An airplane flies at 400 mph with a direction of 120° relative to the air. The plane experiences a wind that blows 40 mph with a direction of 50°.

Part A: Write each of the vectors in linear form. Show all necessary calculations. (6 points)

Part B: Find the sum of the vectors. Show all necessary calculations. (2 points)

Part C: Find the true speed and direction of the airplane. Round the speed to the thousandths place and the direction to the nearest degree. Show all necessary calculations.

Answer:

11000 pounds

Step-by-step explanation:

1 US ton=2000 pounds

multiply the mass value by 2000

5.5ton x 2000pound

=11000pounds

Answer:

6

Step-by-step explanation:

If two secants are drawn from a point outside a circle, then product of one secant segment and its external part equal the product of the other secant segment and its external part.

(Secant-Secant Power Theorem)

(JG)(JH) = (JM)(JK)

(16) X (7) = (8+X)(8)

112=64+8X

8X=48

X=6

two correct answers :

x = -2c

or

x = -2b - 2c

Answer:

Step-by-step explanation:

Let k represent the multiplier of the ratio units that will give actual dimensions. The the height can be represented by k, the breadth by 2k, and the length by 3k. The volume of the room will be ...

  V = LBH

  V = (3k)(2k)(k) = 6k³

  3072 m³ = 6k³ . . . . . use known volume

  512 m³ = k³ . . . . . . . divide by 6

  8 m = k . . . . . . . . . take the cube root

The height of the room is 8 m, its breadth is 16 m, and its length is 24 m.

Answer:

See below ↓↓↓

Step-by-step explanation:

Given :

Solving :

Solution :

Answer:

[tex]\frac{x-3}{x+2}[/tex]

Step-by-step explanation:

[tex]\frac{3x^2+6x-45}{3x^2+21x+30}[/tex]                   Rewrite

[tex]\frac{x^2+2x-15}{x^2+7x+10}[/tex]                      Factor out GCF (3)

[tex]\frac{x^2+5x-3x-15}{x^2+5x+2x+10}[/tex]                 Replace b with factors

[tex]\frac{(x-3)(x+5)}{(x+5)(x+2)}[/tex]                     Factor by grouping

[tex]\frac{x-3}{x+2}[/tex]                               Final answer

For a more detailed explanation, please look at the help image attached. It shows each step on how to factor polynomials.

I hope this helps!

Answer

x=-2

Step-by-step explanation:

If x was equaled to -2 the outcome would be infinity, does this help at all?

Answer:

Step-by-step explanation:

Yes, there are certain values of x that makes given expression undefined in the set of real numbers.

x + 2 ≤ 0 ⇒ x ≤ - 2

If x ∈ ( - ∞ , - 2 ] , given expression is undefined.

Answer:

25 degrees

Step-by-step explanation:

complementary angles are 90 degrees

90-65=25 degrees

Transforming the points involves changing their coordinates

The image of the points are:  (3, 6), (-11, 12) and  (-3, -12)

The coordinates of the points are given as:

X(2, 4)

Y(5,-3)

Z(-7, 1)

The rule of this transformation is:

(x, y) to (y, -x)

So, we have:

X' = (4, -2)

Y' = (-3, -5)

Z' = (1, 7)

The rule of this transformation is:

(x, y) to (2x, 2y)

So, we have:

X'' = (8, -4)

Y'' = (-6, -10)

Z'' = (2, 14)

The rule of this transformation is:

(x, y) to (x, -y)

So, we have:

X''' = (8, 4)

Y''' = (-6, 10)

Z''' = (2, -14)

The rule of this transformation is:

(x, y) to (x -5, y + 2)

So, we have:

X'''' = (3, 6)

Y'''' = (-11, 12)

Z'''' = (-3, -12)

Hence, the image of the points are:  (3, 6), (-11, 12) and  (-3, -12)

Read more about transformation at:

https://brainly.com/question/4289712

The system of equations that represents the imposed constraints is given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

A student may not serve more than 10 total hours per week, hence:

[tex]g + t \leq 10[/tex]

A student must serve at least 1 hour per week at each task, hence:

[tex]g \leq 1, t \leq 1[/tex]

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Answer:

59

Step-by-step explanation:

1534/26=59

It's 59 because I used a calculator

17/10 miles

1/5*1+1/2*3=3/2+14/10=17/10

Answer:

1/5+3/2=2/10+15/10=17/10

Answer:

It's the y-int.

Step-by-step explanation:

I can't really see the graph well

Answer:

-335670

Step-by-step explanation:

Given :

Solving :

It forms a arithmetic sequence

So

a_335:-

So

S_n

Answer: 7.4.

Step-by-step explanation: To find the area of a triangle, you need the base, height, and then divide the results by two.  The following is done below:

A = h x b / 2, where h is the height, b is the base, and A is the area of the triangle.

A = 3.7 x 4 = 14.8.  

Next, 14/8 / 2 = 7.4.

Therefore, 7.4 is your answer.

