In this figure, and are parallel. is perpendicular to line segment . If the length of is a units, then the length of is units.

Answer:

The airplane is 222 miles far from the airport.

Step-by-step explanation:

After a careful reading of the statement, distances can be described in a vectorial way. A vector is represented by a magnitude and direction. That is:

Airplane flies 290 miles (east) (290 km with an angle of 0º)

[tex]\vec r_{A} = (290\,mi)\cdot i[/tex]

Airplane flies 290 miles (northwest) (290 km with and angle of 135º)

[tex]\vec r_{B} = [(290\,mi)\cdot \cos 135^{\circ}]\cdot i + [(290\,mi)\cdot \sin 135^{\circ}]\cdot j[/tex]

The resultant vector is equal to the sum of the two vectors:

[tex]\vec r_{C} = \vec r_{A} + \vec r_{B}[/tex]

[tex]\vec r_{C} = \{(290\,mi) + \left[(290\,mi)\cdot \cos 135^{\circ}\right]\}\cdot i + \left[(290\,mi)\cdot \sin 135^{\circ}\right]\cdot j[/tex]

[tex]\vec r_{C} = (84.939\,mi)\cdot i + (205.061\,mi)\cdot j[/tex]

The magnitude of the final distance of the airplane from the airport is obtained by the Pythagorean Theorem:

[tex]\|\vec r_{C}\|=\sqrt{(84.939\,mi)^{2}+(205.061\,mi)^{2}}[/tex]

[tex]\|\vec r_{C}\| = 221.956\,mi[/tex]

The airplane is 222 miles far from the airport.

Answer:

The speed is 74.0 miles per hour and the angle is 65.1° north-east

Step-by-step explanation:

We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.

Since the wind is moving south east, it is at 45 south of east or a bearing of 135.

Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles

Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles

The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles

The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles

The total vertical displacement of the plane is 176.64 miles - 42.43 miles =   134.21 miles

The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles

The direction of this displacement is thus

Ф = tan⁻¹(total vertical displacement/total horizontal displacement)

= tan⁻¹(134.21/62.43)

= tan⁻¹(2.1498)

= 65.05°

= 65.1° to the nearest tenth degree.

The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.

So the speed is 74.0 miles per hour and the angle is 65.1° north-east

Answer:

84cm²

Step-by-step explanation:

Perímetro de un rectángulo = 2L + 2W

Representemos la longitud del rectángulo = L

En la pregunta anterior se nos dijo que el ancho del rectángulo = es menor que 5 en la longitud

Por lo tanto, ancho del rectángulo = L - 5

Perímetro del rectángulo = 38 cm

Por lo tanto

38 = 2 (L) + 2 (L - 5)

38 = 2L + 2L - 10

38 + 10 = 4L

48 = 4L

L = 48/4

L = 12 cm

La longitud del rectángulo = 12 cm

Como L = 12, encontramos el ancho

Ancho = L - 5

= 12 cm - 5 cm

= 7 cm

El ancho del rectángulo = 7 cm

En la pregunta nos pidieron encontrar el área del rectángulo.

Área del rectángulo = Largo × Ancho

Área del rectángulo = 12 cm × 7 cm

Área del rectángulo = 84cm²

Answer:

<2, <5

Step-by-step explanation:

<2 is a vertical angle so it is equal to 110

<5 is a corresponding angle and since the lines are parallel it is also equal to 110

Answer: 2.5

Step-by-step explanation:

To find a mean, the average, we have to add everything together.

So we add 1 + 4 + 3 + 2, which is equal to 10. The next step to find the average is to divide by the total number of “things” which is the 4 puppeteers.

10/4 is 2.5

Answer:

7 x 9 x 11 x 13  +  13  is a composite number because the answer is a positive number which is 9022.

7 x 9 x 11 x 13  +  13  is a positive integer that can be formed by multiplying small positive numbers which are 7, 9, 11 and 13. Equivalently, 9022 is a positive integer that has at least one divisor other than 1 and itself. For example, 9022 can be divided by 2. 9022 is exactly a number but it is not a prime number.

I hope you will understand my explanation!

Answer:

2.5 or 2 1/2

Step-by-step explanation:

i caculated do order of operations

Answer: X

Step-by-step explanation:

Answer:

There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.

