A ship travels 200 km west from port and then 240 km due south before it is disabled. Illustrate this in a vector diagram. Use trigonometry to find the course that a rescue ship must take from port in order to reach the disabled ship.

Answer:

x= 4/3

x= -1/2

Step-by-step explanation:

2x (3x-4) +1(3x-4) = 0

Distribute

6x^-8x +1(3x -4) = 0

Multiply by 1

6x^2 -8x +3x-4=0

Answer:

(2x + 1) ( 3x - 4) = 0

solve by factoring

2x + 1 = 0

2x = -1

divided by 2 on both sides

x = -1/2

3x - 4 = 0

3x = 4

divided by 3 on both sides

x = 4/3

x¹ = -1/2 , x² = 4/3 is the solution

Answer:

698 fishes

Step-by-step explanation:

Generally, we can represent an exponential growth function as;

y = a•(1 + r)^t

originally, there were 3 fishes

The original value in this case means a = 3

After 6 weeks, there were 31

31 in this case is y

r is the increase percentage or rate

t is the time

So, we have it that;

31 = 3•(1 + r)^6

31/3 = (1 + r)^6

10.33 = (1 + r)^6

ln 10.33 = 6 ln (1 + r)

ln 10.33/6 = ln (1 + r)

e^0.3892 = (1 + r)

1 + r = 1.476

r = 1.476-1

r = 0.476 or 47.6%

So the growth percentage or rate is 47.6%

For 14 weeks, we simply have the value of t as 14;

So ;

y = 3•(1 + 0.476)^14

y = 3(1.476)^14

y = 698 fishes

Answer:

Wages she earn = £124.1

Step-by-step explanation:

Given:

Number of hour work in June = 17 hour

Rate = £7.30 per hour

Find:

Wages she earn

Computation:

Wages she earn = Number of hour work in June x Rate

Wages she earn = 17 x £7.30

Wages she earn = £124.1

Answer:

- 125

Step-by-step explanation:

11 × 12 + 1 - 43x

132 + 1 - 43(6)

132 + 1 - 258

133 - 258

- 125

Answer:

x = 5

Step-by-step explanation:

6x and 30 are vertically opposite angles and are congruent, then

6x = 30 ( divide both sides by 6 )

x = 5

Answer:

c

Step-by-step explanation:

Answer:

-8

the way you meant to write it was -4^2 x 2^-1

Step-by-step explanation:

Answer:

it is 8 but it's not negative 8

I tried negative 8 and it said it was wrong so it must be 8

Answer:

IT IS B ANSWER

Answer:

opposite sides of a parallelogram are equal

2x+15=x+15

2x-x=15-15

x=0

Answer:

x = 0

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, that is

ST = RU , substitute values

2x + 15 = x + 15 ( subtract x from both sides )

x + 15 = 15 ( subtract 15 from both sides )

x = 0

Answer:

1/5

Step-by-step explanation:

A: 1

B: 5

Scale is 1:5

Answer:

[tex]\frac{1}{25}[/tex]

Step-by-step explanation:

Given the scale factor is 5 , then

the scale factor of areas is 5² = 25

Then A is [tex]\frac{1}{25}[/tex] of B's area

Answer:

[tex]x=\frac{3}{4}=0.75[/tex]

Step-by-step explanation:

From the shape of the quadrilateral, we can assume that it is a parallelogram. In a parallelogram, opposite sides are congruent and thus have the same length.

In this case, we are given that two opposite sides have lengths of [tex]4x+5[/tex] and [tex]8[/tex]. Therefore, since the quantities must be equal, we can write the following equation to solve for [tex]x[/tex]: [tex]4x+5=8[/tex]. Solving for [tex]x[/tex], we get:

[tex]4x+5=8[/tex]

[tex]4x=3[/tex] (Use the Subtraction Property of Equality to subtract [tex]5[/tex] from both sides of the equation, which isolates [tex]x[/tex])

[tex]x=\frac{3}{4} =0.75[/tex] (Use the Division Property of Equality to divide both sides of the equation by [tex]4[/tex] to get rid of [tex]x[/tex]'s coefficient)

Hope this helps!

Answer:

720

Step-by-step explanation:

Out of 80 students the no. of students who sign up=48

So, out of 1200 students 48×1200÷80=720 students sign up.

