Find the area of the trapezoids. What is the Area of the trapezoids

A= Square units

There are 98.4252 inches in 2.50m.

Unit Conversion is defined as a process that involves multiplication and division by a numerical factor or a particular conversion factor.

For Example .Convert 2m into cm.

As we know that 1m=100cm

multiplying both sides by 2 we get

2m = 200 cm.

According to the question

It is given that 2.54 cm = 1 inch

\(1cm = \frac{1}{2.54} inch\)

\(100cm=\frac{100}{254} inch\)

\(1m = \frac{100}{2.54}\) ( as 100cm = 1m)

we need 2.50 m So we multiply both sides by 2.50

\(2.50m=\frac{2.50*100}{2.54} \\\\ 2.50m=\frac{250}{2.54}\)

\(2.50m=98.4252 inch\)

Therefore , there are 98.4252 inches in 2.50m.

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The area of the sector is approximately 13.02 square cm. The area of a sector with a central angle of 30° and a radius of 12.5 cm can be found using the formula:

\(A = (\pi /360) xpi\)

where:

A is the area of the sector

θ is the central angle in degrees

r is the radius of the sector

π is a mathematical constant (approximately equal to 3.14)

Substituting the given values, we get:

\(A = (30/360) x pi (12.5)^2\)

A = (1/12) x π(156.25)

A = (13.02) square cm (rounded to two decimal places)

Therefore, the area of the sector is approximately 13.02 square cm.

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What is the area of a sector with a central angle of 30° and a radius of 12. 5 cm?

The width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

A three-dimensional structure with six rectangular faces that are parallel and congruent together is called a rectangular prism. It has a length, width, and height. By multiplying the length, width, and height together, one may get the volume. Contrarily, a cylinder is a three-dimensional shape with two congruent and parallel circular bases. It has a height and a radius, and you can determine its volume by dividing the base's surface area by the object's height. A cylinder has curved edges and no corners while a rectangular prism has straight edges and corners.

The volume of the rectangular cake is given as:

V = length * width * height

Substituting the values we have:

16 * 12 * 3 = 576 cubic inches

Now, for the cylindrical cake to be of the same volume we have:

V = π * radius² * height

π * radius² * 3 = 576

(3.14) * radius² * 3 = 576

radius = 15.6 inches

Hence, the width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

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A translation vector describing the receiver's path < -12, 17 >.

The distance vectors that almost all atoms in the grouping are translated through just to form another cluster inside the solid are defined by translation vectors.

Now, as per the stated question;

The horizontal (lateral, x) change is represented by the number 12. This same player runs 12 yards to the left.

The vertical (up/down, y) transition is represented by the number 17. In addition, the player runs 17 yards up the field.

When you put it all together, you get < -12, 17 >.

Therefore, the receiver's route is defined by translation vector < -12, 17 >.

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\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.25\% of 205.60}}{\left( \cfrac{6.25}{100} \right)205.60}\implies 12.85~\hfill \underset{ \textit{final bill} }{\stackrel{ 205.60~~ + ~~12.85 }{\text{\LARGE 218.45}}}\)

==============================================================

Explanation:

The two integers multiply to 36, so,

ab = 36

which solves to

a = 36/b

Then we want to add the numbers such that we get the smallest possible result.

a+b = (36/b)+b

So we want (36/b)+b to be as small as possible.

Let's say we replace b with x and we consider this function

f(x) = (36/x) + x

The goal is to find when f(x) is smallest, ie, we want to minimize the function.

If we were to graph out the function, we get the curve shown below.

To make things easier, we'll only focus on positive values of x.

The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.

So the input x = 6 leads to the smallest output f(x) = 12.

This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.

In short, a = 6 and b = 6.

----------------------

As a check,

a*b = 6*6 = 36

a+b = 6+6 = 12

We can make a table of various values to help confirm that 12 is the smallest sum.

Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.

The height of the rock as it is thrown upwards is in the shape of a parabola which is described as follows;

Part A: Please find attached the graph of the parabola that describes the height of the rock after being projected into the air, created with MS Excel.

