The sales of a certain product after an initial release can be found by the equation s=12 sqrt (4t) + 10 , where s represents the total sales (in thousands) and t represents the time in weeks after release. Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release.

The operation (-1 1/2)(-3/2) gives 9/4 or 2 1/4 as a mixed number.

To perform the indicated operation: (-1 1/2)(-3/2), we need to multiply the two numbers.

Answer:

Step-by-step explanation:

Z = i √5/3 +36

The given equation (3z - 18)^2 + 59 = 14 has no real solution because after isolating and simplifying the squared term, we would be taking the square root of a negative number, which is not possible in the real number system.

To solve the equation (3z - 18)^2 + 59 = 14 using the square root property, follow these steps:

(3z - 18)^2 = 14 - 59

(3z - 18)^2 = -45

It is important to note that squaring a real number always results in a non-negative number, so a square equal to a negative number indicates there are no real solutions to the equation.

Answer:

The circumference is a irrational number

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

where

D is the diameter

In this problem we have that

[tex]D=d\ units[/tex] ---> is a rational number

substitute

[tex]C=\pi (d)[/tex]

[tex]C=d\pi\ units[/tex]

Remember that

The number π is a irrational number

and

If you multiply a rational number by a irrational number, the result is a irrational number

therefore

The circumference is a irrational number

Answer:

9×80=x×15

x=58lbs

Step-by-step explanation:

Considering no frictions applyd, the value of the report of the two forces ( F- the action force and R- the resistance force) equals the value of the report between the value of the distance from the folcrum to the rock and the value of the distance from the fulcrum to the active force

Answer:

C

Step-by-step explanation:

The general rule for the quadratic function is

[tex]y=ax^2+bx+c[/tex]

Use the data from the table:

[tex]y(50)=130\Rightarrow 130=a\cdot 50^2+b\cdot 50+c\\ \\y(70)=130\Rightarrow 130=a\cdot 70^2+b\cdot 70+c\\ \\y(90)=200\Rightarrow 200=a\cdot 90^2+b\cdot 90+c[/tex]

We get the system of three equations:

[tex]\left\{\begin{array}{l}2500a+50b+c=130\\ \\4900a+70b+c=130\\ \\8100a+90b+c=200\end{array}\right.[/tex]

Subtract these equations:

[tex]\left\{\begin{array}{l}4900a+70b+c-2500a-50b-c=130-130\\ \\8100a+90b+c-2500a-50b-c=200-130\end{array}\right.\Rightarrow \left\{\begin{array}{l}2400a+20b=0\\ \\5600a+40b=70\end{array}\right.[/tex]

From the first equation

[tex]b=-120a[/tex]

Substitute it into the second equation:

[tex]5600a+40\cdot (-120a)=70\Rightarrow 800a=70,\\ \\ a=\dfrac{7}{80},\\ \\ b=-120\cdot \dfrac{7}{80}=-\dfrac{21}{2}=-10.5[/tex]

So,

[tex]2500\cdot \dfrac{7}{80}+50\cdot (-10.5)+c=130\Rightarrow 218.75-525+c=130\\ \\c=130-218.75+525=436.25[/tex]

The quadratic function is

[tex]y=\dfrac{7}{80}x^2-10.5x+436.25\\ \\y=0.0875x^2-10.5x+436.25[/tex]

Answer: 6 days.

Step-by-step explanation:

Inverse proportion equation has the form:

[tex]y=\frac{k}{x}[/tex]

Where "k" is the constant of proportionality.

Let be "y" the time it takes to do a job (number of days) and "x" the number of workers.