Answer:

the answer is B i think

Step-by-step explanation:

Answer:

9(x+3)

Step-by-step explanation:

9x+27

Answer: Chnager your profile pic

Step-by-step explanation:

Answer:

noooooo nittt

Step-by-step explanation:well urv gay

Answer:

x = 10

Step-by-step explanation:

Use Pythagorean Theorem

c2 = a2 + b2

Here you must find the hypotenuse length (x) which is c in the equation. Thus substitute the values given into the equation:

c2 = 6^2 + 8^2

c2 = 100

Square root both sides so

c = 10

Thus length of x is 10

Answer:

It will be 63.9

Step-by-step explanation:

Trust me, I got it right

Answer:

63.6mm² (the last option)

Explanation:

the formula for calculating the area of a circle is πr², where r is the length of the radius.

in this case, we know that 9mm is the length of the diameter of the circle, so we can divide that by 2 to get 4.5mm for the length of the radius.

the question has instructed us to use 3.14 for π (pi), so we can substitute these values into the formula:

πr² = 3.14 × 4.5² = 63.585mm²

we can now round this to the nearest tenth to get 63.6mm², which would be the last option.

i hope this helps! :D

Answer:

.16

Step-by-step explanation:

5 by 30 and you get your answer

Answer:22:2x10x10x10x10x10x10x10x10x10x10... 23:3.4x10 divided by 2.... 24:1.5x10 divided by 9...... 25:5.9x10x10x10x10x10x10x10x10x10x10.... 26: 4.8 x 10 divided by 3..... 27: 6.25x10x10x10x10x10.

Step-by-step explanation:I divide because on some of them it's a negative power so instead of multiplying I'll divide. Hope this helps

Answer:

327 cm²

Step-by-step explanation:

The opposite faces of a cuboid are congruent , front and back, top and bottom, the two side faces, then

SA = 2(9.5 × 8) + 2(5 × 8) + 2(9.5 × 5)

     = (2 ×76) + (2 × 40) + (2 × 47.5)

     = 152 + 80 + 95

     = 327 cm²

Answer:

Step-by-step explanation:

SA = 2B + LA         B = area of base        LA = lateral area

B = area of the rectangle with length of 9.5 and width of 5

  = 9.5(5) = 47.5

LA = perimeter of base times the height

    = [2(9.5) + 2(5)] (8)

    = (19 + 10)(8)

    = 29(8)

    = 232

SA = SA = 2B + LA  = 2(47.5) + 232

     = 95 + 232

     = 327 sq cm

Answer:

Population: 38.64. Sample: 43.20

Answer:

Slope is -3

Equation is y = -3x + 2

Step-by-step explanation:

(0 , 2) and ( -1 , 5)

m= (y2-y1)/(x2-x1)

m= (5 - 2)/(-1 -0)

m= 3/-1

m= -3

y - y1 = m(x - x1)

y - 2 = -3(x - 0)

y - 2 = -3x + 0

y = -3x + 2

Answer:

prob a

Step-by-step explanation:

Answer:

1.1 percent

Step-by-step explanation:

[(9.73 - 9.84) / 9.84 ] * 100 = -1.1 percent change = 1.1 percent decrease

Answer:

550 sit-ups

Step-by-step explanation:

Given

See attachment for chart

Required

Number of sit-ups on March 11

Represent the number of sit-ups with x and the days with y.

So:

[tex](x_1, y_1) = (1,50)[/tex] --- May 1

[tex](x_2, y_2) = (2,100)[/tex] --- May 2

First, we calculate the slope of the line chart.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{100 - 50}{2-1}[/tex]

[tex]m = \frac{50}{1}[/tex]

[tex]m = 50[/tex]

Next, we calculate the equation using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives:

[tex]y = 50(x - 1) + 50[/tex]

[tex]y = 50x - 50 + 50[/tex]

[tex]y = 50x[/tex]

So, on May 11.

[tex]x= 11[/tex]

Substitute 11 for x

[tex]y = 50 * 11[/tex]

[tex]y = 550[/tex]

Answer:

24 classes

Step-by-step explanation:

Let

x = number of classes

Devaughn is a member at the local gym = 120 + 5x

Jerome is not a member = 10x

Equate the total cost of both individuals

120 + 5x = 10x

120 = 10x - 5x

120 = 5x

x = 120/5

x = 24 classes

The total cost of Devaughn and the total cost of Jerome will be equal in 24 classes

Answer

-[tex]\frac{7}{2\\}[/tex]

Step-by-step explanation:

Answer:

-7/2 or -3.5

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Given

The dimension of a rectangular prism is

[tex]L=2\ in[/tex]

[tex]W=112\ in.[/tex]

[tex]h=114\ in.[/tex]

Volume of Prism [tex]V=L\times W\times h[/tex]

[tex]\Rightarrow V=2\times 112\times 114=25,536\ in.^3[/tex]

The volume of the unit cube

[tex]\Rightarrow V_c=14\times 14\times 14=2744\ in.^3[/tex]

Suppose there are n unit cubes to fit in a rectangular prism

[tex]\Rightarrow n=\dfrac{V}{V_c}=\dfrac{25,536}{2744}=9.306\approx 9[/tex]

Answer:

21 Kg

Step-by-step explanation:

Divide 56 Kg by 8 and multiply the answer by 3 , that is

56 Kg ÷ 8 = 7 Kg , then

3 × 7Kg = 21 Kg