Two aircrafts travel from the position P(30°N, 130°W) to Q (50°N, 170°E) all leaving at 0845hrs and at the same speed of 500km/hr. Aircraft A travels due north to the position (50°N, 130°W) and then along a parallel of latitude using the shortest route. Aircraft B travels along a parallel of latitude (30°N, 170°E) and then due north.
(a) If a third aircraft C had left a point R (30°N, 10°W) at the same time as the two above aircrafts left P and flew via the shortest possible distance to point Q, calculate its position when the aircraft A was passing the longitude 180°W. (b) Calculate the arrival local time of the two aircrafts. (5mks) (5mks)​

In the linear equation, the values of x and y are  10 and 5

A linear equation is an algebraic equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0, where x is a variable, A is a coefficient, and B is a constant.

the given equation is 2x+4y = 20

to find the value of x, make y to be zero first

2(0) + 4y = 20

0+4y = 20

4y = 20 making y the subject of the relation to have

y = 5

Then when y = 0

2x +4(0) = 20

2x = 20 therefore making x the subject of the relation,

x = 10

Therefore the values of x and y are 10 and 5 respectively

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The total number of data values (games played) represented in the table is 14.

To determine the total number of data values (games played) represented in the frequency table, we need to sum up the frequencies for each category (number of goals scored).

The frequency represents the number of games in which a particular number of goals was scored.

Let's calculate the total number of games played by summing up the frequencies:

Total number of games played =

Frequency of 0 goals + Frequency of 1 goal + Frequency of 2 goals + Frequency of 3 goals + Frequency of 4 goals + Frequency of 7 goals + Frequency of 9 goals

Total number of games played = 1 + 3 + 2 + 4 + 2 + 1 + 1

Total number of games played = 14

We must add the frequencies for each category (number of goals scored) to get the total number of data values (games played) reflected in the frequency table.

The number of games with a specific amount of goals scored is the frequency.

Let's add up the frequencies to determine the total number of games played:

Total games played = Frequency of 0 goals, Frequency of 1, Frequency of 2, Frequency of 3, Frequency of 4, Frequency of 7, and Frequency of 9 goals.

Total games played: 1 plus 3 plus 2 plus 4 plus 2 plus 1 plus 1

14 games were played in total.

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Answer:

See attachments.

Step-by-step explanation:

The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.

Given function:

[tex]y=\dfrac{5}{x}-2, \quad x > 0[/tex]

Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:

[tex]\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}[/tex]

[tex]\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}[/tex]

[tex]\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}[/tex]

Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

[tex]\hrulefill[/tex]

Given function:

[tex]y=\dfrac{-2}{x+1}+3, \quad x < -1[/tex]

Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:

[tex]\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}[/tex]

[tex]\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}[/tex]

[tex]\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}[/tex]

Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

The statement "an n-ary relation R is a set of n-tuples" refers to a mathematical concept in which an n-ary relation R is defined as a collection or set of n-tuples.

In this context, an n-ary relation refers to a relationship or connection between n elements or entities. It represents a logical association between these elements based on certain criteria or conditions.

An n-tuple, on the other hand, is an ordered sequence or collection of n elements, where the order and position of each element in the sequence are important.

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Answer:

  see below

Step-by-step explanation:

You want the piecewise function that gives straight line segments between domain boundary points (-8, 5), (-2, -9), (1, -2), (8, 4).

The two-point equation for the slope of a line is ...

  m = (y2 -y1)/(x2 -x1)

For the first pair of points, the slope is ...

  m = (-9 -5)/(-2 -(-8)) = -14/6 = -7/3

The attached calculator image shows the computation of slope for the other two segments. Those slopes are 7/3 and 6/7.

The slope-intercept form of the equation for a line can be rearranged to give the y-intercept:

  y = mx + b

  b = y - mx

In the attached, we used the (x1, y1) point for each segment. For the first segment, the y-intercept is ...

  b = 5 -(-7/3)(-8) = -41/3

The other two y-intercepts are computed to be -13/3 and -20/7.

