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a) The area of rectangle ABCD in terms of x and y = 4xy.

b) xy = 10

c) area of triangle EBF​ = 5 m².

Part A) The area of rectangle ABCD:

See the diagram;

The length of rectangle is 2x.

The width of breadth is 2y.

Area = length×breadth

Area = 2x × 2y

Area of ABCD = 4xy m².

Part b) value of xy.

The area of the triangle DEF is 15m².

area ΔDEF = area ABCD - area ΔADE - area ΔBEF - area ΔDFC.

Put the values;

area ΔDEF = 4xy - 2xy/2 - 2xy/2  - xy/2

area ΔDEF = 3xy

equate;

ΔDEF = 3xy and DEF = 15m².

3xy/2 = 15

xy = 10

Thus, the value of xy = 10.

Part c) area of triangle EBF​:

area ΔEBF = xy/2

Put the value of xy = 10.

area ΔEBF = 10/2  = 5

Thus, the area of the triangle EBF 10m².

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The inequality that represents the possible elevations of climbers in the death zone on Mount Everest is 8000 < x ≤ 8850

The given parameter is'

Height = About 8850 meters

Death zone = Location above 8000 meters

Let the height be represented with x

So, the inequality that represents x is

Death zone  < x ≤ Height

This gives

8000 < x ≤ 8850

Hence, the inequality that represents the possible elevations of climbers in the death zone on Mount Everest is 8000 < x ≤ 8850

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Additionally, the picture would contain two parallel side pairs.

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

The parameters are as follows:

A stiff transformation is the translation transformation.

This indicates that it maintains the orientation that is changing.

Two sets of parallel sides comprise the initial figure.

There would be two sets of parallel sides on the picture as a result.

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The ratio is 3 : 2 and for every two incorrect problems he did three problems correctly.

i) Total number of problems =10

Correct problems = 6

Incorrect problems = 4

Ratio =  Correct / incorrect

Ratio = 6/4

Ratio = 3/2

= 3 : 2

ii) The ratio of the number of correct problems to the number of bad problems, i.e. 3:2, represents that for every three problems the student can correct, both problems are wrong.

Hence, the ratio is 3 : 2 and for every two incorrect problems he did three problems correctly.

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The mass of gas contained in the tank is 42.525 g. It is calculated using the concept of density and volume of a substance.

What is density?

Density is generally defined as the mass per unit volume. Its representation is done using the symbol p. SI unit of density is kg / (m)3.

Calculation of the total mass of gas contained in the rectangular tank

Given:

Length of the rectangular tank, l = 27 cm

Breadth of the rectangular tank, b = 7 cm

Height of rectangular tank, h = 11.25 cm

Volume of rectangular tank = l × b × h

= 27 × 7 × 11.25

= 2,126.25 cubic cm

Density = 0.020 g/ml         (1 ml = 1 cubic cm)

Mass / Volume = 0.020

Mass = 0.020 × 2,126.25

= 42.525 g

Hence, the mass of gas contained in the tank is 42.525 g.

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Answer: 5. x=110 degrees

y=70 degrees

6. c=8

Step-by-step explanation:

5. x=110 degrees  ==> x and 110 are congruent angles.

110+y=180      ==> y is the supplement of an angle which is congruent to 110.

110-110+y=180-110

y=180-110

y=70 degrees

6. c/4 = 6/3

c/4 =2

c=8

now, the picture looks a bit misleading, the angle on the bottom-right corner doesn't look at all like a 20° angle, so let me assume the 20° angle is the angle up above, like you see in the picture below, because that looks like a 20° one, and the number there, is not very clear which one is pointing to.

