Flying against the wind, an airplane travels 2280 km in 4 hours. Flying with the wind, the same plane travels 6650 km in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?

Final answer:

The set G is a subset of the universal set U and contains the first seven natural numbers within U: {1,2,3,4,5,6,7}.

Explanation:

In mathematics, particularly in set theory, when we talk about the set G, we are referring to a collection of elements that are all part of a larger universal set, denoted by U. In your case, the universal set U is {1,2,3,4,5,6,7,8,9,10} and the set G is given as {1,2,3,4,5,6,7}. The set G contains the first seven natural numbers within the universal set.

Understanding the concept of the universal set and subsets is fundamental in set theory. The universal set is the set that contains all possible objects (usually numbers in this context) under consideration, and any other set is a subset if all its elements are also elements of the universal set. The subset G in your example is defined by explicitly listing its members, which are all part of the universal set U.

Answer: [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]

Step-by-step explanation:

Since, given [tex]cosec\theta=\frac{8 }{7}[/tex]

And we know that [tex]Cot\theta=\sqrt{cosec^2\theta-1}[/tex]

Therefore, [tex]Cot\theta=\sqrt{cosec^2\theta-1} = \sqrt{(8/7)^2-1}= \sqrt{64/49-1}[/tex]

⇒[tex]Cot\theta=\sqrt{64-49/49}=\sqrt{15/49}=\sqrt{15}/7[/tex]

Thus,  [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]

Answer:

CotA=√15/7

Step-by-step explanation:

cosecA=8/7=hypotenuse/perpendicular

We have to find cotA

We do this by right angled triangle

We use pythagoras theorem to find the base

Base²+Perpendicular²=hypotenuse²

Base²+7²=8²

Base²=15

Base=√15

cotA=Base/Perpendicular

     = √15/7

The x-intercept is (-3,0) and the y-intercept is (0,6).

The correct option is B,

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given information:

4x - 2y = -12.

To find the x-intercept, we set y to zero and solve for x:

4x - 2y = -12

4x - 2(0) = -12

4x = -12

x = -3

So the x-intercept is (-3, 0).

To find the y-intercept, we set x to zero and solve for y:

4x - 2y = -12

4(0) - 2y = -12

-2y = -12

y = 6

So the y-intercept is (0, 6).

Therefore, the answer is b. The x-intercept is (-3,0) and the y-intercept is (0,6).

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Answer:

Step-by-step explanation:

It is B

Answer:

[tex]\frac{-2}{\sqrt{3} }[/tex]

Step-by-step explanation:

Cosec of -120 is to be found out

We can do this in steps

cosec (-120) consider only the - sign.

This implies angle lies in IV quadrant and hence cosec is negative

cosec (-120) =-cosec (120)

Now 120 is written as 180-60

cosec (-120) =- cosec(180-60)

=-cosec 60

(since II quadrant cosec is positive)

= [tex]\frac{-2}{\sqrt{3} }[/tex]

Answer:

d 4 x 5

Step-by-step explanation:

round

Answer:

The correct answer is 17.3

Step-by-step explanation:

Let me know if it helped you

Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. Let's try an example.

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] can be rewritten as [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex].

Now, we are simply multiplying fractions.

Multiply across the numerators and the denominators

[tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex] = [tex]\frac{9}{10}[/tex]

Therefore, [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] = [tex]\frac{9}{10}[/tex]

The error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

According to the question

5x + 4y= 2 ------------------- (1)

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

Now,

solving both equation by elimination method

Multiplying equation (1) by 3 and by 2 to equation (-4)

So, y  can be eliminated

3(5x + 4y)=2 * 3

15x + 12y = 6 -------------- (3)

-4(3x + 3y) = -3*-4

-12x - 12y = 12 -----------------(4)

Now,

Adding both eq(3) and (4)

3x = 18

x = 6

Putting value of x in eq(1)

5*6 + 4y = 2  

30 + 4y = 2

4y = 2 - 30

4y = - 28

y = -6

Hence, the error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .

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Answer: The expression would be [tex]8x+24[/tex]

Step-by-step explanation:

Since we have given that

8 times the total of x and 3

total of x and 3 means sum of x and 3.

Mathematically it is expressed as

[tex]x+3[/tex]

Now, 8 times the above sum.

Mathematically, it is written as

[tex]8(x+3)\\\\=8x+24[/tex]

Hence, the expression would be [tex]8x+24[/tex]

Answer:

1/5

Step-by-step explanation:

A stem-and-leaf plot gets its name from the way the data is structured. The 'stem' represents the highest place value digits of the numbers in the dataset, and the 'leaf' represents the lower place value digits. These plots keep the actual numerical data intact, providing more detail than other data representations like bar graphs or histograms.

The term stem-and-leaf plot, also known as a stemplot, originates from the way data is structured in this type of graphical representation. The 'stem' in a stem-and-leaf plot stands for the highest place value digits of the numbers in the dataset, similar to the stem of a plant that holds up the leaves. The 'leaf' stands for the lower place value digits, similar to the leaves that extend from the stem. For example, in a dataset [23, 24, 33, 35], 2 and 3 would be stems, and the various units (3, 4 for 2 and 3, 5 for 3) would be leaves.