We can find "k" knowing that  it takes 3 workers 16 days to finish a job:

[tex]16=\frac{k}{3}\\\\k=16*3\\\\k=48[/tex]

To find how long will it take 8 workers to finish the job, you must substitute the value of "k" and [tex]x=8[/tex] into [tex]y=\frac{k}{x}[/tex]. Then you get:

 [tex]y=\frac{48}{8}\\\\y=6[/tex]

Answer: [tex]143.99\ ft^2[/tex]

Step-by-step explanation:

We need to find the lenght AC and BC of the triangle by applying these identities:

[tex]cos\alpha=\frac{adjacent}{hypotenuse} \\\\sin\alpha=\frac{opposite}{hypotenuse}[/tex]

Then, AC is:

[tex]sin(45\°)=\frac{AC}{24}\\\\AC=24*sin(45\°)\\\\AC=16.97\ ft[/tex]

And BC is:

[tex]cos(45\°)=\frac{BC}{24}\\\\BC=24*cos(45\°)\\\\BC=16.97\ ft[/tex]

The area will be:

[tex]A=\frac{AC*BC}{2}[/tex]

Substituting values, we get:

 [tex]A=\frac{(16.97\ ft)(16.97\ ft)}{2}=143.99\ ft^2[/tex]

Answer:

n = 17.

Step-by-step explanation:

The opposite angles of a parallelogram are congruent so we have:

4n - 2 =  2n + 32

4n - 2n = 32 + 2

2n = 34

n = 17.

Answer:

D. size and shape

Step-by-step explanation:

Triangles are congruent if they have the same size and shape.

Answer:

Step 2

Step-by-step explanation:

Let

[tex]A(-1,6), B(-1,-2), C(3,6), D(3,-2)[/tex]

Plot the vertices to better understand the problem

see the attached figure

The area of the rectangle is equal to

[tex]A=bh[/tex]

we have

[tex]b=BD\\ h=BA[/tex]

step 1

Find the base b (BD)

[tex] B(-1,-2),D(3,-2)[/tex]

[tex]b=\left|3\right|+\left|-1\right|=4\ units[/tex]

step 1 is correct

step 2

Find the height h (BA)

[tex]B(-1,-2),A(-1,6)[/tex]

[tex]h=\left|6\right|+\left|-2\right|=8\ units[/tex]

step 2 is not correct

step 3

Find the area

[tex]A=(4)(8)=32\ units^{2}[/tex]

Therefore

Sara first make a mistake in finding the area of the rectangle in Step 2

Answer:

step 2

Step-by-step explanation:

Answer:

f(x) = (x+2)(x-8)/(x-6)(x+4) <-> x=6,x=-4

i(x) = (x-4)(x-6)/(x-2)(x+8)  <-> x=2,x=-8

k(x) = (x-2)(x+8)/(x+6)(x-4) <-> x=-6,x=4

m(x) = (x+4)(x-6)/(x+2)(x-8)  <-> x=-2,x=8

Step-by-step explanation:

The function is discontinuous if the denominator is zero.

We will check for which function the values are given

1) f(x) = (x+2)(x-8)/(x-6)(x+4)

if x = 6 and x = -4 the  denominator  is zero

So, x=6 and x=-4 given

2) g(x) = (x+4)(x-8)/(x+2)(x-6)

if x = -2 and x = 6 the  denominator  is zero

So, x= -2 and x= 6 not given so, g(x) will not be considered

3) h(x)= (x+2)(x-6)/(x-8)(x+4)

if x = 8 and x = -4 the  denominator  is zero

So, x= 8 and x= -4 not given so, h(x) will not be considered

4) i(x) = (x-4)(x-6)/(x-2)(x+8)

if x = 2 and x = -8 the  denominator  is zero

So, x= 2 and x= -8 given

5) j(x) = (x-2)(x+6)/(x-4)(x+8)

if x = 4 and x = -8 the  denominator  is zero

So, x= 4 and x= -8 not given so, j(x) will not be considered

6) k(x) = (x-2)(x+8)/(x+6)(x-4)

if x = -6 and x = 4 the  denominator  is zero

So, x= -6 and x= 4  given

7) l(x) = (x-4)(x+8)/(x+6)(x-2)

if x = -6 and x = 2 the  denominator  is zero

So, x= -6 and x= 2  not given so, l(x) will not be considered

8) m(x) = (x+4)(x-6)/(x+2)(x-8)

if x = -2 and x = 8 the  denominator  is zero

So, x= -2 and x= 8 given

Answer:

3.08 x [tex]10^{3}[/tex]

Step-by-step explanation:

3080 = 3.08 x 1000 = 3.08 x [tex]10^{3}[/tex]

Answer:

[tex]h=7\sqrt{11}\ units[/tex]

Step-by-step explanation:

The altitude to the hypotenuse of a right tringle is the geometric mean of the two segments that it divides the hypotenuse into.