The piecewise function that models the given data is ...

  [tex]\boxed{y=\begin{cases}-\dfrac{7}{3}x-\dfrac{41}{3}\quad&-8\le x\le-2\\\\\dfrac{7}{3}x-\dfrac{13}{3}\quad&-2 < x\le1\\\\\dfrac{6}{7}x-\dfrac{20}{7}\quad&1 < x\le8\end{cases}}[/tex]

__

Additional comment

There is nothing in this problem statement that requires the function be continuous. However, we have made it so this function is continuous in the region where it is defined.

The same repetitive computations are handled nicely by a spreadsheet.

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Answer:

Multiplicative identity for any real number is 1.

Step-by-step explanation:

The number that belongs in the green box is 130.4 units.

In Mathematics and Geometry, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

a + c + b = 180°

12° + 27° + b = 180°

39° + b = 180°

b = 180° - 39°

b = 141°

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

sinA/a = sinB/b

sin141/a = sin12/43

a = 43sin141/sin12

a = 27.108/0.2079

a = 130.4 units.

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Answer:

[tex]\dfrac{7}{9}[/tex]

Step-by-step explanation:

Let x be the denominator.

If the numerator is 2 less than the denominator, then the expression for the numerator is (x - 2):

[tex]\dfrac{x-2}{x}[/tex]

If 3 is added to both the numerator and the denominator, and the answer is 5/6, then:

[tex]\dfrac{x-2+3}{x+3}=\dfrac{5}{6}[/tex]

Now we can solve the equation for x.

Simplify the numerator in the fraction on the left of the equation:

[tex]\dfrac{x+1}{x+3}=\dfrac{5}{6}[/tex]

Cross mutliply:

[tex]6(x+1)=5(x+3)[/tex]

Expand the brackets:

[tex]6 \cdot x +6 \cdot 1 = 5 \cdot x + 5 \cdot 3[/tex]

[tex]6x+6=5x+15[/tex]

Subtract 5x from both sides of the equation:

[tex]6x+6-5x=5x+15-5x[/tex]

[tex]x+6=15[/tex]

Subtract 6 from both sides of the equation:

[tex]x+6-6=15-6[/tex]

[tex]x=9[/tex]

Therefore, the value of x is 9.

Now substitute the found value of x into the original rational expression:

[tex]\dfrac{x-2}{x}=\dfrac{9-2}{9}=\dfrac{7}{9}[/tex]

Therefore, the original fraction is:

[tex]\boxed{\dfrac{7}{9}}[/tex]

Hello!

Event A:

is a 5 or 6 = 2 numbers on 6 = 2/6 = 1/3

EventB:

is not a 1 = 2,3,4,5,6 = 5/6

P(A and B) = 1/3 x 5/6 = 1x5/3x6 = 5/18 ≈ 0.28

The answer is 0.28.

The probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 20 + 12 + 4 = 36

probability of A = P(A) = 20/36

probability of B = P(B) = 12/36

probability that either event A or B will occur = 20/36 + 12/36

probability that either event A or B will occur = (20 + 12)/36

probability that either event A or B will occur = 32/36

probability that either event A or B will occur = 0.89

Therefore, the probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

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The width of the vegetable garden is 8 feet.

To determine the width of the vegetable garden.

Given information:

Flower garden length = 6 feet

Flower garden width = 4 feet

Vegetable garden length = Flower garden length

Area of the flower garden = half the area of the vegetable garden

To find the width of the vegetable garden, we need to find the area of both gardens.

Area of the flower garden = length × width

Area of the flower garden = 6 feet × 4 feet

Area of the flower garden = 24 square feet

Since the area of the flower garden is half the area of the vegetable garden, we can set up the following equation:

24 square feet = (1/2) × Area of the vegetable garden

To solve for the area of the vegetable garden, we multiply both sides of the equation by 2:

2 × 24 square feet = Area of the vegetable garden

48 square feet = Area of the vegetable garden

Now that we know the area of the vegetable garden is 48 square feet, we can find the width.