One of the main purposes of a stem-and-leaf plot is that it keeps the actual numerical data intact, as opposed to other graphical representations like bar graphs or histograms which group data into classes, thus providing a more detailed view of the data distribution.

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No, 30,150 resistors are not enough to assemble 1922 radios.

To determine if 30,150 resistors are enough to assemble 1922 radios, we need to calculate the total number of resistors required and then account for the defective resistors.

 First, let's calculate the total number of resistors needed for 1922 radios. Since each radio requires 15 resistors, the total number of resistors required is:

[tex]\[ 1922 \text{ radios} \times 15 \text{ resistors/radio} = 28830 \text{ resistors} \][/tex]

 Next, we need to account for the defective resistors. Given that one out of every 25 resistors is defective, we can calculate the number of defective resistors in a batch of 28830 resistors. However, to simplify the calculation, we can calculate the number of non-defective resistors we expect to get from every 25 resistors. Since 24 out of 25 are expected to be non-defective, we have:

[tex]\[ \frac{24}{25} \[/tex] { non-defective resistors per 25 resistors}

 To find out how many non-defective resistors we would get from 28830 resistors, we multiply the total number of resistors by the ratio of non-defective to total resistors:

[tex]\[ 28830 \times \frac{24}{25} = 28224 \[/tex] { non-defective resistors}

 Now, we compare the number of non-defective resistors needed (28830) to the number of non-defective resistors we can expect to have (28224). We find that:

[tex]\[ 28830 - 28224 = 606 \text{ resistors} \][/tex]

 This means we are short by 606 non-defective resistors to assemble all 1922 radios. Therefore, 30,150 resistors are not enough.

 To confirm this, let's calculate the total number of resistors needed including the defective ones. Since we know that for every 28830 non-defective resistors we need 1/25 more to account for the defective ones, we have:

[tex]\[ 28830 \times \frac{25}{24} = 30156.25 \text{ resistors} \][/tex]

 This shows that we actually need more than 30,150 resistors to account for the defective ones and meet the requirement for 1922 radios. Hence, the answer is no, 30,150 resistors are not enough."

Sample Answer: No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.

Answer:

No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.

Step-by-step explanation:

With the given translation rule, to find new coordinates of a point L in trapezoid JKLM, apply it to the original coordinates by moving right by 8 units and down by 3 units. If original coordinates of L were (2,5), new coordinates will be (10,2).

In geometry, a translation is a type of transformation that slides a figure along a straight line. In this case, the translation rule given is (x, y) -> (x+8, y-3). This means that every point in the trapezoid is being moved 8 units to the right (increase in x-coordinate) and 3 units down (decrease in y-coordinate).

Per your question, to find the new coordinates of point L after the translation, you simply need to apply this rule to the original coordinates of point L. If for example, the original coordinates of point L were (2, 5), its new coordinates after the translation would be calculated as follows: (2+8, 5-3) = (10, 2).

This is how you find the new coordinates of a point after a translation in geometry.

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Answer:

From the given expression of parabola, it is clear that the parabola is upward opening.

Step-by-step explanation:

Concept: In the equations of parabolas, when the expression having x variable has the power of 2, then the parabola opens in the y-axis. The equation of parabola is of the form X² = 4aY.

In this case, if a > 0, then the parabola opens in the upward direction.

Given equation is (x - 5)² = 4×3(y + 2). Here the expression of x has the power 2 and a = 3 > 0. So, the parabola is upward opening.

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Final answer:

The given parabolic equation has a positive coefficient for the (y + 2) term, indicating that it opens upward.

Explanation:

The equation given is in the form of a transformed parabolic equation, which can be identified as [tex](x - h)^2 = 4p(y - k),[/tex]where the vertex of the parabola (h,k) and the value of p determine the direction in which the parabola opens.

In the equation [tex](x - 5)^2 = 12(y + 2),[/tex] the presence of the squared term on x and the fact that the coefficient of the (y + 2) term is positive indicates that the parabola opens upward.

In this case, if a > 0, then the parabola opens in the upward direction.

The coefficient of the squared term is 4p, which in this case is positive, confirming the direction of the parabola as opening upwards.

Answer:

The answer is C.

g = w + 8

g = w − 4

Hope This Helps!

The solutions of the equations [tex]x^3-6x^2+9x=0[/tex] is:

                         x=0 or x=3

The solutions of the graph of the equation are the possible values of x at which the graph meets the x-axis at a point.

The function f(x) is given by:

[tex]f(x)=x^3-6x^2+9x[/tex]

The function f(x) could also be written as:

[tex]f(x)=x^3-3x^2-3x^2+9x\\\\i.e.\\\\f(x)=x^2(x-3)-3x(x-3)\\\\i.e.\\\\f(x)=(x^2-3x)(x-3)\\\\i.e.\\\\f(x)=x(x-3)(x-3)[/tex]

i.e. If

[tex]f(x)=0[/tex]

then

[tex]x(x-3)(x-3)=0\\\\i.e.\\\\x=0\ or\ x=3[/tex]

By the help of the graph we may observe that the function meets the x-axis at x=0 or x=3.

it is 9 squares high and the base is 6 squares wide

9*6 = 54

54/2 = 27

 area = 27 square units