[tex]\cos(64^o )=\cfrac{\stackrel{adjacent}{h}}{\underset{hypotenuse}{18}}\implies 18\cos(64^o)=h \\\\[-0.35em] ~\dotfill\\\\ \cos(20^o )=\cfrac{\stackrel{adjacent}{h}}{\underset{hypotenuse}{x}}\implies x=\cfrac{h}{\cos(20^o )}\implies x=\cfrac{18\cos(64^o)}{\cos(20^o )}\implies x\approx 8.4[/tex]

Make sure your calculator is in Degree mode.

The above statement describes the equation of a circle whose endpoints of a diameter are (-0,0) and (4,-6):

(x + 2)² + (y + 3)² = 3.6

The simple form equation of a circle is: (x – x1)² + (y – y1)²= r², where (x, y) are arbitrary coordinates upon that circumference of the circle, r seems to be the radius of the circle. and (x1, y1) are indeed the coordinates of the circle's center.

Given points are:

(-0,0) and (4,-6)

Find that diameter's length using the locations of the locations as well as the distance formula.

d = √((x₂ - x₁)² + (y₂ - y₁)²)

  = √((4 - (-0))² + (-6 - 0)²)

 = √((4 )² + (-6 )²)

= √(16 + 36)

= √(52)

= 7.2

Radius will be r/2

7.2/2

= 3.6

To obtain the coordinates of the center, use the interest in obtaining and the midpoint formula.

[tex]C=\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]

C = (-0 + 4)/2 , (-6 + 0)/2

C = -2 , -3

To write this circle equation, use the radius and the center coordinates.

(x - h)² + (y - h)² = r²

(x - (-2))² + (y - (-3))² = 3.6

(x + 2)² + (y + 3)² = 3.6

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The equal class prior probabilities, gaussian classes with unique means, and a common covariance matrix that isn't always diagonal. The particular choice for ∑ where d is 2 is µ[tex]_{2}[/tex]-µ[tex]_{1}[/tex].

A Gaussian function in mathematics is a function with the base form and parametric extension for all real constants a, b, and c that are not zero. This function is frequently referred to as a Gaussian. It bears the name of the mathematician Carl Friedrich Gauss. A Gaussian's graph has the recognizable symmetric "bell curve" shape. The parameters a and b determine the height and location of the curve's peak, respectively, while the parameter c, also known as the standard deviation or Gaussian RMS width, determines the width of the "bell." Gaussian functions are frequently used in statistics to characterize the normal distributions, in signal processing to build Gaussian filters, and in image processing where two-dimensional Gaussians are utilized for Gaussian blurring.

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The simplest form of the ratio 35:30 is 7/6.

Given, the ratio is 35:30

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organizations is shown by the part-to-part ratio.

We can refer to a fraction as being in its simplest form when it cannot be further spelled out or reduced. Divide the denominator and numerator by their respective least common multiples to reduce a fraction.

divide the numbers by 5

35/30

= 7/6

therefore the simplest fraction is 7/6.

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The equation that represents the equal distribution of ' d ' dumplings among Eli and Ana is -

x = nd/2.

Unitary method is used to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given is a situation in which Eli and Ana are having dinner. They both have same number of dumplings to eat and each dumpling container contains 'd' dumplings.

Let's assume that there are 'n' containers of dumplings and both Eli and Ana got 'x' number of dumplings. Now -

In 1 container we have - 'd' dumplings

In 'n' containers, we will have -  n × d   dumplings.

Both Ana and Eli got same number of dumplings = x.

Therefore -

x + x = n × d

2x = nd

x = nd/2

Therefore, the equation that represents the situation is -

x = nd/2

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Answer:

k = -10

Step-by-step explanation:

(-8-3k)/2 = 11

Multiplying both sides with 2:

2{(-8-3k)/2} = 11(2)

-8-3k = 22

-8-3k+8 = 22 + 8

-3k = 30

k = 30/-3

k = -10

Check:

(-8-3k)/2 = 11

Putting the value of k that is -10:

{-8-3(-10)}/2 = 11

(-8+30)/2 = 11

22/2 = 11

11 = 11

Hence, it is proved that, k is, in fact, equal to -10

[tex]{ \red{ \bold{9d}}} \: + \: { \red{ \bold{3}}} [/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{(6d + 5)}}} - { \blue{ \tt{(2 - 3d)}}}[/tex]

[tex]{ \blue{ \tt{6d + 5 - 2 + 3d}}}[/tex]

[tex] = { \blue{ \tt{9d + 3}}}[/tex]

Answer:

36.25

Step-by-step explanation:

You need to find out how much he makes an hour. To do that you divide how much he made by 13 hours. Which was 7.25. Than multiply 7.25 by 5. And you get your answer which is 36.25.

The same goes for any money scenario when you are trying to find out like how much an individual 'peach' is in the whole bag. Or take it for what you will it was an example.

By using the exponential value calculation, the value of 5^5/5^2 is 125.

The multiplier is represented by the base B, which is written as "B x," and the exponent "x," which indicates how many times the base is multiplied. When "8" is the base, "3" is the exponent, and the entire equation is the power, the result is 8X8X8=512.

It can be expressed as -

5⁵ / 5² = 5×5×5×5×5 / 5×5

= 5 × 5 × 5

= 5³

= 125

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The base of the triangle is 9 2/11 cm.

Given the height of the triangle is = 2 3/4 cm

area of the triangle is = 12 5/8 cm²

we know the area of the triangle is = 1/2 × b × h

but base = ?

therefore, 12 5/8 cm² = 1/2 × b × 2 3/4 cm

convert improper fraction to proper fraction.

101/8 = 1/2 × b × 11/4

101/8 = 11b/8

like terms gets cancelled

101 = 11b

b = 101/11

b = 9 2/11 cm

Hence we get the base of the triangle as 9 2/11 cm.

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Answer:

(10,-86)

Step-by-step explanation:

Plug in the x values to see if they equal to the y value.

-9(10)+4 = -86.

x = 10

y = -86

The room has a 68 by 33 square foot space and perimeter.

based on the information provided:

a) The room's area is 8 x 8.5,

=68 square feet.

and the room's circumference is

2(8+8.5) = 33 ft

b). Yes, the baseboard and carpet will have the same area and perimeter.

What is a rectangle's perimeter?

Considering that the polygon's perimeter is equal to the sum of its sides. As a result, the perimeter (P) of a rectangle is given by P = the total of its four sides. P = a + b + a + b (Opposite sides of rectangle are equal)

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The Initial amount is 14.76 and the decay factor is 1.4 while the percentage rate of change is 40%.

We are given the function as;

y = 1.4^(t + 8)

Now, the general formula for an exponential decay function is;

f(x) = abˣ

where;

a = initial amount

b = decay factor

x = number of time intervals

Now, using laws of exponents, our initial function can be written as;

y = 1.4⁸ × 1.4^(t)

Now, 1.4⁸ = 14.76

Thus, we now have the expression as;

y = 14.76(1.4^(t))

Comparing with the general equation of exponential decay gives us;

14.76 = initial amount

1.4 = decay factor

t = number of time intervals

If decay factor is 1.4, then this denotes 140% which means that the percentage rate of change is 40%

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Answer:

bein estas for

Step-by-step explanation:

lerni :) kaj preterpasi

The van can carry 13 students and the bus can carry 53 students.

A van can carry = 13

A bus can carry = 53

The equations will be derived from the conditions given in the question:

Let x be the no. of students in van

Let y be the no. of students in bus

     13x + 9y = 646……………(1)

      6x + 3y = 237………………(2)

Multiplying (2) with 3

13x + 9y = 646……………(3)

18x + 9y = 711 …………...(4)

Subtracting equation (3) from (4)

18x + 9y = 711

- (13x + 9y = 646)

We get:

5y = 65

y = 13

Now, plug the value of y into one of the preceding equations:

13x + 9(13) = 646

Solving this we get

x = 53

Hence, The van can carry 13 students and the bus can carry 53 students

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The correct option is (d) 18.

