A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.​

Teniendo en cuenta la definición de sistema de ecuaciones lineales, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en ambas ecuaciones.

En este caso, se dispone de un recipiente de 24 litros de capacidad y de tres medidas, A, B y C.

Se sabe que el volumen de A es el doble del de B → A=2B

Las tres medidas llenan el depósito → A+ B +C= 24 L

Las dos primeras medidas llenan hasta la mitad del recipiente → A +B= 24 L÷2 → A +B= 12 L

Entonces, el sistema de ecuaciones a resolver es el formado por las tres ecuaciones anteriormente mencionadas.

Existiendo diversos métodos para resolver un sistema de ecuaciones, se decide resolver mediante el método de sustitución, que consiste en despejar una de las dos variables en una de las ecuaciones del sistema y sustituir su valor en la otra ecuación.

En este caso, reemplazando la primer ecuación en la tercera ecuación se obtiene:

2B +B= 12 L

3B= 12 L

B= 12 L÷3

B= 4 L

Reemplazando este valor en la primer ecuación se obtiene:

A=2B

A=2×4 L

A= 8 L

Finalmente, para obtener el valor de C se reemplaza el valor de A y B en la segunda ecuación:

A + B + C= 24 L

8 L + 4 L + C= 24 L

12 L + C= 24 L

C= 24 L - 12 L

C= 12 L

Finalmente, cada medida tiene una capacidad de A= 8 L, B= 4 L y C= 12 L.

Aprende más sobre sistemas de ecuaciones lineales:

brainly.com/question/15924499

brainly.com/question/17411423

#SPJ1

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

[tex]3x + 18 = 11x - 6 [/tex]

[tex]24 = 8x[/tex]

[tex]x = 3[/tex]

Answer:

k = 7d

Step-by-step explanation:

y = mx + b

slope (m): 7 kilometers each day

x: Brian runs over d days

y - intercept (b): when x = 0, y = 0 since it will be day 0

y:  total kilometers, k

Answer:

k = 7d

Step-by-step explanation:

The standard form of an equation is :

y = mx + b

Here, the variables for y and x are k and d respectively.

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

It is given that Brian runs 7 kilometers each day. Hence, that is our rate of change, m. The value of b will be 0 as he starts from 0 km.

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

So, the equation is :

k = 7d

Answer:

Step-by-step explanation:

The area of the equilateral triangle is [tex]\frac{\sqrt{3}}{4}(6)^{2}=\boxed{9\sqrt{3}}[/tex]

Answer:

P(AUB)=P(A)+P(B)

Step-by-step explanation:

I found it somewhereI don't know?Trust me:)

The  length of the radius (r) to the nearest tenth is 13.2

The theorem states that the square of the longest side is equal to the sum of the square of other two sides.

In order to determine the radius of the circle, we will use the theorem above to have:

AO² = AB² +r²

Given

AB = 15

AO = 20

Substitute

20² = 15² +r²

r² = 400 - 225

r² = 175

r = 13.2

Hence the  length of the radius (r) to the nearest tenth is 13.2

Learn more on Pythagorean theorem here: https://brainly.com/question/343682

#SPJ1

Answer:

21 316/729

Key rules to solve:

Step-by-step explanation:

[tex]\left(\frac{2-1}{2\cdot \:7\frac{1}{3}}\right)^6[/tex]

[tex]=\left(\frac{2-1}{2\cdot \frac{22}{3}}\right)^6[/tex]

[tex]=\frac{\left(2-1\right)^6}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]

[tex]=\frac{1}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]

[tex]=\frac{1}{\frac{7256313856}{729}}[/tex]

[tex]\rightarrow 21 \frac{316}{729}[/tex]

Answer:

mean for data set 1 is 41

data set 1 MAD is 16.4

data set 2 MAD is 16.8

mean for data set 2 is 38

Step-by-step explanation:

Finding the mean:

formula: sum of the data set / total number of terms

sum of the data set: 18 + 29 + 35 + 58 + 65 = 205

total number of terms: there is 5 numbers in the data set

mean = 205 / 5

mean = 41

MAD (Mean Absolute Value):

step 1: Find the mean of the data (above)

step 2: Find the distance between each data and mean.

18, 29, 35, 58, 65

Distance between 18 and 41 is 23               (41 - 18 = 23)

Distance between 29 and 41 is 12               (41 - 29 = 12)

Distance between 35 and 41 is 6               (41 - 35 = 6)

Distance between 58 and 41 is -17             (41 - 58 = -17)

Distance between 65 and 41 is -24           (41 - 65 = -24)

step 3: take the absolute value of any negative numbers

|-17| and |-24| is 17 and 24

step 4: add all the distances

23 + 12 + 6 + 17 + 24 = 82

step 5: divided it by the number of data

82 / 5 = 16.4

formula: sum of the data set / total number of terms

sum of the data set: 19 + 26 + 27 + 45 + 73 = 190

total number of terms: there is 5 numbers in the data set

mean = 190 / 5

mean = 38

MAD (Mean Absolute Value):

step 1: Find the mean of the data (above)

step 2: Find the distance between each data and mean.