1st segment = 77 units

2nd segment = 7 units

Altitude = h units

So,

[tex]h^2=77\cdot 7\\ \\h^2 =7\cdot 11\cdot 7\\ \\h=\sqrt{7\cdot 11\cdot 7}=7\sqrt{11}[/tex]

Answer:

Part a) When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

part c) The slope of the equation is -0.1 and the units are dollars per minute

Step-by-step explanation:

we have

[tex]B=40-0.1n[/tex]

where

B is balance in dollars on the card

n is the number of minutes

Part a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?

we know that

The B-intercept is the value of B when the value of n is equal to zero

so

For n=0

substitute and find the value of B

[tex]B=40-0.1(0)=\$40[/tex]

therefore

When Marcos purchased the card, the balance on the card was $40

This is the B-intercept

Part b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?

we know that

The n-intercept is the value of n when the value of B is equal to zero

so

For B=0

substitute and find the value of n

[tex]0=40-0.1n[/tex]

[tex]0.1n=40[/tex]

[tex]n=400\ minutes[/tex]

therefore

Mark will have spoken 400 minutes when he runs out of money

This is the n-intercept

Part c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?

we have

[tex]B=40-0.1n[/tex]

This is is the equation of the line into slope intercept form

[tex]m=-0.1\frac{\$}{minute}[/tex] -----> slope of the equation

[tex]b=40[/tex] ------> the B-intercept

The units of the slope are dollars per minute

Marcos purchased a top-up card with an initial balance of $40 (B-intercept). He will run out of money after 400 minutes of call time (n-intercept). The charge rate is $0.1 per minute (slope).

a) The money on the card when he purchased it is given by the constant term in the equation, which is $40. This is the B-intercept, because it is the value of B when n = 0 (meaning no minutes have been used).

b) Marcos will have run out of money when B = 0. To find this, set B = 0 and solve for n: 0 = 40 - 0.1n, which leads to n = 400. So, Marcos will have talked for 400 minutes when he runs out of money. This is the n-intercept. It represents the value of n when B = 0 (meaning there is no money left on the card).

c) The slope of this equation is -0.1. In the context of this problem, the slope represents the rate at which money is deducted from the balance for each minute of talk time. Therefore, the units on the slope are dollars per minute.

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Answer

Y= 3 × 2 + 6x + 1 = 6 + 6x +1 = 6x + (6+1) = 6x + 7

Answer:

This is a function, so the answer is a plot, you can see it in the attached picture

Step-by-step explanation:

This is a function, the best way to go here is to graph.

First lest find the roots of 3x2+6x+1, you do this by using the quadratic equation

[tex]x_{1} = \frac{-b + \sqrt{b^{2}-4ac }}{2a}\\x_{2} = \frac{-b - \sqrt{b^{2}-4ac }}{2a}[/tex]

Where a=3, b=6, c=1

Using that, you get, x1 = -1 - sqrt(2/3) which is a negative number, and x2=sqrt(2/3) - 1 which is a negative number.