Hope this helps! :)

Answer:

x = -2 - i,  -2 + i.

Step-by-step explanation:

3x2 = -12x - 15

3x^2 + 12x + 15 = 0

Divide through by 3:

x^2 + 4x + 5 = 0

x^2 + 4x = -5

Completing the square:

x^2 + 4x + 4 = -5 + 4

(x + 2)^2 = -1

x + 2 =  √-1 = i

x = -2 - i, -2 + i.

Answer:

186

Step-by-step explanation:

186-50%= 93 or since 50% is half off 93×2=186.

Answer:

264.54 cm

Step-by-step explanation:

Multiplying

answer:

d

perimeter = 52.56 inches

area = 137.12 square inches

The total perimeter of the given figure is 60.56 inches and the total area of the given figure is 137.12 square inches. Therefore, option D is the correct answer.

The composite shape with trapezium and semicircle is given.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

The total perimeter = Perimeter of trapezium + Circumference of semicircle

Perimeter of trapezium = (8+10+10+20)

= 48 inches

Circumference of semicircle =πr

Here radius=8/2

= 4 inches

Now, 3.14×4 =12.56 inches

The total perimeter = 48+12.56

= 60.56 inches

Total area= Area of trapezium + Area of semicircle

Area of trapezium =1/2 (a+b)×h

= 1/2 (20+8)×8

= 28×4

= 112 square inches

Area of semicircle =πr²/2

= (3.14×4²)/2

= 25.12

Total area= 112+25.12

= 137.12 square inches

The total perimeter of the given figure is 60.56 inches and the total area of the given figure is 137.12 square inches. Therefore, option D is the correct answer.

To learn more about the perimeter visit:

https://brainly.com/question/6465134.

#SPJ2

Answer:

15)

ABCD is quadrilateral

∠MBC+∠ABC=180°

∠ABC = [tex]\tt 180-71=109^o[/tex]

The sum of all angles of quadrilateral = 360°

[tex]\tt 10x+6+12x-2+8x-1+109=360^o[/tex]

[tex]\tt 31x+112=360[/tex]

[tex]\tt 31x+112-112=360-112[/tex] ( Subtract 112 from both sides)

[tex]\tt 31x=248[/tex]  (Simplify)

[tex]\tt \cfrac{31x}{31}=\cfrac{248}{31}[/tex] (Divide both sides by 21)

[tex]\tt x=8[/tex]

___

16) Find m∠v

The polygon has 6 sides

Sum of angles:- (6-2)=180= 720°

so,

[tex]\tt 90+9x-19+111+5x+8+128+7x+3=720[/tex]

[tex]\tt 2x+321=720[/tex]

[tex]\tt 21x+321-321=720-321[/tex] ( Subtract 321 from both sides)

[tex]\tt 21x=399[/tex] (Simplify)

[tex]\tt \cfrac{21x}{21}=\cfrac{399}{21}[/tex] ( Divide both sides by 21)

[tex]\tt x=19[/tex]

Therefore, m∠v=19

____

Answer:

length: 40, width: 20

Step-by-step explanation:

length = 1/2×80/1 = 40

width = 1/4 × 80/1 = 20

hope this helps =)

Answers:

Sample Variance = 31.03

Sample Standard Deviation = 5.57

See the table below.

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

Explanation:

M refers to the midpoint of each interval. The midpoint is [tex]M = \frac{a+b}{2}[/tex] where a,b are the left and right endpoints.

For example, [tex]M = \frac{0+4}{2} = \frac{4}{2} = 2[/tex] in the first row.

Multiply the frequency with the midpoint to get the third column. Summing this column of values leads to 4+49+180+153+154 = 540 shown at the bottom of that column.

Divide this sum over the sum of the frequencies (2+7+15+9+7 = 40) and we arrive at [tex]\overline{x} = \frac{540}{40} = 13.5[/tex] which is the sample mean xbar.

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

After we determine xbar, we subtract it from each value of M. Then we square the result to get [tex](M - \overline{x})^2[/tex]. Multiply that with the column f to get the new column [tex]f(M-\overline{x})^2[/tex].

This column is added to arrive at 1210 shown in the table below. Divide this over the sum of the frequencies minus 1. So we divide by n-1 = 40-1 = 39 to get roughly 31.03

This is the sample variance.

The square root of this is sqrt(31.03) = 5.57 and this is the approximate sample standard deviation.

Answer:

-10x + 11/x

Step-by-step explanation:

I think you mean to simplify

1/3x(5+(7)(4))-10

= -30x + 33/3x

= -10x + 11/x

Using the slope concept, it is found that the shuttle traveled 3.2 miles while Marion was watching.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

Initially, the angle of elevation is of 16º, with an elevation of 1 mi, hence:

[tex]\tan{16^\circ} = \frac{1}{x_1}[/tex]

[tex]x_1 = \frac{1}{\tan{16^\circ}}[/tex]

[tex]x_1 = 3.5[/tex]

Then, at the end, the angle will be of 74º, with the elevation remaining constant, hence:

[tex]\tan{74^\circ} = \frac{1}{x_2}[/tex]

[tex]x_2 = \frac{1}{\tan{74^\circ}}[/tex]

[tex]x_2 = 0.3[/tex]

The distance is:

[tex]d = x_1 - x_2 = 3.5 - 0.3 = 3.2[/tex]

The shuttle traveled 3.2 miles while Marion was watching.