19, 26, 27, 45, 73

Distance between 19 and 38 is 19                (38 - 19 = 19)

Distance between 26 and 38 is 12              (38 - 26 = 12)

Distance between 27 and 38 is 11               (38 - 27 = 11)

Distance between 45 and 38 is -7             (38 - 45 = -7)

Distance between 73 and 38 is -35           (38 - 73 = -35)

step 3: take the absolute value of any negative numbers

|-7| and |-35| is 7 and 35

step 4: add all the distances

19 + 11 + 12 + 7 + 35 = 84

step 5: divided it by the number of data

84 / 5 = 16.8

Let me know if you have any questions !

For this problem, we need to use our integral knowledge to set up the problem:

The bounds will be from 2 to 6, cutting tiny horizontal bars into the graph, to approximate the area

Now for the function inside the integral:

 ⇒ it is the top function minus the bottom function

       ⇒ function within integral = x² - 0

Let's put it all together and solve:

   [tex]Area=\int\limits^6_2 {x^2-0} \, dx =\int\limits^6_2 {x^2} \, dx=\frac{6^3}{3} -\frac{2^3}{3} \\Area=\frac{6^3-2^3}{3} =\frac{216-8}{3} =\frac{208}{3}[/tex]

Answer: 208/3 ≈ 69.333

Hope that helps!

By applying the equation of dilation, the coordinates of the vertices of the triangle ABC are A'(x, y) = (-12, 0), B'(x, y) = (0, -9) and C'(x, y) = (-12, -9).

A dilation is a type of rigid transformation. Rigid transformations are transformations applied to geometric loci such that Euclidean distances are conserved.

There is a triangle and its image must be a triangle, the new triangle is found by transforming the three vertices of the prior one following this formula:

A'(x, y) = P(x, y) + k · [A(x, y) - P(x, y)]     (1)

Where:

If we know that P(x, y) = (0, 0), A(x, y) = (-4, 0), B(x, y) = (0, -3) and C(x, y) = (-4, -3), then the new vertices of the triangle are, respectively:

Point A

A'(x, y) = (0, 0) + 3 · [(-4, 0) - (0, 0)]

A'(x, y) = (-12, 0)

Point B

B'(x, y) = (0, 0) + 3 · [(0, -3) - (0, 0)]

B'(x, y) = (0, -9)

Point C

C'(x, y) = (0, 0) + 3 · [(-4, -3) - (0, 0)]

C'(x, y) = (-12, -9)

Lastly, we draw the two triangles, which are presented in the image attached below.

To learn more on dilations: https://brainly.com/question/13176891

#SPJ1

The value of ABC when AC is given as 152 will be 76°.

It should be noted that the angles that are opposite to equal sides are equal and that the angle sum property of triangle is 180°.

In this case, (2 × ABC) = 152°

2ABC = 152°

ABC = 152°/2

ABC = 76°

In conclusion, the correct option is C.

Learn more about angles on:

brainly.com/question/3652233

#SPJ1

The diagram shows that the triangles on the graph had similar ratios, as such their vertical heights to their horizontal are equivalent.

Option D is correct.

The slope of a graph determines the steepness of the graph and it is the difference between two points on the y-coordinate(rise) and the difference between two points on the x-coordinate(run).

[tex]\mathbf{slope = \dfrac{rise}{run}}[/tex]

[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]

[tex]\mathbf{slope = \dfrac{ y_2-y_1}{x_2-x_1}}[/tex]

From the diagram attached, we can see that the triangles on the graph had similar ratios, as such their vertical heights(y-coordinates) to their horizontal (x-coordinates) are equivalent.

Learn more about the slope of a graph here:

https://brainly.com/question/19376563

#SPJ1

Answer:

she should get ready by 11:10

Step-by-step explanation:

Add All the time up 75(1 hour 15min=60+75)+40+25+30=170minutes

170minutes/60= 2 hour 50minutes

subtract 2 hour 50minutes from 2:00

= 11:10

Answer:

Bala = 279$

Peter = 1395$

Step-by-step explanation:

Peter has 5 times as much Money as Bala.

They have $1674 in total.

How much more money has Peter than bala

Bala has 1 unity

Peter has 5 unity

total unity = 6

Find 1 unity

1674 : 6 = 279

Bala = 279

Peter = 5 * 279 = 1395

Answer: 8/10

Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10

Answer:

8

Step-by-step explanation:

8 is the answers I think

Answer:

Using it's concept, it is found that the probability of randomly selecting a tree or a flower is given by:

[tex]p = \frac{8}{15}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, out of 30 cards, 8 + 8 = 16 are trees or flowers, hence the probability is given by:

[tex]p = \frac{16}{30} = \frac{8}{15}[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

the answer is -3/4 c

Step-by-step explanation:

it's down 3 over 4

Based on the function shown on the graph, we can find the domain to be C. x ≥ 0.

