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Answer:

To use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse, we need to find the length of the longest side (also known as the hypotenuse) by squaring each side, adding the results, and taking the square root of the sum.

So,

63^2 = 3969

58^2 = 3364

30^2 = 900

Now, we add 3969 and 3364 to get 7333, and take the square root to get approximately 85.62.

Since 63, 58, and 30 are the lengths of the sides of the triangle, we can compare the length of the longest side (85.62) to the sum of the other two sides (63 + 58 = 121) to determine if the triangle is right, acute, or obtuse.

85.62^2 = 7326.23

121^2 = 14641

Since 7326.23 is less than 14641, the triangle is acute.

Answer:

The correct answer is: domain: all real numbers, range: all real numbers greater than or equal to -5.

We can see that the function is a polynomial of degree 4, which means it is defined for all real numbers. Also, as x^4 is always non-negative, the minimum value of the function occurs when x=0, and it is f(0) = -4. Therefore, the range of the function is all real numbers greater than or equal to -4. However, since the function is increasing as we move away from 0, the range is actually all real numbers greater than or equal to the minimum value of -4 plus the vertical shift of -1, which is -5.

The evaluation of the trigonometric identities can be presented as follows;

(a) cos(θ) = -√(51)/10

(b) sin(θ + π/76) = (7·√3 - √(51))/20

(c) cos(θ - π/3) =  (7·√3 - √(51))/20

Trigonometric identities are equations involving trigonometric ratios, in which the values correct far all possible values of the input variable.

(a) The value of sin(θ) = 7/10

The location of the angle θ is quadrant II, therefore;

The adjacent side to the angle θ is -ve, therefore;

cos(θ) =  (√10² - 7²)/10 = -√(51)/10

(b) sin(θ + π/6) = sin(θ) × cos(π/6) + sin(π/6) × cos(θ)

sin(θ + π/6) = 7/10 × √3/2 + 1/2 × (-√(51)/10) = 7/10 × √3/2 - 1/2 × √(51)/10

sin(θ + π/6) = (7·√3 - √(51))/(2 × 10) = (7·√3 - √(51))/(20)

(c) cos(θ - π/3) = cos(θ)·cos(π/3) + sin(θ)·sin(π/3)

Therefore;

cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2

cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2 = (7·√3 - √(51))/20

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Answer:

x=16

Step-by-step explanation:

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Answer:

x = 16

Step-by-step explanation:

First find height (h) of the triangle:

15² = 9² + h²

h² = 15² - 9² = 144

h = √144 = 12

Now you can find the base angle Ф of the 12-9-15 triangle:

Ф = sin⁻¹(12/15) = 53.1°

Find the measure of the other base angle by knowing that the sum of the interior angles of a triangle = 180:

180 - 90 - 53.1 = 36.9°

Now you can find x:

tan(36.9) = 12/x

x = 12/tan(36.9) = 16

The total area of the exercise room is 160 square feet.

The number of square yards equivalent to this total area is 17. 78 square yards.

Since the rubber flooring is sold in whole square yards, Juan must purchase exactly 18 square yards.

To find the area of the exercise room, you should divide it into two different rectangles and then add up their areas.

Rectangle 1 length = 16 ft

Rectangle 1 width = ( 13 - 6 ) = 7 ft

Rectangle 2 length = ( 16 - 8 ) = 8 ft

Rectangle 2 width = 6 ft

The area is therefore :

= ( 16 x 7 ) + ( 8 x 6 )

= 160 square feet

1 square yard is 9 square foot so 160 square foot is:

= 160 / 9

= 17. 78 square yards

The area of rubber flooring that Juan must purchase would then be the whole number of 18 square yards which is 17.78 rounded up.

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By answering the above question, we may infer that As a result, (x, y) = is the answer to the system of equation (3, 0).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equations in the system are:

x + 2y = 3 ... (1)

x - 3y = 3 ... (2)

We may use equation (2) to solve for x in terms of y:

x = 3 + 3y

If this value of x is substituted into equation (1), the result is:

(3 + 3y) + 2y = 3

If we simplify this equation, we get:

5y = 0

Hence, y = 0. Inputting y = 0 into the equation we found for x results in:

x = 3 + 3(0) = 3

As a result, (x, y) = is the answer to the system of equations (3, 0).

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The solution of the equation is x = -0.21 and x = -1.79 and the steps used are from the quadratic formula.

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic problem. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

Given that, the equation is:

8x² + 16x + 3

The steps that could be used to solve the following equation are:

The quadratic formula is given as:

-b ± √b² - 4ac / 2a

Substitute the values:

x = -16 ± √(16)² - 4(8)(3) / 2(8)

x = -16 ± √256 - 96 / 16

x = - 16 ± 12.64 / 16

x = - 16 + 12.64/16 and x = - 16 - 12.64 / 16

x = -0.21 and x = -1.79

Hence, the solution of the equation is x = -0.21 and x = -1.79 and the steps used are from the quadratic formula.

