I need help please and thank you

Answer: 15.85km

Step-by-step explanation:

The car starts at the point (0,0)

Let's define east as the positive x-axis and north as the positive y-axis.

first, the car travels 10km southeast, so the angle is -45° from the east.

Then the new position of the car is:

(10km*cos(-45°), 10km*sin(-45°)) = (7.07km, -7.07km)

Now, from this point the car travels 15km with an angle of 60° (counting from the east)

So the new position is:

(7.07km + 15km*cos(60°), -7.07km + 15km*sin(60°)) = (14.57km  , 5.91km)

The magnitude of a vector (x, y) is √(x^2 + y^2)

So the magnitude of the vector (14.57km  , 5.91km) is:

√((14.57km)^2 + (5.91km)^2) = 15.85km

The magnitude of the car's resultant vector is 15.72.

Given that,

A car travels 10km southeast,

And then 15 km in a direction 60 degrees north of east.

We have to find,

The magnitude of the car's resultant vector.

According to the question,

To resultant direction calculate by using the sum of vectors following all the steps given below.

A car travels 10 km southeast,

And then 15 km in a direction 60 degrees north of east.

The first vector has module is 10 and angle is 315°,

In the south direction, the angle is  270° and east is 360°,

So the angle in southeast,

[tex]\rm = \dfrac{270+360}{2}\\\\= \dfrac{630}{2}\\\\= 315 \ degree[/tex]

The second vector has module 15 and angle = 40°

Decompose both vectors in their horizontal and vertical component:

The horizontal component of the first vector is,

[tex]\rm = 10 \times cos(315) = 10 \times 0.70= 7.07[/tex]

The vertical component of the first vector is,

[tex]= \rm 10 \times sin(315) = -7.07[/tex]

The horizontal component of the second vector is,

[tex]\rm = 15 \times cos(60) = 15 \times 0.5= 7.5[/tex]

The vertical component of the second vector is,

[tex]\rm = 15 \times sin(40) = 15 \times 0.86= 12.99[/tex]

The sum of the horizontal component of the resultant vector is,

[tex]= 7.07+7.5=14.57[/tex]

And the sum of the vertical component of the resultant vector is,

[tex]= -7.07+12.99=5.91[/tex]

The magnitude of the vector (14.57km, 5.91km) is:

Therefore,

The magnitude of the car's resultant vector is,

[tex]\rm Resulatant = \sqrt{(14.57)^2+ (5.91)^2}\\\\ Resulatant = \sqrt{212.28+ 34.92} \\\ \\ Resulatant = \sqrt{247.20}\\\\ Resulatant = 15.72[/tex]

Hence, The required magnitude of the car's resultant vector is 15.72.

For more details refer to the link given below.

https://brainly.com/question/16541081

Answer:n=-9/2m

Step-by-step explanation:

Step 1: Add 3n to both sides.

-2m-5n+3n=7m-3n+3n

-2m-2n=7m

Step 2: Add 2m to both sides.

-2m-2n+2m=7m+2m

-2n=9m

Step 3: Divide both sides by -2.

-2m/-2=9m/-2

n=-9/2

Hope I helped

Answer:

n= -9m/2

Step-by-step explanation:

-2m-7m-5n=7m-7m-3n

-9m-5n+5n= -3n+5n

-9m=2n

n= -9m/2

Answer:

C. y=1/2 x + 5

Step-by-step explanation:

In the attached file

Please consider the attached file.

We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.

We will use Pythagoras theorem to solve for KJ as:

[tex]KJ^2=KM^2+MJ^2[/tex]

[tex]KJ^2=6^2+3^2[/tex]

[tex]KJ^2=36+9[/tex]

[tex]KJ^2=45[/tex]

Now we will take positive square root on both sides:

[tex]\sqrt{KJ^2}=\sqrt{45}[/tex]

[tex]KJ=\sqrt{9\cdot 5}[/tex]

[tex]KJ=3\sqrt{5}[/tex]

Therefore, the length of line segment KJ is [tex]3\sqrt{5}[/tex] and option D is the correct choice.

Answer:

Step-by-step explanation:

what is the length of line segment kJ

Answer:

A is correct, when two lines have 1 intersection (1 solution).

Step-by-step explanation:

B Two lines are parallel => No intersection (no solution).

C Two lines are coincident => Many intersection (many solutions).

Hope this helps!

:)

Step-by-step explanation:

As these two lines are not parallel so going to intersect at one point so having one solution

[tex]\text{Solve by plugging in 3 to x:}\\\\f(x)=5+4(3)^2\\\\f(x)=5+4(9)\\\\f(x)=5+36\\\\f(x)=41\\\\\boxed{f(3)=41}[/tex]

Answer:

hope this helps

Step-by-step explanation:

f(x) = 5 + 4x^2, then f(3)

5 + 4(3)^2

5+4(9)

5+36

41

Answer:3000m and 3km

Step-by-step explanation:

To convert from cm to m,divide by 100 and from m to km,divide by 1000

Answer:

Step-by-step explanation:

A

Answer:

D.