These number represent values that makes the function equals =0

Now if we make x=0, the result is y=1,

We have a better idea of what is to plot and it is shown on the attached picture

Answer:

Step-by-step explanation:

[tex]5+20\cdot2^{2-3x}=10\cdot2^{-2x}+5\qquad\text{subtract 5 from both sides}\\\\20\cdot2^{2-3x}=10\cdot2^{-2x}\qquad\text{divide both sides by 10}\\\\2\cdot2^{2-3x}=2^{-2x}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\2^{1+2-3x}=2^{-2x}\\\\2^{3-3x}=2^{-2x}\iff3-3x=-2x\qquad\text{subteact 3 from both sides}\\\\-3x=-2x-3\qquad\tex\qquad\text{add}\ 2x\ \text{to both sides}\\\\-x=-3\qquad\text{change the signs}\\\\x=3[/tex]

Answer:

The volume of cylinder = 540π inches²

Step-by-step explanation:

Points to remember

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

Here r = 6 inches and height h = 15 inches

Volume =  πr²h

 =  π * 6² * 15

 =  π * 36 * 15

 = 540 πinches²

The volume of cylinder = 540π inches²

Answer:

-18

Step-by-step explanation:

= |3 – 10| - (12 / 4 + 2)^2

= 7 - (3 + 2)^2

= 7 - (5)^2

= 7 - 25

= -18

Final answer:

Only options b (74) and c (80) could have their square roots between 8 and 9, as their values lie between 64 (8 squared) and 81 (9 squared).

Explanation:

To find which numbers could have their square roots lying between 8 and 9, we need to consider the squares of these two numbers. 8 squared is 64 and 9 squared is 81. Therefore, any number that has a square root between 8 and 9 must be greater than 64 and less than 81.

Thus, the values that could be the number with the square root between 8 and 9 are 74 and 80.

Answer:

$28.

Step-by-step explanation:

p(x) = -2(x - 9)^2 + 100

If the prices (x) = 15 dollars we work out the profit by substituting x = 15 in the above formula:

p(15) = -2(15 - 9)^2 + 100

= -2 * 6^2 + 100

= $28.

Answer:

28

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin(32)/19 = sin(B)/12  

cross multiply  

12 sin(32) = 19 sin(B)  

sin(B) = 12 sin(32) /19 = 0.334686  

B = sin°-1(0.334686)  

B = 0.321272 radian  

B = (0.321272)*180/pi degrees = 19.55°  

C = 180-32-19.55 = 128.45°  

sin(32)/19 = sin(128.45)/ c  

cross multiply  

c sin(32) = 19 sin(128.45)  

c = 19 sin(128.45) /sin(32) =28.08....

[tex]-p^2 + 14p=0\\-p(p-14)=0\\p=0 \vee p=14[/tex]

Answer:

10

Step-by-step explanation:

Answer:

[tex]\large\boxed{-9y^5}[/tex]

Step-by-step explanation:

[tex]-3y\cdot3y^4=(-3\cdot3)(y\cdot y^4)\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=-9y^{1+4}=-9y^5[/tex]

Answer:

a) 0.2514

b) 0.6827

c) 0.0918

Step-by-step explanation:

Average life span of batteries = u = 300 hours

Standard deviation = s = 75 hours

Given that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.

Part a) Less than 250 hours

In order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.

The formula for z-score is:

[tex]z=\frac{x-u}{s}[/tex]

Using the values, we get:

[tex]z=\frac{250-300}{75}=-0.67[/tex]

From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514

P(z < -0.67) = 0.2514

Thus, the  the probability that the life span of battery will be less than 250 hours is 0.2514

Part b) Between 225 and 375 hours

In order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.

225 into z-score will be:

[tex]z=\frac{225-300}{75}=-1[/tex]

375 into z-score will be:

[tex]z=\frac{375-300}{75}=1[/tex]

Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:

P(-1 < z < 1 ) = 0.6827

Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827

Part c) More than 400 hours

In order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.

The formula for z-score is:

[tex]z=\frac{x-u}{s}[/tex]

Using the values, we get:

[tex]z=\frac{400-300}{75}=1.33[/tex]

From the z-table the probability of z score being more than 1.33 comes out to be:

P( z > 1.33) = 0.0918

Thus, the probability that the life span of battery will be more than 400 hours is 0.0918

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=4(\frac{1}{2})^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

r is the rate

b=1+r

In this problem we have

a=4 ----> initial value (y-intercept)

b=1/2

so

1+r=1/2

r=1/2-1=-1/2

r=-0.5=-50% ----> is negative because is a decrease rate

using a graphing tool

The graph in the attached figure

Answer:

Yes, A is correct.