Answer:

5

Step-by-step explanation:

Since y equals 200 + 10x and y also equals 5x, then

200 + 10x = 50x

Subtract 10x from both sides.

200 = 40x

Divide both sides by 40.

5 = x

Answer: He must sell 5 sculptures.

Answer:

80 pages

Step-by-step explanation:

Let's use a ratio to solve:

pages : seconds

   12    :       9

    4     :       3

    [tex]p[/tex]     :      60

It would seem that [tex]p[/tex] would equal 80. The printer can print 80 pages in 60 seconds or one minute.

Answer:

All real values of x such that x ≥-3

Step-by-step explanation:

g(x) = sqrt(x+3)

A sqrt must be greater than or equal to zero

sqrt (x+3) ≥ 0

Square each side

x+3≥ 0

Subtract 3 from each side

x ≥-3

The restrictions on x are x ≥-3

That means the domain is x ≥-3

All real values of x such that x ≥-3

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

[tex]g(x)=\sqrt{x+3}[/tex]

A square root must have a value of greater than or equal to 0.

[tex]\sqrt{x+3}\geq 0[/tex]

Square both sides.

[tex]x+3\geq 0[/tex]

Subtract 3 from both sides.

[tex]x\geq -3[/tex]

Answer:

Radius = 6.46 meters

Height = 1.46 meters

Step-by-step explanation:

The volume of a cylinder = πr²h

In the above question, we were given

r = (x + 5) meters

h = x meters

Volume = 192 cubic meters

Hence,

192 = π × (x + 5)² × x

192 = π × (x² + 10x + 25) × x

192 = π × (x³ + 10x² + 25x)

Divide both sides by π

192/π = x³ + 10x² + 25x

61.115498147 = x³ + 10x² + 25x

x³ + 10x² + 25x - 61.12

This Quadratic equation is a polynomial

x = 1.46119

From the above:

Radius = (x + 5)meters

Radius = 1.46119 + 5 = 6.46119 meters

Approximately to 2 decimal places = 6.46 meters

Height = x meters

Height = 1.46119 meters

Approximately to 2 decimal places = 1.46 meters

Answer:

H. 1/9.

Step-by-step explanation:

The area of a circle is calculated by solving for π[tex]r^2[/tex].

The smallest circle has an area of π[tex]1^2[/tex] = π * 1 = π.

The middle ring will then have an area of π[tex]2^2[/tex] - π = π * 4 - π = 4π - π = 3π.

The largest ring will then have an area of π[tex]3^{2}[/tex] - π[tex]2^{2}[/tex] = 9π - 4π = 5π.

5π + 3π + π = 9π

So, the probability of hitting the innermost circle will be π / 9π = 1 / 9.

Your answer is H. 1/9.

Hope this helps!

Answer:

Option C

x²+ 2x -24=0

x²+6x-4x-24= 0

x(x+6) -4(x+6) = 0

(x+6)(x-4) = 0

x= -6 and 4

Therefore, for x = 4 and -6 , the above given equation is true.

Answer:

2πr + 4a = 8

Step-by-step explanation:

Answer:

x=6, y=2.5

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Surface area is the combined area of the 2 dimensional planes.

6 × 5 + 3 × 4 × 1/2 × 2 + 6 × 3 + 4 × 6

30 + 12 + 18 + 24

= 84

The surface area is 84 square centimeters.

Answer: The mathematics terms of ratio are the indicates many times one number contains to the another number.

Step-by-step explanation:Terms of ratio may be specified both constitution number or value to the equal correspond to the equal ratio.

"a to b"

"a:b"

There are Sixteen and eight apples and lemon in the table of fruit the ratio(that is 16:8 to the equivalent the ratio 8:4).

a:b=(a+b):a or ratio is equivalently a:b=(1+b/a):1.

The number in a terms ratio quantities of both numbers are to be positive

Answer:

44.8

Step-by-step explanation:

cos α = adjacent leg/hypotenuse

cos 48° = 30/x

x = 30/(cos 48°) = 44.8

Answer:

1. (2,1)

2. (6,-1)

3.(-2,3)

Answer:

1. (2,1)

2.  (6,-1)

3. (-2,3)

Step-by-step explanation:

Each of the answer is consistent system because the lines intersect at one point, which is one solution.

