal to its circumference, which is a circle with a diameter of 2πr.

We will now enter the radius value into the algorithm to determine how many revolutions the wheel must make. To reach the desired result, divide the total distance by the distance covered in one revolution to determine the number of revolutions needed to travel 25 m.

r = [tex]\frac{50}{2}[/tex] = 25 cm

The radius of the wheel is 25 cm.

Now we put the value of r in the formula of circumference.

2πr = 2π×25

2πr = 50π cm

Total distance is 25 m. So we convert m in cm by multiplying the 100.

Now the total distance is 2500 cm.

2500 = n × 50π

Now putting the value of π = 3.14

2500 = n×50 × 3.14

2500 = n×157

Divide by 157 on both side, we get

n = 15.924

n = 16(approx)

Hence, approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

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Using the regression concept to find the equation and applying derivative, The rate of change is 10.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. The dependant variable's predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. 

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

from the given data,

y= a + bx is our regression line.

a=8 and b =10

y=8+10x is the line.

derivate the line , we get,

[tex]\frac {dy}{dx} = 10[/tex]

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The sales tax rate on the item = 8%

We know that the sales tax is nothing but the purchase price times the percentage of tax.

An item costs $430 before tax.

This means, the purchase price is 430 dollars.

The sales tax is $34. 40

To find: the sales tax rate as a percentage

First we find a ratio of the sales tax to the cost of the items before tax.

Sales tax / Pre-tax value of item = (34.40) / 430

Now we write a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

i.e., (34.40) / 430 = sales tax percent / 100

So, the sales tax percent  = 8%

Therefore, the sales tax is of 8%

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Audrey and Billy are as far as 367 meters apart.

The displacement of an object is its distance covered or moved in a specific direction. Displacement is an example of vector quantity.

A vector quantity is generally any type of quantity which can be expressed in magnitude and direction. Some examples include: weight, displacement, acceleration, force, etc.

Since Audrey walked 285 meters west and Billy walked 213 meters south from the same starting location, then we can determined the distance far apart by applying the Pythagorean theorem.

So that,

/hyp/^2 = /opp/^2 + /adj/^2

Let their distance apart be represented by s,

s^2 = 231^2 + 285^2

      = 53561 + 81225

s  = (134586)^1/2

s = 366.86

Audrey and Billy are as far as 367 meters apart.

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1) 1000 AA Batteries in one Case.

2) 10,000 AA Batteries in One carton.

3) 100,000 AA Batteries in 10 cartons.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The Store sells AA batteries in the order below:

⇒ 10 batteries in 1 packages

⇒ 10 packages in 1 box

⇒ 10 boxes in 1 case

⇒ 10 cases in 1 Carton

1) We want to determine how many AA batteries are in 1 Case;

Using Multiplication

Number of AA Batteries in 1 Case = 10 Batteries × 10 package × 10 box

                                                    = 1000 AA Batteries

2) We want to determine how many AA batteries are in 1 Carton;

From Part (a),

There are 1000 AA Batteries in 1 Case.

Since, There are 10 Cases in 1 carton.

Number of Batteries in 1 carton = 10 × 1000

                                                 = 10,000 AA Batteries

3) 10 Cartons

⇒ 1 carton = 10000 AA Batteries

Therefore, We get;

⇒ 10 Cartons = 10 × 10000

                    = 100,000 AA Batteries

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Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

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The correct option is option (E) 15

To calculate the number of cookies they will need, they first determine the number of students who will be attending the meeting. Since attendance is down by 25%, the number of students attending is 108*(1-0.25) students.

=108 students * 0.75 = 81 students.

To figure out the number of cookies they will need, they multiply the number of students by the number of cookies per student, which is 81 students * 2 cookies= 162 cookies.

Since each recipe makes 15 cookies, they need to make 162 cookies / 15 cookies/recipe = 10.8 recipes.

Since they cannot make partial recipes, they round up and make 11 recipes of cookies for their smaller party.

As 11 is not a given  option, we consider the option which is greater than 11, which is 15.

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Point O is where the diagonals in a rhombus MNLP intersect. If the side is 8 inches long and the measure of the angle MNL is 120 degrees, then NP is 8 inches.