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Answer:

24.6063 ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

If two bakers can make 30 loaves in 1 hour, then we can use proportionality to find how many hours it would take for 3, 5, 6, and 15 bakers to make 30 loaves.

Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:

2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.

Therefore:

3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.

5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.

6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.

15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.

Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.

A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.

(i) The exponential function that models the decay of the substance is given by:

[tex]N(t) = Noe^(-0.088t)[/tex]

(ii) If [tex]400g[/tex] of the substance is present at to, then  [tex]No = 400g[/tex] . Therefore, the amount of the substance remaining after 3 days is:

[tex]N(3) = 400e^(-0.0883) = 309.21g[/tex]  (rounded to two decimal places)

(iii) The rate of change of the amount of the substance after 3 days is given by:

 [tex]dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day[/tex] (rounded to two decimal places)

(iv) To find the number of days it takes for half of the original [tex]400g[/tex] of the substance to remain, we need to solve the equation:

[tex]N(t) = 0.5No[/tex]

[tex]0.5No = Noe^(-0.088t)[/tex]

[tex]0.5 = e^(-0.088t)[/tex]

[tex]ln(0.5) = -0.088t[/tex]

[tex]t = ln(0.5)/(-0.088) = 7.89 days[/tex] (rounded to two decimal places)

Therefore, after  [tex]7.89[/tex] days, half of the original  [tex]400g[/tex] of the substance will remain.

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The relative minimum point is B. Option B is the correct option.

What is the relative minimum?

The function's graph makes it simple to locate relative minima. It is the pivotal point in the function's graph. Relative minima are locations where the function's graph shifts from decreasing to increasing. A point that is lower than the points to its left and right is said to be at its relative minima.

The points of the graph function are A, B, C, D.

The lowest point among the given points on the graph is B.

Thus the relative minimum point is B.

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The percent decrease in the amount of land that Patty owns now is approximately 15.00%. Destiny's time at yesterday's race was 187 minutes.

To find Destiny's time at yesterday's race, we can first calculate the time reduction as a percentage of her previous time, and then subtract that reduction from her previous time.

The time reduction is 15% of 220 minutes -

0.15 x 220 = 33

So, she took 33 minutes less at yesterday's race.

Her time at yesterday's race is -

220 - 33 = 187 minutes

Therefore, time value is obtained as 187 minutes.

The percent decrease in the amount of land that Patty owns can be calculated by finding the difference between her old and new land sizes, dividing that by her old land size, and then multiplying by 100 to convert to a percentage.

The difference between her old and new land sizes is -

2,220 - 1,887 = 333

Dividing that by her old land size and multiplying by 100, we get -

(333/2220) x 100 ≈ 15.00

Therefore, the percent decrease is obtained as 15.00%.

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Answer:

(-4,-3,7,8)

Step-by-step explanation:

the inputs are the X values , the X values are the first number on the parenthesis (X , Y) , the outputs are the Y values

Answer:

x=3

x=-7

Step-by-step explanation:

Answer:1004.8

Step-by-step explanation:

divide 8 by 2 since we need the radius which gives us 4. Then square it by the second power which will give you 16 since 4x4 equals 16. Then multiply 16 by pie/3.14 and you should get 50.24. then multiply it by the height which is 20in and you should get the answer which is 1004.8

The expression that describe the area of the shaded part is 1/3 × 1/2 (optionD)

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

therefore the area of the shaded part is l× w

On the vertical row 3 boxes are shaded out of 6

and on the horizontal 3 are shaded out of 9 boxes

A = 3/6 × 3/9

A = 1/2 × 1/3

therefore the area of the shaded part = 1/3 × 1/2

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Most nations adopt the international standard ISO 216, which specifies the dimensions of an A4 sheet.

ISO (International organization fr Standardization) is an independent, non-governmental body that develops standards to ensure the effectiveness, safety, and quality of goods, services, and systems.

Obtaining an ISO quality management certification can greatly benefit your company by increasing productivity, efficiency, and customer satisfaction.

The international standard ISO 216, which is widely used worldwide, specifies the dimensions of an A4 sheet. A4 paper measures 210 x 297 mm r 21 x 29.7 cm.

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The surface area of the cone is 48π square centimeters (or approximately 150.8 square centimeters if we use a decimal approximation for π).

Calculating a cone's surface area is as follows:

[tex]\mathrm{SA = \pi r\² + \pi r \boldsumbol l }[/tex]

where l is the cone's slant height and r is the base's radius.

The radius and slant height in this instance are 4 cm and 8 cm, respectively. Therefore:

[tex]SA = \pi (4\²) + \pi (4)(8) \s= 16 \pi + 32 \pi \s= 48 \pi[/tex]

Hence, the cone's surface area is 48 square centimetres (or around 150.8 square centimetres if we round to the nearest decimal).

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Answer:

Candice had 2 cans left over.

The center of dilation is located inside figure V.

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Center of dilation is defined as the point which is fixed on a plane. All the points are dilated about this point.