The number if dogs attended the inter-species dance party is 18.

A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the order of a selection is irrelevant. You can choose the items in just about any order in combinations.

Now, as per the given question.

If every cat danced with a 3 dogs, the total would be;

3 x 12 = 36 cat and dogs pairs.

Even so, every dogs just danced with 2 cat, implying that there had to be a mix-up. Then,

Number of dogs = 36/2 = 18

Therefore, the total number of dogs present in the inter-species dance party are 18.

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The component form of a vector refers to breaking the vector into components with unit vectors denoting the direction of each component. The general component form angled vectors in a two-dimensional space is given by:

[tex]\vec v=|v|cos\theta\hat{x}+|v|sin\theta\hat{y}[/tex]

where |v| is the magnitude of the vector component and theta is the angle of the vector.

Using the magnitude and angle given for vector u we can write its component form :

[tex]\vec u=|u|cos\theta_u \hat{x}+|u|sin\theta_u \hat{y}\\\vec u=|5|cos(9)\hat{x}+|5|sin\(9) \hat{y}\\\vec v=5cos9_u\hat{x}+5sin9_u\hat{y}[/tex]

Doing the same for v

[tex]\vec v=|v|cos\theta_u \hat{x}+|v|sin\theta_u \hat{y}\\\vec v=|1|cos5_u \hat{x}+|1|sin5_u \hat{y}\\\vec v=1cos5_u\hat{x}+sin5_u\hat{y}[/tex]

Now adding both vector together

[tex]\vec u+\vec v=(5cos9_u\hat{x}+5sin9_u\hat{y})+(cos5_u\hat{x}+sin5_u\hat{x})\\\vec u+\vec v=(5cos9_u\hat{x}+cos5_u\hat{x})+(5sin9_u\hat{y}+sin5_u\hat{y})[/tex]

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There may be a maximum of 16 shirts in each row to ensure that all the rows have the same length. Option D

The same elements at play

There are a total of sixteen polo shirts on exhibit.

80 jerseys from various teams are now on exhibit.

Each row is limited to just one kind of polo shirt.

The following are the factors that make up 80:

1, 2, 4, 5, 8, 10, 16, 20, and 80

The factors of 16 are as follows: 1, 2, 4, 8, 16.

The number 16 is the most frequent factor between the numbers 80 and 16.

Therefore, the greatest number of shirts that may be placed in each row such that the length of all of the rows is the same is 16.

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If we can write

[tex]5x^2 + nx + 48 = (ax + b) (cx + d)[/tex]

then expanding the right side gives

[tex]5x^2 + nx + 48 = acx^2 + (ad+bc)x + bd[/tex]

so that [tex]ac=5[/tex], [tex]ad+bc=n[/tex], and [tex]bd=48[/tex], where [tex]a,b,c,d[/tex] are integers. We want to maximize [tex]ad+bc[/tex].

5 is prime, so [tex](a,c)[/tex] can be either (1, 5) or (5, 1). Let [tex]a=5[/tex] and [tex]b=1[/tex]. Then maximizing

[tex]ad+bc=5d + c[/tex]

is just a matter of picking the largest possible value for [tex]d[/tex], which is 48. Then [tex]\max\{ad+bc\}=5\times48+1\times1=\boxed{241}[/tex].

Answer:

50 miles per hour

Step-by-step explanation:

You want to put the total amount over the hours.

The number of significant digits the quotient should have is 5. Option D

Significant digits are important single digits from 0 to 9 in the coefficient of an expression.

They are also known as meaningful digits.

Significant figures or digits are the zeros that occur between any two non zero digits.

From the information given, we have;

Let's take the quotient

3.021 x 10^9 /1.0482 x 10^−4

This gives;

2. 88208 × 10^13

We can see that the number of significant digits are 5

Thus, the number of significant digits the quotient should have is 5. Option D

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