Step-by-step explanation:

A statistical question can answered by collecting data and having various answers. The other options refer to a specific person/thing and give only one piece of data while the last option refers to many teachers and many pieces of data.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

yes

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

Brother's age =24

Om's age =19

Step-by-step explanation:

Let bro's age be x

Let om's age be x-5

x+x-5=43

2 x -5=43

2 x = 43+5

2 x = 48

x = 24

Answer:

X is 108, infinite

Step-by-step explanation:

You have to determine how many weeks it takes them to make that much, then you add the total. you can determine how many weeks it takes by multiplying

Answer: So you have to first find out how many weeks Alicia needs to work and write it like this (an example)

3x?=9 something like that hope i helped

Step-by-step explanation:

Answer:

28 snakes are missing

Step-by-step explanation:

7 times 104 = 728

7 times 100 = 700

728 minus 700 = 28 snakes are missing

Answer:

a. 135 is correct

Step-by-step explanation:

We have the following information:

dogs lover: 150

cats lover: 120

as the null hypothesis:

H, there are equal number of dogs lover and cats lover, so the expected frequency in each cell will be equal and that is:

f = (150 + 120) / 2

f = 270/2 = 135

so option a. 135 is correct

Answer:

  2.2×10⁹

Step-by-step explanation:

The distributive property is useful here. Recognize that 10⁹ is a common factor:

  (5.4×10⁹) - (3.2×10⁹) = (5.4 -3.2)×10⁹ = 2.2×10⁹

Answer: 2.2×10⁹

Step-by-step explanation:

Hello!

[tex]\boxed{ \bf The~radius~of~the~sphere~is~6~mm.}[/tex]

We know that:

V = [tex]\frac{4}{3}[/tex]πr³

904.32 = [tex]\frac{4}{3}[/tex]πr³

To figure out the radius, we have to undo the above. We can undo the fraction by multiplying by it's reciprocal:

[tex]\frac{3}{4}[/tex] × [tex]\frac{904.32}{1}[/tex] = [tex]\frac{4}{3}[/tex]πr³ × [tex]\frac{3}{4}[/tex]

678.24 =  πr³

Next, we're going to divide both sides by pi:

[tex]\frac{678.24}{\pi } = \frac{\pi r^{2} }{\pi }[/tex]

215.90 = r³

To undo the, we must find the cube root of 215.90.

r = 6

Answer:

[tex]radius = 6mm[/tex]

Step-by-step explanation:

Volume of a sphere.

Use this formula

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

Now solve for r

[tex]r = (3 \frac{v}{4\pi} ) ^{ \frac{1}{3} } \\ = (3 \times \frac{904.32}{4 \times \pi} ) ^{ \frac{1}{3} } \\ ≈

5.99899mm

[/tex]

Answer:

It is 4

Step-by-step explanation:

Answer:

(p+e)/(r-n) =  x

Step-by-step explanation:

p + nx=rx-e

Add e to each side

p +e+ nx=rx-e+e

p +e+ nx=rx

Subtract nx from each side

p +e+ nx - nx=rx-nx

p+e = rx -nx

Factor out x

p+e = x(r-n)

Divide each side by (r-n)

(p+e)/(r-n) =  x(r-n)/(r-n)

(p+e)/(r-n) =  x

Answer: True

Step-by-step explanation:

In triangles MNP and QRS:

NP=RS (hypotenuses);

∠P=∠S (acute angles).

Then, triangles MNP and PRS are congruent by HA theorem.

which makes the answer true

Answer:

True

Step-by-step explanation:

I just took the test, A-p-e-x

Answer:

If there are 800 trees and 1/4 of them die to this disease.

Step-by-step explanation:

800=400x2=800/2=400 so 100/400 die so 200/800 die so in 4 years time the whole population will die.

Answer:

P(t)=800(3/4)^t

Step-by-step explanation:

Answer:

The cop = 40 and the baseball cap = 3 and the baseball bat = 21

Step-by-step explanation:

So 40 - 21 + 3(2) = 25

Answer:

25

Step-by-step explanation:

look at the whole thing first. you see that the field = player so first you do 120/3. you get 40. then for teh second you have two "40's" and an unknown. so you do 101-80 because 40+40=80 and get 21. for the fourth you have 21/?=7 . we can do 21/7=3 to find this. so the helmet is 3. for the final we have 40-21+6 and that equals 25. thank you ;)

If the pattern continues, so that each term is separated by a distance of 3, then the sequence is given by the recursive rule

[tex]\begin{cases}a_1=1\\a_n=a_{n-1}+3&\text{for }n>1\end{cases}[/tex]

From this definition, we can write [tex]a_n[/tex] in terms of [tex]a_1[/tex]:

[tex]a_2=a_1+3[/tex]

[tex]a_3=a_2+3=(a_1+3)+3=a_1+2\cdot3[/tex]

[tex]a_4=a_3+3=(a_1+2\cdot3)+3=a_1+3\cdot3[/tex]

[tex]a_5=a_4+3=(a_1+3\cdot3)+3=a_1+4\cdot3[/tex]

and so on, up to

[tex]a_n=a_1+(n-1)\cdot3[/tex]

(notice how the subscript on a and coefficient on 3 add up to n)

or

[tex]a_n=1+3(n-1)=3n-2[/tex]

Answer:

n=1/2 of n x 8 divided by 4 -2

Step-by-step explanation:

Answer:

90 km/hr

Step-by-step explanation:

If x is the speed of the slower car, and x+20 is the speed of the faster car, then:

5x + 5(x+20) = 1000

x + x + 20 = 200

2x + 20 = 200

x + 10 = 100

x = 90

Answer:

[tex]3.18cm[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Dividing 4x^2 - 13x + 8  by x + 5 or x - (-5), in synthetic division form:

-5)        4          |       -13      |          8

           ↓               4 x (-5)     (-5) x (-33)  

           4                 -33               173

=> Quotient is 4x - 33 and remainder is 173

=> (4x^2  - 13x + 8)/(x + 5) = (4x - 33) + 173/(x + 5)

Hope this helps!

:)

Answer:

-5/4 -13 8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(1+isqrt(3))(1+2isqrt(3))=1+2i√3+i√3+i√3*2i√3=3i√3-5=-5+3i√3

Answer:

vaulue is 4

Step-by-step explanation: