Suppose a river flows south to north at a velocity of 1 m/s, and a motorboat traverses the river from east to west at a speed of 2.5 m/s. At what angle should the boat be oriented south, relative to the westward direction, such that the boat will be traveling due west? Round to the nearest degree.

Answer:

(26/9 , -7/9)

Step-by-step explanation:

Here,

let the points be

X(-1,7) = (x1, y1)

Y(4,-3) = (x2,y2)

and let the ratio be...

m:n = 7:2

and.. let the point that divides the line be

P(x,y)

now using the section formula for internal division..

P(x,y) = ( m.x2 + nx.1 / m+ n , my2+ny2/m+n )

= ( 7.4+2.-1 / 7+2 , 7.-3 + 2.7/7+2 )

= ( 26/9 , -7/9 )

Answer:

The midpoint of the data when it is arranged in order.

Step-by-step explanation:

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

For example, the median of the following set of numbers is 5

1, 2, 5, 10, 20

Range is the difference between the highest and lowest values of a set of observations

Range = highest value - lowest value

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Answer:

1/4/3÷5/9

1/4/3÷9/5

1/4/3/5

Answer:

Option 4.

Step-by-step explanation:

Tan(X)=perpendicular/base

Tan(X)=48/14

X=arctan(48/14)=74

Given:

Amount = Rs. 9,144

Time = 3 years.

Rate of simple interest = 9%

To find:

The principal value.

Solution:

The formula for simple interest is:

[tex]I=\dfrac{P\times r\times t}{100}[/tex]

Where, P is principal, r is the simple rate of interest, and t is the number of years.

Putting [tex]r=9,t=3[/tex] in the above formula, we get

[tex]I=\dfrac{P\times 9\times 3}{100}[/tex]

[tex]I=\dfrac{27P}{100}[/tex]

[tex]I=0.27P[/tex]

We know that,

[tex]\text{Amount}=\text{Principal + Interest}[/tex]

[tex]9144=P+0.27P[/tex]

[tex]9144=1.27P[/tex]

Divide both sides by 1.27, we get

[tex]\dfrac{9144}{1.27}=P[/tex]

[tex]7200=P[/tex]

Therefore, the principal value is Rs. 7200.

Answer:

3/40 cup

Step-by-step explanation:

3 1/3 =10/3

10/3 to 1 is 1/4 to x

i then proceeded to use the butterfly method to find the answer

Answer:

b<4

Step-by-step explanation:

- 3b-5> - 8 or b - 4 < 0

Solve the first inequality

- 3b-5> - 8

Add 5 to each side

- 3b-5+5> - 8 +5

-3b> -3

Divide by 3, flipping the inequality

-3b/-3 < -3/-3

b <1

Then solve the second inequality

b-4<0

Add 4 to each side

b<4

Put them back together

b<1 or <4

Merge them since they overlap

b<4

Answer:

1beg-------------50kg

10beg------------x

x=500kg to grames 500×1000=500000grams

Answer:

500000g

Step-by-step explanation:

first of you multiply the 50kg with the 10 bags

which gives 500kg

then you convert 500kg to grams

which is 500kg/1×1000g/1kg

when you cancel out the kg what is left is to multiply both sides and then you get 50000g.

Answer:

hwukebhejsnsknbjbbjkkkkkkkk

Answer:

The answer is B

Step-by-step explanation:

If u use calculator,u will get the ans as x¹=6 and x²= -2 but u have to change it to the opposite which means negatif to positive(-2=2) and positive to negative(6= -6).Hope u can understand...sorry,English isn't my first language

Answer:

x= 6 and x=-2

Step-by-step explanation:

find the two factors that when multiplied will get -12 and when summed up will get -4.

so -6 and 3

(xsquare-6) +(2x -12)=0

x(x-6)+2(x-6)=0

(x-6)=0 (x+2)=0

group like terms

x=6. x=-2

Answer:

60

Step-by-step explanation:

REASONS:-

1ST STEP

[tex]6x + 7 = 8x - 17 [/tex]

GIVEN LHS = RHS

2ND STEP

[tex]7 = 2x - 17[/tex]

Bez +ve 6x when move to another side will change to -ve so it reduces 8x to 2x

3RD STEP

[tex]24 = 2x [/tex]

Bez -ve 17 when move to another side will change to +ve so it increases 7 to 24

4TH STEP

[tex]12 = x[/tex]

Bez 2 in multiplication when move to another side will change to division so it reduces 24 to 12

5TH STEP

[tex]x = 12[/tex]

it the answer we obtained after solving

Answer: 7

Step-by-step explanation:

Answer:

(x-4y)(x-3y) ÷(x+8y)(x-8y)×(x+8y)÷3(x-3y)

=3(x-4y)÷(x-8y)

Answer:

The speed of Sara is 78.4 km/h.

Step- by-step explanation:

Manuel and Sara travel a certain distance, and the times they use are in the ratio 21/15. Manuel's speed is 56km / h. What is Sara's speed?

Let the distance is d.

speed of Manuel = 56 km/h

time taken by Manuel = 21 t

time taken by Sara =  15 t

Let the speed of Sara is v.

Distance = speed x time

For Manuel:

d = 56 x 21 t ..... (1)

For Sara:

d = v x 15 t ..... (2)

From (1) and (2)

56 x 21 t = v x 15 t

v = 78.4 km/h

In this question, a piece-wise function is asked to be graphed.

Piece-wise function:

A piece-wise function is a function that has different definitions, depending on the input.

In this question, the function has three different definitions:

When x is less than -2, the definition is:

[tex]g(x) = \frac{x}{2} + 3[/tex]

When x is between -2 and 3, inclusive, the function is:

[tex]g(x) = 2[/tex]

When x is greater than 3, the definition is:

[tex]g(x) = 2x - 3[/tex]

The graphic is given by the image at the end here, with the closed circle indicating the inclusive on the intervals.

For another example of a piece-wise graphic, you can check https://brainly.com/question/24324639.

Answer:

D

Step-by-step explanation:

edge!

Answer:

The same lines (answer)

Step-by-step explanation:

The equations can be written in slope-intercept form y = mx + c (where 'm' is slope and 'c' is the y-intecept) as,

y-3 = 2(x-3) .......(1)        ;   y + 5 = 2(x+1) ...........(2)    

y = 2x - 6 + 3                ;  y = 2x + 2 - 5    

y = 2x -3                       ;  y = 2x - 3

Comparing with slope intercept form we have,

m1 = 2                           ; m2 = 2

c1 = -3                           ; c2 = -3

If the slopes are equal the lines are parallel and since y-intercepts are also equal means they are the same lines (overlapping)

Answer:

Lateral surface area= circumference*height

120=12*h

h=10cm

Answer:

h=10 cm

Step-by-step explanation:

cicumference of a circle C=2πr=12

lateral surface area of cylinder=2πrh

120=12h

h=120/12=10 cm

Answer:

D. 7

Step-by-step explanation:

I guessed on it because i had the same problem and then i checked and it was right!

Solution :

Colored marble            Prize

     Red ----  10               20

    Blue --- 38                 10

   Green --- 26               5

P(red)  =  10/74  =  5/37

P(blue)  =  38/74  =  19/37

P( green)  = 26/74  =  13/37

Therefore,

 X      →     Red          Blue      Green

P(X)           5/37        19/37      13/37

The expected values are :

[tex]$20 \times \frac{5}{37} - 10 \times \frac{19}{37} - 5 \times \frac{13}{37}[/tex]

= -4.189

Thus it is not profitable to play the game.

Answer:

C

Step-by-step explanation:

g(x) is larger than f(x) and not the same size so B and D are out of question because those are translation not dilation.

f(x) is stretched in the vertical direction to get g(x). So this means the scale factor has to be greater than 1. so A is wrong.

The answer is c

Answer:

I would say it is D

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Answer:

D. 14.1

Step-by-step explanation:

Use sin, opposite over hypotenuse.

sin67 = 13/X

solve for X

Step-by-step explanation:

3x+1 = 5x-1

3x+2= 5x

2x= 2

x= 1

Answer: Rs 5000 sum of money amount to Rs 6000 in two years at the rate of 10% per annum.​

Step-by-step explanation:

Amount = Rs 6000

T = 2 year

R = 10%

So

I = A-P

so

I = PTR/100

or, A-P = (P*2*10)/100

or, 6000-P = 20P/100

or, 600000-100P = 20P

or, 600000 = 120P

or, P = 600000/120

so, P = Rs 5000

Answer:

dont understand clearly

Step-by-step explanation:

dont understand clearly

We shall proceed in hit and trial method

Find some nearest multiples of 252

Yes last one is square of 42

So smallest no is 7