Domain; [0, 4]

Range; [0, 256]

Part B: The function that models the scenario, obtained using the vertex form of a parabola is; h(x) = -16·(x - 2) + 256

A parabola is a geometric shape defined as the set of points that are both equidistant from  a fixed point, known as the focus and a fixed line, known as the directrix.

To create a graph to represent the scenario, we can use the vertex form of a quadratic function, which is; y = a·(x - h)² + h

Where; (h, k) is the vertex of the parabola. We know that the height of the edge of the cliff from which the rock is thrown is 192 feet, so the initial height of the rock is 192 feet

The maximum height = 256 feet

The time to reach the maximum height = 2 seconds

Therefore; The coordinate of the vertex = (2, 256)

The time the rock takes to reach the ocean from the max height = 4 seconds

Total time the rock is in the air = 6 seconds

Therefore, we get;

y = a·(x - h)² + k

192 = a·(0 - 2)² + 256 = 4·a + 256

192 = 4·a + 256

192 - 256 = -64 = 4·a

-64 = 4·a

a = -64/4 = -16

a = -16

The equation is therefore;

y = -16·(x - 2)² + 256

The above function can be used to create the graph of the motion of the rock as follows;

The x-intercept is the point where y = 0, therefore, the x-intercept is 6

y = 0 = -16·(x - 2)² + 256

16·(x - 2)² = 256

(x - 2)² = 256/16 = 16

x - 2 = √(16) = 4

x = 4 + 2 = 6

x = 6

The x-intercept is; (6, 0)

The y-intercept is the point where x = 0, therefore;

y = -16·(x - 2)² + 256

y = -16·(0 - 2)² + 256 = 192

The y-intercept is; (0, 192)

Please find attached the required graph of the function created with MS Excel

Part B; The function of the graph is; f(x) = -16·(x - 2)² + 256

The domain of the function for the motion of the rock is; [0, 6] since the rock is in the air for 6 seconds

The range of the function is; [0, 256], since the maximum height reach is 256 feet and the lowest height reached is the ocean level or zero feet.

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If the function f(x) = |x-5| + 2, then the value of f(3) is 4

The function

f(x) = |x-5| + 2

The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators

Here the function consist of the absolute value symbol.

|-a| = a

The absolute value of the positive and the negative number will be always positive.

The function is f(x) = |x-5| + 2

Then,

f(3) = |3-5| + 2

= |-2| + 2

= 2 + 2

= 4

Therefore, the value of f(3) is 4

I have answered the question in general, as the given question is incomplete

The complete question is:

If f(x)=|x−5| + 2, find the value of f(3).

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Answer:

what do you need help with?

Step-by-step explanation:

The probability for -2.51 ≤ Z ≤ -1.53 is 0.0570.

The probability for Z ≥ -2.12 is 0.9830.

To find the probability for the given scenarios, we can use the Z-table or standard normal distribution table, which provides the cumulative probabilities for a standard normal random variable Z.

1) For -2.51 ≤ Z ≤ -1.53:

Find the cumulative probability for Z = -1.53 and Z = -2.51 using the Z-table. Then subtract the cumulative probability of Z = -2.51 from the cumulative probability of Z = -1.53.

P(-1.53) = 0.0630
P(-2.51) = 0.0060

P(-2.51 ≤ Z ≤ -1.53) = P(-1.53) - P(-2.51) = 0.0630 - 0.0060 = 0.0570

2) For Z ≥ -2.12:

Find the cumulative probability for Z = -2.12 using the Z-table. Since we want the probability that Z is greater than or equal to -2.12, we need to subtract the cumulative probability from 1.

P(-2.12) = 0.0170

P(Z ≥ -2.12) = 1 - P(-2.12) = 1 - 0.0170 = 0.9830

So, the probability for -2.51 ≤ Z ≤ -1.53 is 0.0570, and the probability for Z ≥ -2.12 is 0.9830.

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Answer:ASA

Step-by-step explanation:

Answer:

the answer is asa

Step-by-step explanation:

i just did this question

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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Answer:

OKay so one-half + k greater-than 8 is the same thing as 1/2 + k > 18.  The correct answer for this is  ¨The sum of one-half and a number is greater than eighteen.¨ This is because 1/2 and k are added together hence the word sum. Furthermore, ¨>¨ means greater than.