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

x=120°

Step-by-step explanation:

120×2=240

360-240=120

x=120

Answer:

Angle x = 120 Degrees

Step-by-step explanation:

Formula for finding out total interior angles in a polygon = (Number of sides - 2) x 180 Degrees

e.g. Triangle have 3 sides

3 - 2 = 1

1 X 180 = 180

A Triangle has a total of 180 Degrees

Total Interior angle of a hexagon = 720 Degrees

Interior angle of a regular hexagon is 720 / 6 = 120

360 Degrees in a circle

360 - 120 - 120 = 120

answer:

A=46°

a=17.983 (tenths- 18, hundredths- 17.98)

b=17.366 (tenths- 17.4, hundredths- 17.37)

explanation:

1. find angle A

it shows that the angle corresponding with the side length of 25 is a right angle, meaning it's 90°. using that information and the angle given to us (44°), we're able to find the missing angle. since all the angles in a triangle always add up to 180°, we can add the two angles together and then subtract that from 180° to find the missing angle.

90°+44°=134°

180°-134°=46°

A=46°

2. find side a

using the law of cosines, we're able to find the length of side a. cosine of an angle equals [tex]\frac{adjacent}{hypotenuse}[/tex]. we'll be using angle B (44°) for our angle. after we plug in the values, we can just solve the equation to find side a.

cosine44°=[tex]\frac{a}{25}[/tex]
(multiply both sides by 25)

25cosine44°=a
a=17.983

3. find side b

finding the length of side b is very similar to how you found side a. you can use the law of cosines again (make sure you use the right side lengths and angles!), but i used the law of sines. the sine of an angle equals [tex]\frac{opposite}{hypotenuse}[/tex]. we're going to be using the same angle for this.

sine44°=[tex]\frac{b}{25}[/tex]

(multiply both sides by 25)

25sine44°=b

b=17.366

--

if this helped, please consider giving brainliest !

Answer: 45

Step-by-step explanation:

A right isosceles triangle can only ever have two equal sides, since he sum of the three angles of any triangle is equal to 180 degrees, do the quick math of 180 - 90 = 90, then 90/2 = 45. Both remaining angles of the triangle are 45 degrees, including x, and when you add all angles together 90 + 45 + 45 it equals 180 degrees.

Answer:

1800 m²

Step-by-step explanation:

The surface area of a prism is the sum of the areas of its faces.

⇒ Surface area of rectangle prism = 2(LH) + 2(BH) + 2(LB)

⇒ Surface area of rectangle prism = 2(LH) + 2(BH) + 2(LB) = 450 m²

⇒ 2(LH + BH + LB) = 450 m²

Finding the surface area if the dimensions are doubled:

⇒ 2[(2L × 2H) + (2B × 2H) + (2L × 2B)]

⇒ 2[(4LH) + (4BH) + (4LB)]

⇒ 2[4LH + 4BH + 4LB]

⇒ 2[4(LH + BH + LB)]

⇒ 2[2 × 2(LH + BH + LB)]

⇒ 2[2(450)]                                                           [2(LH + BH + LB) = 450 m²]

⇒ 2[900]

⇒ 1800 m² (Option C)

Answer:

4 years

Step-by-step explanation:

basically, multiple 16,250 by 107.9%, get the product and multiply that product by 107.9%+ 7.9% and keep on doing that until you eventually get to about 33,000 which is a bit more than double 16,250 but 4 years is still the minimum years it will take to get AT LEAST double. :)

Go through second method

Area of one traingle'-

Area of two triangles=6cm²

Area of rectangle

Total:-

Answer:

Method 1

Find the area of the rectangle, 45 cm².  Subtract the area of the cut-out triangle from the rectangle,  45 - 6 = 39 cm²

Method 2

Separate the ribbon into two triangles and a rectangle.

33 + 3 + 3 = 39 cm²

Step-by-step explanation:

Formulae

Method 1

Area of the rectangle:

= 3 × 15

= 45 cm²

Area of the cut-out triangle:

= 1/2 × 3 × 4

= 6 cm²

Find the area of the rectangle, 45 cm².  Subtract the area of the cut-out triangle from the rectangle,  45 - 6 = 39 cm²

Method 2

Area of the rectangle:

= 3 × (15 - 4)

= 3 × 11

= 33 cm²

Area of one triangle:

= 1/2 × (3 ÷ 2) × 4

= 3 cm²

Separate the ribbon into two triangles and a rectangle.

33 + 3 + 3 = 39 cm²