A rhombus is a quadrilateral with all of its sides being the same length and both pairs of opposite sides being parallel. The following formula can be used to determine the length of diagonals when applying the law of cosines to triangles made out of the rhombus's diagonal (x) and sides(a): diagonal [tex]x=a\sqrt{2+2\cos \theta}[/tex].

Given the sides of the rhombus, MNLP is 8 inches each and the ∠MNL is 120°. Then, let's take the diagonal NP as x and calculate this using the above formula as follows,

[tex]\begin{aligned}x&=8\sqrt{2+2\cos120^{\circ}}\\&=8\sqrt{2+2(-0.5)}\\&=8\sqrt{2-1}\\&=\mathrm{8\;inches}\end{aligned}[/tex]

The required answer is 8 inches.

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In the given case, Matthew would have a negative z score and John would have a positive z score.

A z-score is a measurement of how far an observation or data point is from the distribution's mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative. Therefore, it is possible that John's z-score would be positive, showing that he is taller than the average for his age group if he is one of the tallest children in his class at the age of 7.

In contrast, if 12-year-old Matthew is among the smallest students in his class, it is likely that his z-score will be negative, suggesting that he is shorter than the norm for his age group. Therefore, John would have a positive z-score but Matthew would have a negative one if he is shorter than average for his age group.

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Answer:

ANGLE 5 IS CONGURENT TO ANGLE 4

PLEASE MARK BRAINLIEST

Uma is correct, because getting an even number is an event.

The term probability refers to the likelihood of an event occurring.

Given that;

Bridget says that when a standard number cube is rolled getting an even number is an outcome.

And, Uma says that getting an even number is an event.

Now,

We know that;

When a standard number cube is rolled then getting an even number is an event.

Hence, Uma statement is correct.

Thus, Uma is correct, because getting an even number is an event.

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Answer:     [tex]\frac{3}{8}[/tex]➗[tex]\frac{3}{4}[/tex]

Step-by-step explanation:  Are you looking to work out and calculate how to multiply 3/8 by 3/4? In this really simple guide, we'll teach you exactly what 3/8 times 3/4 is and walk you through the step-by-process of how to multiply two fractions together.

Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:

Divide by how many digits there are after adding up all the digits. the total divided by the count.

Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5. This can be determined by looking at the sales data for each product over the months of January through June.

In every month, Product 5 has the highest sales figures among all the products. This suggests that Product 5 is the most popular among customers and would likely attract the most attention if it were to be placed in the window.

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Answer:

Step-by-step explanation:

180-120=60

60+50=110

180-110=70

the missing angle is 70 degrees

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

or in this case, hourly wage :)

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{200}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{200}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{0}}} \implies \cfrac{ 200 }{ 10 } \implies \cfrac{20}{1}\cfrac{dollars}{hour}\qquad \textit{\$20 per hour}[/tex]

The formula to calculate the distance:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute and solve:

d = √(-5(-2))² + (-4-1)²

d = √7² + (-5)² = √49 + 25

d = √74 ====> Alternative "A"

The equations are;

a) y = -7/2x - 13

b) -2/7x - 46/7

We know that the equation of the line that we have here can be written in the general form as the equation that is given as; y = mx + c

We have that

m = slope of the line

c = intercept of the line

As such, we have;

-7x-2y=6 or y = 6 + 7x/-2

or

y = -3 - 7x/2

For the parallel line m = - 7/2

y - (-6) = -7/2(x - (-2))

y + 6 = -7/2x - 7

y = -7/2x - 13

For the perpendicular line m = - 2/7

y - (-6) = -2/7(x - (-2))

y + 6 = -2/7x - 4/7

y = -2/7x - 46/7

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Answer:

The slope is 0.75.

The equation is y=0.75x-2

Step-by-step explanation:

The number of green and black marbles will be 15 and 20 black marbles respectively.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

We have the following information:

5 red marbles

6 blue marbles

3 green marbles

4 black marbles

2 yellow marbles

Total marble = 20 marbles

The number of green marbles:

= 3/20 × 100

= 15

The black marbles will be:

= 4/20 × 100

= 20

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