Step-by-step explanation:

Hope this helps, have an Amazing day!

Answer:

x=12?

Step-by-step explanation:

there is no image or equation

The positive root of the quadratic equation x² - 5x = 14 is 7.

A quadratic equation in its standard form is expressed as;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation in the question.

x² - 5x = 14

Rearrange in standard form
x² - 5x - 14 = 0

Plug the values of a, b and c into the quadratic formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -(-5) ±√( (-5)² - ( 4 × 1 × -14) )) / (2 × 1)

x = ( 5 ±√( 25 - ( -56 ) )) / 2

x = ( 5 ±√( 25 + 56 )) / 2

x = ( 5 ±√( 81 )) / 2

x = ( 5 ± 9 )/2

x = ( 5 - 9 )/2, x = ( 5 + 9 )/2

x = (-4)/2, x = (14)/2

x = -2, x = 7

Therefore, the solutions are x = -2 and x = 7.

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Answer:

Step-by-step explanation:

Sure! I'll perform the mathematical operations using the given numbers and apply the rules of precision. Please find the results below:

(9.11) + (6.232)

The sum of 9.11 and 6.232 is 15.342.

(7.4023) x (19)

The product of 7.4023 and 19 is 140.844.

(9.162) - (2.39)

The difference between 9.162 and 2.39 is 6.772.

(0.00482) x (213)

The product of 0.00482 and 213 is 1.02786.

(8.73) / (5.198)

The division of 8.73 by 5.198 is 1.67920734.

(7644) / (0.13)

The division of 7644 by 0.13 is 58,800.

Please note that the results are rounded to the appropriate number of decimal places based on the precision rules.

The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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The time required for the population to triple is nearly 8 years if the population of a community is known to increase at a rate proportional to the number of people present at time t and an initial population p0 has doubled in 5 years.

Given that the population is increasing at a rate proportional to the number of people present at time t.

the population growth is modeled by the following differential equation:

\(\frac{dP(t)}{dt} = kP(t)\)

P(t) = Po\(e^{kt}\)           ..(1)

Initially given that population doubled in five years

i.e. P(5) = 2Po

Putting it in equation(1)

2Po = Po\(e^{5k}\)

taking logs is both sides

ln 2 = 5k

k = ln2/5 = 0.1386

therefore, P(t) = Po\(e^{0.1386t}\)

Now, the time required for the population to triple or P(t) 3Po

3Po = Po\(e^{0.1386t}\)

ln3 = 0.1386t

or t = 7.9265 = 7.9

Therefore, the time required for the population to triple is nearly 8 years.

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The equation obtained for Kim will be t = x/2

Equation obtained for Jake will be t = (x - 6)/1.5

As for the problem, Kim and Jake are competing in the big race. And the values of their speed are given below.

Kim moves at a 2-meter-per-second running pace.

Jake moves at a 1.5 meter per second running pace (3 meters per 2 seconds)

Jake gets 6 meters ahead of Kim.

To get equations for the same case to both persons we should get it as,

Let x be the complete race distance and t be either Kim's or Jake's total race time.

Time = Speed/Distance

Kim's time equation is t = x/ 2.

The time equation that Jake uses is t = (x - 6)/1.5.

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Based on the information, the width of the river is approximately 71.508 meters

We can use the tangent function, which relates the angle and the sides of a right triangle. The formula is:

tan(angle) = opposite / adjacent

In this case, the adjacent side is the 60 meters that the surveyor walked, and the opposite side is the width of the river that we need to find.

Using the formula, we can rearrange it to solve for the opposite side:

opposite = adjacent * tan(angle)

Plugging in the values:

opposite = 60m * tan(50°)

opposite = 60m * tan(50°)

opposite ≈ 60m * 1.1918

opposite ≈ 71.508 meters

Therefore, the width of the river is approximately 71.508 meters.

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A surveyor needs to calculate the width of a river. From a point A located in front of a tree

bowl on the opposite shore, walk 60 meters (m) to the right. If the angle between the river bank

and the line of sight to the tree at this point is 50°, what is the width of the river?