Answer:

Step-by-step explanation:

Let breadth of the room be 'x'

Let length of the room be '[tex]2 \frac{1}{2} x = \frac{5}{2} = 2.5 \: x[/tex]'

Perimeter ( P ) = 70 cm

Now, let's find the breadth of the room 'x '

Perimeter of rectangle = [tex]2(l + b)[/tex]

plug the values

[tex]70 = 2(2.5x + x)[/tex]

Collect the like terms

[tex]70 = 2 \times 3.5x[/tex]

Calculate the product

[tex]70 = 7x[/tex]

Swap the sides of the equation

[tex]7x = 70[/tex]

Divide both sides of the equation by 7

[tex] \frac{7x}{7} = \frac{70}{7} [/tex]

Calculate

[tex]x = 10 \: cm[/tex]

Breadth = 10 cm

Now, Let's find the length of the room ' 2.5x '

Length of the room = [tex]2.5x[/tex]

Plug the value of X

[tex] = 2.5 \times 10[/tex]

Calculate the product

[tex] = 25 \: cm[/tex]

Thus , The length and breadth of the room is 25 cm and 10 cm respectively.

Hope this helps..

Best regards!!

Answer:

Step-by-step explanation:

to decrease a number by 40% i would do

100% = number you got

50% divide by 2

10%= dived 100% number by 10 then take the 10% away from the 50% to get 40%

then take the 40% away from the 100%

hope this helps :)

[tex]A = 1500(1.00167)^{12t}[/tex]

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

Explanation:

You could use the formula

[tex]A = P(1+\frac{r}{n})^{nt}[/tex]

to plug in P = 1500, r = 0.02 and n = 12 to get the answer above. This is the compound interest formula. The interest rate r is divided into n = 12 to account for monthly compounding. The original exponent t turns into 12t. So for instance, if t = 2 years go by, then 12*t = 12*2 = 24 months have gone by.

Answer:

B. [tex]1\frac{1}{7}[/tex]

Step-by-step explanation:

[tex]-9\frac{2}{7}[/tex]=[tex]-\frac{65}{7}[/tex]

[tex]-10\frac{3}{7}[/tex]=[tex]-\frac{73}{7}[/tex]

[tex]-\frac{65}{7}[/tex]-([tex]-\frac{73}{7}[/tex])=8/7

8/7=[tex]1\frac{1}{7}[/tex]

Hope this helped!!!

Answer:

c     15

Step-by-step explanation:

Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.

We can use the Pythagoren theorem.

a^2 + b^2 = c^2

x^2 + 20^2 = (x + 10)^2

x^2 + 400 = (x + 10)(x + 10)

x^2 + 400 = x^2 + 10x + 10x + 100

400 = 20x + 100

20x = 300

x = 15

Answer:

[tex]Slope (m) = -\frac{2}{3}[/tex]

Step-by-step explanation:

To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.

Thus, on the line, let's pick 2 points as our coordinate pairs at:

When x = -6, y = 5 => (-6, 5), and

When x = 3, y = -1 => (3, -1)

Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)

[tex] Slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] Slope (m) = \frac{-1 - 5}{3 - (-6)} [/tex]

[tex] Slope (m) = \frac{-1 - 5}{3 + 6} [/tex]

[tex] Slope (m) = \frac{-6}{9} [/tex]

[tex]Slope (m) = -\frac{2}{3}[/tex]

Step-by-step explanation:

v= 4/3πr³

4/3×314/100×8×8×8

•

= 2,143.573

Answer:

Step-by-step explanation:

7x² - 4x - 3 = 0

Rewrite - 4x as a difference

That's

7x² - 7x + 3x - 3 = 0

Factorize the expression

7x( x - 1) + 3 ( x - 1) = 0

(7x + 3)( x - 1 ) = 0

7x + 3 = 0 x - 1 = 0

7x = - 3 x = 1

x = -3/7

The solutions are

x = - 3/7 or x = 1

Hope this helps you

Answer: 52.9

Step-by-step explanation:

The value 5 is rounded up.

Hope it helps <3

Answer:

52.9

Step-by-step explanation:

round up using the last number. since its 5, you round up