obtain expressions in component form for the position vectors having the following polar coordinates.

Answer:

(3, - 1 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = R (4, - 5 ) and (x₂, y₂ ) = D (2, 3 )

midpoint = ( [tex]\frac{4+2}{2}[/tex] , [tex]\frac{-5+3}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (3, - 1 )

To ski a distance of 36 miles at the speed of 5 miles per 45 minutes, will take 324 min

The formula and procedure we will use to solve this exercise is:

t = x/v

Where:

Information about the problem:

Calculating the velocity we have:

v = x/t

v= 5 miles/45 min

v = 0.111 miles/ min

Applying the time formula from the uniformly rectilinear motion (URM), we have:

t = x/v

t = 36 miles/0.111 miles/ min

t = 324 min

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

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1.5 doller = 100* $ 1.5  = 150 peniess

After 50 minutes = 20 gallons of water

Solution :

Pennies :

The dollar is the United States' 100-cent coin. It takes 100 pennies to equal a dollar

1. Girl deposit 5 pennies for each day

which means after 10 days = 50 pennies

Her sister gave her 3 pennies = 53 pennies total she has

To make the $1.50  into her piggy beg

She needs how many pinnies to do so.

1 doller = 100 pennies

1.5 doller = 100* $ 1.5  = 150 peniess

2.

Gallons :

A gallon of water by definition is 128 fluid ounces in the United States. Water bottles can vary in size, but the total number of bottles making up 128 ounces can fit in a gallon. For example, if the water bottle is 16 ounces in size, then 8 of these make up a gallon.

pool capacity = 1500 gallons of water

then

every 5 minutes = 2 gallons of water

then,

after 50 minutes = 2*10 gallons of water

= 20 gallons of water

After 50 minutes = 20 gallons of water

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A student is not correct when he stated that a triangle can be formed with side lengths 3 in, 5 in, and 9 in because 3 + 5 < 9.

A triangle is a polygon with three sides and three vertices.

To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 3, b = 5, and c = 9

a + b > c : 3 + 5 > 9     8 > 9     False

a + c > b : 3 + 9 > 5     12 > 5     True

b + c > a : 5 + 9 > 3     14 > 3     True

If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.

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Answer: 30, 60, 90 triangle ==> Option 3

Step-by-step explanation:

Lets say Angle A is the angle opposing the line of a triangle that has the length of 6. Lets say Angle B is the angle opposing the line of the same triangle that has the length of [tex]6\sqrt{3}[/tex].

sin A=6/12=1/2

sin A=30 degrees.

sin B=[tex]\frac{6\sqrt{3}}{12}[/tex]=[tex]\frac{\sqrt{3}}{2}[/tex]

sin B=60 degrees.

Hence, triangle is 30, 60, 90 triangle ==> Option 3

Answer:

1.) like terms and 2.) since all you did was combine like terms you didn't change the value, it's the same as before just "fixed" so yes

x would be 20 inches and y would be 32 inches.

Answer:

51.3

Step-by-step explanation:

[tex]\tan y=10/8 \\ \\ y=\arctan(10/8) \\ \\ \approx 51.3^{\circ}[/tex]

Answer:

45

Step-by-step explanation:

Answer:

Step-by-step explanation:

To compare fractions you need to bring them to the same format.

1) Convert 3/5 to decimal:

Compare:

2) Convert 0.85 to fraction:

Bring 3/5 to the same denominator:

Compare:

Other answers are possible.

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

Explanation:

Let's say 10 is the median, and we'll have four values above it and four below. This gives 4+1+4 = 9 total items. One such example could be {6,7,8,9,10,11,12,13,14}. This is the set of whole numbers from 6 to 14 inclusive.

Due to the symmetry of that list, the mean = median = 10

The only problem is the max is 14, when we want it to be 15. We can fix this by adding 1 to each of the upper four values {11,12,13,14} to get {12,13,14,15}.

To balance things out, subtract 1 from each of the lower four values. So we go from {6,7,8,9} to {5,6,7,8}. This balancing is to keep the mean the same at 10.

Therefore, the set  {6,7,8,9,10,11,12,13,14} becomes {5,6,7,8,10,12,13,14,15} which is one possible answer.

There are infinitely many other possible answers. The data set does not have to be symmetric like this.

Answer:

.7456

Step-by-step explanation:

The question is asking for the area under the curve from 1 to 2 ....see diagram.....this is approx .75

Answer:

p(-x)(3)-T(10x+2)(3)

P(-3x)-T(30x+6)

Answer:

Step-by-step explanation:

First we Need to write the Equation as It is

K + 12 = 8

Then we keep the Variable which is K in the right of the equal to and move the rest to the left.