This can be situated inside or outside the preimage and image.

We can find the position of center of dilation by connecting corresponding vertices of the image and preimage and extend the line up to which all the lines intersect.

The intersecting point is the center of dilation.

Using this concept, here, the center of dilation is inside V.

Hence the center of dilation is located inside the figure V.

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In a normal distribution curve, the mean is equal to center of the curve

In a normal distribution curve, the mean is equal to the center of the curve, also known as the peak, and is represented by the highest point on the curve.

The mean of a normal distribution is also the point around which the data points are symmetrically distributed, with an equal number of data points on both sides of the mean. This is why the mean is often referred to as the "average" of a normal distribution.

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Answer: (4,9)

Step-by-step explanation: The X is going to flip signs as you mirror across the y axis.

Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To determine whether Atul's allowance is above or below the average, we need to calculate the average allowance for all the friends, including Atul.

To do his, we add up all the amounts and divide by the total number of friends:

Average allowance = (120+180+100+50+250+200+200+220+150+100+100+150+130+200+180+100+150+100+180+150+120+150+100+150+100+120+180+200+50) / 29

Average allowance = 162.07

So, the average allowance for Atul's friends, including himself, is Rs. 162.07 per day.

Since Atul's allowance is Rs. 120 per day, we can see that his allowance is actually less than the average.

Therefore, Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.

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Answer:

How long will it take 6 people to wash all the cars?   5 hours 20 minutes

If you only have 2 hours and 40 minutes to wash all the cars how many people will you need?   12 people

Step-by-step explanation:

The important thing to realize here is that the time taken to wash x cars is inversely proportional to the number of people

That is represented mathematically as
y ∝ 1/x

The more the number of people, the less time it takes

We can write this as a proportionality equation:
y = k/x

where k is referred to as the constant of proportionality

We have the information: 4 people take 8 hours.

Plugging these two values into the equation

4 = k/8

k = 4 x 8 = 32 hours

So it takes 1 person 32 hours to wash all the cars

If there were 6 people instead
6 = 32/h where h is the time taken for 6 people to wash 30 cars

h = 32/6 = 16/3 hours = 5 1/3 hours
= 5 hours and 20 minutes

2 hours and 40 minutes = 2 40/60 hours = 2 2/3 hours

Converting to improper fraction
2 2/3 = (2 x 3 + 2)/3 = 8/3 hours

Plugging this value of x into the equation gives

y = 32/(8/3)

32 ÷ 8/3 is computed by flipping the fraction and multiplying

32 ÷ 8/3 = 32 x 3/8 = 12 people

The number that was added to complete the square is (7/2)²

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²+7x+27=0

Add and subtract (7/2)² = 49/4

x² + 7x + 27

= ( x² + 7x + 49/4) - 49/4 + 27=0

= (x + 7/2)² - 59/4

Now we can rewrite the original equation as:

(x + 7/2)² - 59/4 = 0

Adding 59/4 to both sides, we get:

(x + 7/2)² = 59/4

Taking the square root of both sides, we get:

x + 7/2 = ±√59/2

Solving for x, we get:

x = -7/2 ±√59/2

Therefore, the number that was added to complete the square is (7/2)²

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We may calculate the distance from Carlos and the tree as [tex]D = 781.23[/tex] ft using trigonometric relationships.

Many functions in trigonometry offer excellent illustrations of how calculus may be used in practical situations. By the way, basic trigonometry primarily deals with the algebraic features of circular functions, therefore basic calculus is not always simpler than basic trigonometry. On the other hand, calculus is fundamentally non-algebraic in nature.

The mnemonic SOHCAHTOA makes it simple for us to recall the three primary trigonometric ratios.

Then one of the cathetus of the triangle is equal to:

[tex]275ft - 6ft = 269ft[/tex]

That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.

Then we can use the relation:

Where:

[tex]a=19^{0}[/tex]

opposite cathetus [tex]=269ft[/tex]

adjacent cathetus [tex]=D[/tex]

Replacing that, we get

[tex]tan(19^{0} ) = 269ft/D[/tex]

Solving for D, we get:

[tex]D = 269ft/tan(19^{0} ) = 781.2ft[/tex]

So we conclude that Carlos is at [tex]781.23[/tex] ft of the tree.

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Answer:144

Step-by-step explanation:

Answer:144

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

your add odd number 1,3,5,7,9,11,13...

The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.

A function in mathematics is a relationship between a domain—a set of possible inputs—and a range—a set of potential outputs—with the property that each input is linked to precisely one output. Frequently, a mathematical expression, equation, or formula will be used to describe a function. They are a fundamental idea in calculus, algebra, and other branches of mathematics, used to explain how one quantity relies on another.

given

Let Q(x) = 7.25x 36.25 be a model for his daily earnings, where x is the quantity of bracelets he sells.

Q(5) = 23.5, which indicates that Quincy will make $23.50 if he sells 5 wristbands today.

The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.

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