Area of the vegetable garden = length × width

48 square feet = 6 feet × width

To solve for the width of the vegetable garden, we divide both sides of the equation by 6:

48 square feet / 6 feet = width

8 feet = width

Therefore, the width of the vegetable garden is 8 feet.

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Hello!

men = 10/26 = 5/13

women = 2/29

P = 5/13 x 2/29 = 10/377

Vector g is from the red jet ski to the green boat. The magnitude is √26 and the direction angle is 248.7°, the component form of vector g is approximately (-3.8, -1.4).

To write the component form of vector g, we need to determine the horizontal and vertical components of the vector.

Given:

Magnitude of g = √26

Direction angle = 248.7°

To find the horizontal component (g_x) and vertical component (g_y) of vector g, we can use the following trigonometric formulas:

g_x = magnitude * cos(angle)

g_y = magnitude * sin(angle)

Substituting the given values:

g_x = √26 * cos(248.7°)

g_y = √26 * sin(248.7°)

Now, let's calculate the values:

g_x = √26 * cos(248.7°) ≈ -3.8

g_y = √26 * sin(248.7°) ≈ -1.4

Therefore, the component form of vector g is approximately (-3.8, -1.4).

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Answer:

c=19

Step-by-step explanation:

11=c-8

+8  +8

19=c

11=c-8

move the variable to the left - hand side and change it sign: 11-c= -8

move the constant to the right-hand side and change its sign: -c= -8-11

calculate the difference: -c = -19

change the signs on each side c=19

Answer:

shaded area ≈ 69.53 cm²

Step-by-step explanation:

the shaded area (A) is calculated as

A = area of square - area of circle

area of square = 18² = 324

area of circle = πr² ( r is the radius )

the diameter of the circle = 18 , so r = 18 ÷ 2 = 9

area of circle = π × 9² = 81π

then

A = 324 - 81π ≈ 69.53 cm² ( to 2 decimal places )

Answer:

ab(3a + 4b)

Step-by-step explanation:

Here are the steps on how to write the expression

3a^2 b + 4ab^2 as an equivalent algebraic expression:

1. Factor out the greatest common factor, which is ab.

2. The expression becomes ab(3a + 4b).

3. This is an equivalent algebraic expression to 3a^2 b + 4ab^2.

steps:

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

To simplify the expression 3a^2b + 4ab^2, [ we can factor out the common factor of ab from both terms: Step 1: Take out the common factor of ab. 3a^2b + 4ab^2 = ab(3a + 4b) Now the expression is in its factored form.

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

We have,

Let's solve the problem step by step.

-Let's assume that the number of sheep in the second pen is 7x, where x is a positive integer representing the number of multiples of 7.

Similarly, let's assume that the number of sheep in the third pen is 7y, where y is a positive integer representing the number of multiples of 7.

According to the given information, the shepherd placed a total of 63 sheep in the pens:

7 + 7x + 7y = 63

We can simplify this equation by dividing both sides by 7:

1 + x + y = 9

Now we need to find positive integer values for x and y that satisfy this equation.

Since we know that there were more sheep in the third pen, y should be greater than x.

Let's try different values for x and y:

If x = 1, then y = 9 - (1 + 1) = 7

If x = 2, then y = 9 - (2 + 1) = 6

If x = 3, then y = 9 - (3 + 1) = 5

If x = 4, then y = 9 - (4 + 1) = 4

We can see that when x = 1, y = 7, which satisfies the condition that there were more sheep in the third pen.

Therefore, the number of sheep in the second pen (7x) is 7 x 1 = 7, and the number of sheep in the third pen (7y) is 7 x 7 = 49.