K = 8 - 12 ( Note that when moving a number to the other side, the sign will

                  change)

Then Do 8 - 12 or -12 + 8

The answer will come

K = -4

Hope you Are clear

The private spilled 0.35 litres of fuel

The first step is to convert 6.5 hectolitres to litres

= 6.5 × 100

= 650 litres

Next is to convert millilitres to litres

= 350/1000

= 0.35 litres

Hence the number of litres spilled is 0.35 litres

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Answer:

1. 2.4*10^-11

2. 5.6*10^12

3. 1.5*10^-13

4. 2.1*10^-1

Step-by-step explanation:

1) (6 x 10^-8) x (4 x 10^-4)=

6*4*10^-8 *10^-4=

24*10^(-8-4)=

24*10^-12=

2.4*10^1 *10^-12=2.4*10^-11

2) (7 x 10^6) x (8 x 10^5)=

7*8*10^6 *10^5=

56*10^11=

5.6*10^1 *10^11=5.6*10^12

3) 0.000 000 000 05 x 0.003=

5*10^-11 *3*10^-3=

5*3*10^-11 *10^-3=

15*10^-14=1.5*10^-13

4) (3 x 10^-8) x (7 x 10^6)=

3*7*10^-8 *10^6=

21*10^(-8+6)=

21*10^-2=2.1*10^-1

Answer:

He returns the pedalo after 3.00 pm

Answer:

6: 480

1: 80

3: 240

I hope this is what you meant, and I hope I was able to help you!

Answer: x = 88 degrees

Step-by-step explanation:

The angles of a triangle add up to 180 degrees.

So

48 + x + (x - 44) = 180

48 + 2x - 44 = 180

2x + 4 = 180

2x = 176

x = 88

Angle B = 88 degrees

Angle C = 44 degrees

Answer:

x>-3

Step-by-step explanation:

collect like terms by changing the signs ..

x+4>-3x-8:to: x+3x>-8-4

Hence find the value of x

:4x>-12

4x/4 >-12/4

x>-4

The equation of the line in fully simplified slope-intercept form is y = -x - 8.

It is assumed that a line in the graph will pass through some points on the x and y-axes.

We must determine the line's fully simplified intercept.

we know the standard form of a line that is

y = mx + b

here, m is a slope and b is the constant

On the graph, there are the y-intercept (0,-8) and the x-intercept (-8,0).

The slope of the line passing through these points is:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ [/tex]

[tex]slope = \frac{ 8 - 0}{ 0 - 8} [/tex]

slope = 8/(-8)

slope = -1

then find the value of b

if x = 0 y = -8 then

y = mx +b

-8 = -1(0) + b

-8 = b

the value of b is -8

After inserting the values for m and c, the line's equation will be.

y = - x - 8

Hence y = -x - 8 is the equation of the line in fully simplified slope-intercept form.

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Answer:

C

Step-by-step explanation:

machine a makes 4.25 ounces per minute and B makes 4.5 ounces per minute.

The cost of the one canoe is $25.

According to the statement

We have to find that the cost of the one canoe.

So, For this purpose, we know that the

The cost function will be accustomed find the common cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

The girls group rented 2 canoes and three inner tubes for a complete cost of $80. The boys group rented 1 canoe and seven inner tubes for a complete cost of $95.

Then

Let c is that the cost of renting a canoe and t is that the cost of renting inner tubes.

For the ladies,

2c + 3t = 80

For the boys,

c + 7t = 95

Solving the system of equations, multiply the second equation by 2 and subtract them.

2c + 3t  = 80

2c + 14t = 190

11t = 110  

t = 10

Now,

Substitute t to either equations,

c = 95 - 7t

c = 95 - 7(10)

c = 25

So, The cost of the one canoe is $25.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

The girls group rented 2 canoes and 3 inner tubes for a total cost of $80. The boys group rented 1 canoe and 7 inner tubes for a total cost of $95. What is the cost to rent 1 canoe?

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Answer:

Solve for x:

x= 1/ 2 (2y-1)+ 3y/ 2 (2y-1)

Evaluate: x= 2

Step-by-step explanation:

Answer:

true;the expression s are the same for all values of the variables

Answer:

19

Step-by-step explanation:

When y = 7

Replace 7 with y.

[tex]7 + 12 = 19[/tex]

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Considering the given area of the square, it is found that it's side length is an irrational number.

This problem is incomplete, but researching it on a search engine, it asks if the side length of the square of area 89 cm² is rational or irrational.

The area of an square of side length s is given by s squared, as follows:

A = s².

In this problem, the area is of 89 cm², hence:

s² = 89.

s = sqrt(89).

The square root of 89 is a non-exact root, hence it cannot be represented by fraction and is an irrational number.

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Step-by-step explanation:

2.1

2.2

2.3

2.4

2.5

2.6

2.7

i don't know if thats what you were asking for but yea

Answer:

a geometric model shows the lay out of places like earth it tells us where our best water sources are.