The domain refers to where all the values of x and y for the function fall within the graph.

As seen from the graph, there is no negative value of x and the lowest value of x is 0.

The domain for x is therefore:

x ≥ 0.

Find out more on graph domain at https://brainly.com/question/12463513.

#SPJ1

The expected count for the cell corresponding to the white car in the sampling will be 204.

From the information given, the certain car model comes in four different colors, and can either have automatic or manual transmission.

The expected count for the cell corresponding to the white car will be:

= 96 × 204/384

= 51

Learn more about sampling on:

brainly.com/question/17831271

#SPJ1

Answer:

Y=-0.22X+6.33

Step-by-step explanation:

Y-yo=m(X-x0)

punto A=(-3,5)

punto B=(6,3)

ecuacion de la recta: Y-yo=m(X-x0)

m=Pendiente=[tex]\frac{5-3}{(-3-6)} =\frac{2}{-9}[/tex]

sea B(6,3)  xo=6  y yo=3

reemplazando:

Y-6=[tex]\frac{-2}{9}[/tex](X-3)

Y-6=-0.22X+0.33

Y=-0.22X+6.33

As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.

Answer:

12X3/-a=`12

Step-by-step explanation:

12x3=36
36xa/+=12

The length of the rope Kurt started with is 13 1/3 inches

From the question, we are to determine the total length of the rope

From the given information,

The first piece was 4 4/5 inches long

and

The second piece was 8 1/2 inches long

Then,

The length of the rope Kurt started with will be

4 4/5 + 8 1/2

[tex]4\frac{4}{5} + 8\frac{1}{2}[/tex]

First, convert the fractions into improper fractions

[tex]\frac{24}{5} + \frac{17}{2}[/tex]

The Lowest common multiple (LCM) of the denominators is 10.

Then, we get

[tex]\frac{(2\times 24) + (5 \times 17)}{10}[/tex]

= [tex]\frac{48 + 85}{10}[/tex]

= [tex]\frac{133}{10}[/tex]

= [tex]13 \frac{1}{3}[/tex]

Hence, the length of the rope Kurt started with is 13 1/3 inches.

Learn more on Calculating lengths here: https://brainly.com/question/26496891

#SPJ1

The scatter plot for the data will be A. A graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.1), (5 foot 1 inch, 9.5), (5 foot 2 inches, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8).

A scatter plot is a set of points plotted on horizontal and vertical axes that show the extent of correlation between the variables.

In this case, the scatter plot for the data will be a graph has height on the x-axis, and weight on the y-axis, from 9 to 10.8 in increments of 0.2. Points are at (5, 9.1), (5 foot 1 inch, 9.5), (5 foot 2 inches, 9.8), (5 foot 3 inches, 10), (5 foot 4 inches, 10.4), (5 foot 5 inches, 10.8).

Learn more about scatter plot on:

https://brainly.com/question/6592115

#SPJ1

Answer:

Step-by-step explanation:

The total number of bags in the bottle = 20 + 15 = 35

Then

the probability that the first bag is blue = 20/35

If we replace the first bag :

the probability that the second (picked) bag is blue = 15/35

Conclusion:

If two bags are picked at random one after the other with replacement

Then

the probability that the first bag is blue and then red is :

(20÷35)×(15÷35)

= (4÷7)×(3÷7)

= 12÷49

= 0.244897959184

[tex]\huge\sf\underline{Answer}[/tex]

Let's find out ~

Given :-

Solution :-

[tex]\sf\rightarrow \:LSA \: of \: cuboid \: = 2h \: ( \: l + b \: )[/tex]

[tex]\sf\rightarrow \: 180 = 2h \: (10 + 5)[/tex]

[tex]\sf\rightarrow180 = 2h \: \times 15[/tex]

[tex]\sf\rightarrow 180 = 30h \: [/tex]

[tex]\sf\rightarrow \: 30h \: = 180[/tex]

[tex]\sf\rightarrow \: h = \frac{180}{30} [/tex]

[tex]\sf\rightarrow \: 6[/tex]

Thus , the height of cuboid is 6m

Using it's concept, it is found that the relative frequency of 6th graders who rode a car is given by:

D. 55%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The number of 6th graders is given by:

N6 = 576 - (219 + 189) = 168.

The number of 6th graders who rode a car is:

N6C = 168 - 75 = 93

Hence the relative frequency is given by:

r = 93/168 = 55%.

Hence option D is correct.

More can be learned about relative frequencies at https://brainly.com/question/14398287

#SPJ1