Thus,

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

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The complete question:

A shepherd put sheep in pens. In a corral he placed 7 sheep, in the

second and in the third pen he placed multiples of 7. If in total he placed 63

sheep, knowing that where more sheep, was in the third corral.

How many sheep could he put in pens 2 and 3?

To find the previous population, we need to determine the population before the 27% decrease. Here's how we can calculate it:

Let's assume the previous population is P.

According to the problem, the current population is 7300, which represents 100% - 27% of the previous population:

(100% - 27%) * P = 7300

To simplify the equation, convert 27% to decimal form:

(100% - 0.27) * P = 7300

Simplifying further:

0.73P = 7300

Divide both sides of the equation by 0.73:

P = 7300 / 0.73

P ≈ 10000

Therefore, the previous population was approximately 10,000.

~~~Harsha~~~

The equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

The given coordinate points are (0, 9) and (15/2, 5).

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

Here, (0-7.5)²+(9-5)²=r²

56.25+16=r²

r=8.5

Now, the equation is (x-0)²+(y-9)²=8.5²

x²+y²-18y+18=72.25

x²+y²-18y+18-72.25=0

x²+y²-18y-54.25=0

Therefore, the equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

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All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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Answer:

7) No

8) Yes

9) Yes

Step-by-step explanation:

Plug each possible solution into the inequality and see if it holds true:

If x=1 (Not a solution)

[tex]\displaystyle 3(1)-2\stackrel{?}{ < }2-2(1)\\3-2\stackrel{?}{ < }2-2\\1\nless0[/tex]

If x=1/2 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{2}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{2}\biggr)\\\frac{3}{2}-2\stackrel{?}{ < }2-1\\\\\frac{1}{2} < 1[/tex]

If x=1/3 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{3}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{3}\biggr)\\1-2\stackrel{?}{ < }2-\frac{2}{3}\\\\-1 < \frac{4}{3}[/tex]

The complete statements are;

m<Y = 90 degrees

m<M = 56.3 degrees

m<Z = 57 degrees

XY = 8

YZ = 12

To determine the values, we need to know the following;

From the image shown, we have that;

1. The measure of <Y is 90 degrees; angle at right angle

2. For m<M , we have;

Using the tangent identity, we have;

tan M = 12/8

tan M = 1.5

M = 56. 3 degrees

3. For m<Z, we have;

33 + m<Y + m<Z = 180

collect like terms

m<Z = 57 degrees

4. NM = XY

XY = 8

5, YZ = 12

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1)

The trigonometric functions :

sinA = 5/13 , cosA = 13/12 , tanA = 5/13

Given,

Right angled triangle with:

P = 5

B = 12

H = 13

Then trigonometric ratios,

sinA = P/H

cosA = B/H

tanA = P/B

Hence the ratios can be defined as,

sinA = 5/13

cosA = 12/13

tanA = 5/12

2)

The value x in the radical form 10.77

Given,

Right angled triangle,

Perpendicular = 4

Base = 10

Hypotenuse = x

Apply pythagora's theorem,

P² + B² = H²

4² + 10² = H²

16 + 100 = H²

H = 10.77

Hence the value of x is 10.77 .

3)

The value of x in radical form

Given,

P = 56

B = x

H = 106

Apply pythagora's theorem,

P² + B² = H²

56² + x² = 106²

x = 90

Hence the value of x is 90 .

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Answer:

$27.01

Step-by-step explanation:

100% + 19.3% = 119.3%.

$32.22 = 119.3%

divide both sides by 119.3:

(32220/1193) = 1

multiply by 100 to get 100% ie the bill before the tip:

$27.01 = 100%

$27.01 is bill to nearest cent

A full circle has [tex]360^{\circ}[/tex].

[tex]\dfrac{4}{9}\cdot 360^{\circ}=160^{\circ}[/tex]

The mark angle is [tex]160^{\circ}[/tex].

Answer:

history Is a good subject

Answer:

Step-by-step explanation:

3.14 . 11= 150/360