The correct option is a. mean: $64 median: $65 mode: $71, the mean is the average of all the values in a data set.

To calculate the mean, add up all the values and then divide by the number of values. In this case, the mean is $64.

The median is the middle value in a data set when the values are arranged in ascending or descending order. In this case, the median is $65.

The mode is the most frequently occurring value in a data set. In this case, the mode is $71.

Here is a table of the data with the mean, median, and mode calculated:

Value | Mean | Median | Mode

------- | -------- | -------- | --------

$71 | $64 | $65 | $71

$66 |     |     |

$81 |     |     |

$53 |     |     |

$64 |     |     |

$71 |     |     |

$68 |     |     |

$45 |     |     |

$50 |     |     |

$61 |     |     |

$63 |     |     |

$75 |     |     |

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Answer:   If x is less than -120, then x-120 will be less than zero, so we have:

|x-120| = -(x-120)

And since x is less than -120, we have:

|x-120| = -(x-120) = -x + 120

Therefore, the simplified expression for |x-120| when x<-120 is -x + 120.

Step-by-step explanation: I would reallyyyyyyyyyyyyyyyyy apreciate brainliest

Answer:

135°

Step-by-step explanation:

You want QRT. So if you look at it you have a straight line, which equals 180°. you already have an angle at 45° so all you do is 180-45 and that equals 135°

Answer:

B

Step-by-step explanation:

This ones pretty simple, all you need to do is write the two varible equations for how many fruits they bought and how much it cost.

In the first one there are 3 apples and 4 oranges, x represents the price of the apples and y represents price of the number of oranges, so the equation would be written like this:

3x+4y=

Then after the equal sign you put how much the total price was in total, which is 4.25 in the first one so

3x+4y=4.25

On the second equation there are 5 apples and 2 oranges, again x will be the price of the apples, and y will be the price of the oranges. The total price of both apples and oranges is 4.75 for this one, so the equation would be written like this:

5x+2y=4.75

Both equations together would be

3x+4y+4.25

5x+2y=4.75

This is the anwser

Answer:

gogle it you are gonna find a video

Step-by-step explanation:

hope this helps

The answer is 8.125, simpson's 3/8 rule is a numerical integration method that uses quadratic interpolation to estimate the value of an integral.

The rule is based on the fact that the area under a quadratic curve can be approximated by eight equal areas.

To use Simpson's 3/8 rule, we need to divide the interval of integration into equal subintervals. In this case, we will divide the interval from 0 to 4 into four subintervals of equal length. This gives us a step size of h = 4 / 4 = 1.

The following table shows the values of the function and its first and second derivatives at the midpoints of the subintervals:

x | f(x) | f'(x) | f''(x)

------- | -------- | -------- | --------

1 | -2.25 | -5.25 | -10.5

2 | -1.0625 | -3.125 | -6.25

3 | 0.78125 | 1.5625 | 2.1875

4 | 2.0625 | 5.125 | -10.5

The value of the integral is then estimated using the following formula:

∫_a^b f(x) dx ≈ (3/8)h [f(a) + 3f(a + h) + 3f(a + 2h) + f(b)]

Substituting the values from the table, we get:

∫_0^4 (-x^4 - 2 - 4x^3 + 2x^5) dx ≈ (3/8)(1) [-2.25 + 3(-1.0625) + 3(0.78125) + 2.0625] = 8.125, Therefore, the value of the integral is 8.125.

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Answer:

$58 dollars

Step-by-step explanation:

Step 1: Find price of Red Fabric. So Brenda bougt 72 inches. So we convert that to amount of yards.(36 inches=1 yard). So the equation is 72/36=2 yards. Then do 7.25x2= $14.50 for red fabric.

Step 2: Find price of Black Fabric. So Brenda bought 3 times more the red favric. So she 216(72x3 is how I got the number). Now divide 216 by 36. That equals 6. So now do 7.25x6= $43.50

Step 3: Add the prices. So now add the price of the red and black fabric to find the answer. So $43.50 + $14.50= $58

Hence, the answer is $58 dollars.

Thank You