Answer:

1/2520

Step-by-step explanation:

First you have to find out how many different combinations can be created

7×6×5×4×3×2×1 = 5040

There is only two combinations that will spell out algebra

2/5040= 1/2520

[tex](f+g)(x)=2x^2+3+x-2=2x^2+x+1\\\\(f+g)(2)=2\cdot2^2+2+1=8+3=11[/tex]

Answer:

11

Step-by-step explanation:

(f+g)(2) means f(2)+g(2).

f(2) means we need to replace the x's in f(x)=2x^2+3 with 2.

This gives us f(2)=2(2)^2+3.

Let's simplify f(2)=2(4)+3=8+3=11.

g(2) means we need to replace the x's in g(x)=x-2 with 2.

This gives us g(2)=2-2

Let's simplify g(2)=0.

Now f(2)+g(2) means we just add the result of f(2) to the result of g(2).

So the problem is what is 11+0?

Answer is 11

First of all, let's write this statement in vector form. For the fist vector we have:

Magnitude 3.5 m/s, direction angle 35°:

Let's say this is vector [tex]\vec{A}[/tex], so the magnitude is:

[tex]\left|\vec{A}\right|=3.5m/s[/tex]

And the direction is defined as:

[tex]\theta = 35^{\circ}[/tex]

So the components are:

[tex]Ax=\left|\vec{A}\right| cos\theta \\ \\ Ax=3.5 cos35^{\circ}=2.86m/s \\ \\ \\ Ay=\left|\vec{A}\right| sin\theta \\ \\ Ay=3.5 sin35^{\circ}=2m/s[/tex]

So vector [tex]\vec{A}[/tex] is:

[tex]\vec{A}=2.86i+2j[/tex]

For the second vector:

Magnitude 4 m/s, direction angle 150°:

Let's say this is vector [tex]\vec{B}[/tex], so the magnitude is:

[tex]\left|\vec{B}\right|=4m/s[/tex]

And the direction is defined as:

[tex]\theta = 150^{\circ}[/tex]

So the components are:

[tex]Bx=\left|\vec{B}\right| cos\theta \\ \\ Bx=4 cos150^{\circ}=-2\sqrt{3}m/s \\ \\ \\ By=\left|\vec{B}\right| sin\theta \\ \\ By=4 sin150^{\circ}=2m/s[/tex]

So vector [tex]\vec{B}[/tex] is:

[tex]\vec{B}=-2\sqrt{3}i+2j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=\vec{A}+\vec{B}=(2.86i+2j)+(-2\sqrt{3}i+2j) \\ \\ \boxed{\vec{R}=-0.60i+4j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{Rx^2+Ry^2} \\ \\ Rx=Ax+Bx \\ \\ Ry=Ay+By \\ \\ \\ \left|\vec{R}\right|=\sqrt{(-0.6^2)+(4)^2} \\ \\ \boxed{\left|\vec{R}\right|=4.05m/s}[/tex]

Magnitude 4.5 m/s, direction angle 55°:

Let's say this is vector [tex]\vec{C}[/tex], so the magnitude is:

[tex]\left|\vec{C}\right|=4.5m/s[/tex]

And the direction is defined as:

[tex]\theta = 55^{\circ}[/tex]

So the components are:

[tex]Cx=\left|\vec{C}\right| cos\theta \\ \\ Cx=4.5 cos55^{\circ}=2.58m/s \\ \\ \\ Cy=\left|\vec{C}\right| sin\theta \\ \\ Cy=4.5 sin55^{\circ}=3.68m/s[/tex]

So vector [tex]\vec{C}[/tex] is:

[tex]\vec{C}=2.58i+3.68j[/tex]

For the second vector:

Magnitude 3 m/s, direction angle 135°:

Let's say this is vector [tex]\vec{D}[/tex], so the magnitude is:

[tex]\left|\vec{D}\right|=3m/s[/tex]

And the direction is defined as:

[tex]\theta = 135^{\circ}[/tex]

So the components are:

[tex]Dx=\left|\vec{D}\right| cos\theta \\ \\ Dx=3 cos135^{\circ}=-\frac{3\sqrt{2}}{2} \\ \\ \\ Dy=\left|\vec{D}\right| sin\theta \\ \\ Dy=3 sin135^{\circ}=\frac{3\sqrt{2}}{2}[/tex]

So vector [tex]\vec{D}[/tex] is:

[tex]\vec{D}=-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=\vec{C}+\vec{D}=(2.58i+3.68j)+(-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j) \\ \\ \boxed{\vec{R}=0.46i+5.80j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{(0.46)^2+(5.8)^2} \\ \\ \boxed{\left|\vec{R}\right|=5.83m/s}[/tex]

Magnitude 4.5 m/s, direction angle 55°:

This is vector [tex]\vec{E}[/tex], so the magnitude is:

[tex]\left|\vec{E}\right|=3m/s[/tex]

Direction:

[tex]\theta = 70{\circ}[/tex]

Components:

[tex]Ex=\left|\vec{E}\right| cos\theta \\ \\ Ex=3 cos70^{\circ}=1.02m/s \\ \\ \\ Ey=\left|\vec{E}\right| sin\theta \\ \\ Ey=3 sin70^{\circ}=2.82m/s[/tex]

So:

[tex]\vec{E}=1.02i+2.82j[/tex]

For the second vector:

Magnitude 5 m/s, direction angle 210°:

[tex]\vec{F}[/tex]:

[tex]\left|\vec{F}\right|=5m/s[/tex]

Direction:

[tex]\theta = 210^{\circ}[/tex]

Components:

[tex]Fx=5 cos210^{\circ}=-\frac{5\sqrt{3}}{2} \\ \\ \\ Ey=5 sin210^{\circ}=-\frac{5}{2}[/tex]

Then:

[tex]\vec{F}=-\frac{5\sqrt{3}}{2} i-\frac{5}{2}j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=(1.02i+2.82j)+(-\frac{5\sqrt{3}}{2}i-\frac{5}{2}j) \\ \\ \boxed{\vec{R}=-3.31i+0.32j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{(-3.31)^2+(0.32)^2} \\ \\ \boxed{\left|\vec{R}\right|=3.32m/s}[/tex]

Magnitude 6 m/s, direction angle 120°:

[tex]\left|\vec{W}\right|=6m/s[/tex]

Direction:

[tex]\theta = 120^{\circ}[/tex]

Components:

[tex]Wx=6 cos120^{\circ}=-3m/s \\ \\ \\ Wy=6 sin120^{\circ}=3\sqrt{3}m/s[/tex]

So:

[tex]\vec{W}=-3i+3\sqrt{3}j[/tex]

For the second vector:

Magnitude 2 m/s, direction angle 240°:

[tex]\vec{Z}[/tex]:

[tex]\left|\vec{Z}\right|=2m/s[/tex]

Direction:

[tex]\theta = 240^{\circ}[/tex]

Components:

[tex]Zx=2 cos240^{\circ}=-1 \\ \\ \\ Zy=2 sin240^{\circ}=-\sqrt{3}[/tex]

Then:

[tex]\vec{Z}=-i-\sqrt{3}j[/tex]

THE SUM OF THESE TWO VECTORS IS:

[tex]\vec{R}=(-3i+3\sqrt{3}j)+(-i-\sqrt{3}j) \\ \\ \boxed{\vec{R}=-4i+2\sqrt{3}j}[/tex]

THE MAGNITUDE OF THE RESULTANT VECTOR IS:

[tex]\left|\vec{R}\right|=\sqrt{(-4)^2+(2\sqrt{3})^2} \\ \\ \boxed{\left|\vec{R}\right|=5.29m/s}[/tex]