A sailboat is headed due north, and its sail is set perpendicular to the wind, which is from the south of west. The component of the force of the wind in the direction of the heading is 480N, and the component perpendicular to the heading (the drift component) is 650 N. What is the force exerted by the wind, and what is the direction of the wind?

Answer:you have 2 lines that cross.

the left angle formed is equal to 3x + 8

the right angle formed is equal to 5x - 20.

the bottom angle formed is equal to 5x + 4y

since the lines are crossed, the opposite angles to each other are equal.

this means that:

3x + 8 = 5x - 20

solve for x to get x = 14 degrees.

the angle on the left side will be equal to 3(14) + 8 = 50 degrees.

the angle on the right side will be equal to 5(14) - 20 = 50 degrees.

this is at it should be since the angles are equal to each other.

since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.

since those 2 angles are equal, then each one must be equal to 130 degrees.

one of those angles is equal to 5x + 4y.

you get 5x + 4y = 130

since x was already found to be 14, replace x with 14 to get:

5(14) + 4y = 130

solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.

when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.

your answers are:

x = 14 degrees

y = 15 degrees

2 of the angles measure 50 degrees each.

2 of the angles measure 130 degrees each.

Answer:

36mins

Step-by-step explanation:

So, the time of travel to cover 5 1/5 miles at a speed of 8 2/3 mph is 36 minutes.

The time taken for the 5 feet of snow to accumulate is 20 hours.

In this case, Smsnow was falling at the rate of 3 inches per hour and if the snow keeps acclimating, we want to know how long will 5 feet of snow to accumulate.

Since 1 foot = 12 inches

5 feet = 5 × 12

= 60 inches

Therefore the time taken will be the division and this will be:

= 60 / 3

= 20

It'll take 20 hours.

Learn more about inches on:

brainly.com/question/876758

#SPJ1

Answer:

2.8 x 10º

Step-by-step explanation:

Because if you travel 10 spaces in the number 280,000,00.

Step-by-step explanation:

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

Slope = 5/2

x1 = -6

y1 = y

x2 = 4

y2 = 8

5/2 = (8-y) / (4 - (-6))

5/2 = (8-y) / (4+6)

5/2 = (8-y) / 10

5 x 10 = 2 x (8-y)

50 = 16 - 2y

2y = 16 - 50

2y = -34

y = -17

The thing that can be conluded about the diagram is that the ponds are the same length. This is according to the SAS theorem.

According to the SAS theorem, if two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent.

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. If two triangles meet one of the following criteria, they are congruent. All three corresponding side pairs are equal. Two corresponding side pairs and their corresponding angles are equal.

In this case, the triangle for the frog pond and duck pond are the same.

Learn more about triangles on:

https://brainly.com/question/1675117

#SPJ1

The purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.

Let us understand the post hoc tests:

Post hoc tests are an essential component of ANOVA. When at least three group means are tested for equality using ANOVA, statistically significant findings suggest that not all of the group means are equal. ANOVA results, on the other hand, do not specify which differences between pairs of means are significant. Use post hoc tests to investigate variations between various group averages while keeping the experiment-wise error rate under control.

There are a lot of post hoc tests that you can be used but the main purpose of the post hoc tests is always the same.

Thus, the purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.

To learn more about post hoc tests visit:

https://brainly.com/question/13179431

#SPJ1

Check step-by-step explanation.

In order to form the table, we must take several values of x (any values you want to evaluate) and find it's correspondent y value. This is how you  do it:

[tex]y=3x+12[/tex]

[tex]x=0, \\y=3(0)+12\\y=12[/tex]

As you may notice, we are just substituting the x value for the x variable into the equation and calculating y. Do this with several values and form a table (check attached image 1).

[tex]x=1, \\y=3(1)+12\\y=15[/tex]

[tex]x=2, \\y=3(2)+12\\y=18[/tex]

Using the calculated points, draw them in the cartesian plane. Remember that "x" means how many spaces you move horizontally, and "y" means vertical spaces.

Check attached image 2.

Let's take point (2, 18) as an example. This point is generated when you substitute the x value of 2, meaning 2 hotdogs and the souvenir hat. Then, the functions gives a result of 18, which would be the cost of those 2 hotdogs in addition to the souvenir hat. Point (0, 12), on the other hand, means that you didn't buy any hotdogs but you still have to pay $12 for the souvenir hat.

Answer: (3x^2)(y^3√y)

Step-by-step explanation:

1. To simplify the radical

> break the radicand (the number under the radical sign) into a product (the result of two numbers being multiplied together) of known factors.

2. Assume all numbers are real.

Answer:

  (c)  50 units²

Step-by-step explanation:

You want to know the area of the rectangle with vertices (-5, 5), (-1, 7), (4, -3), and (0, -5).

The distance formula can be used to find the lengths of the sides. That formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

The distance between the first two points is ...

  d = √((-1 -(-5))² +(7 -5)²) = √(4² +2²) = √20

The distance between the next two points is ...

  d = √((4 -(-1))² +(-3 -7)²) = √(5² +(-10)²) = √125

The area is the product of two adjacent side lengths:

  A = LW

  A = (√125)·(√20) = √(125·20) = √2500 = 50 . . . . square units

The area of the rectangle is 50 units².

The inequality has a solution set of  {-∞, 13} in order to make it equal

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. An inequality shows the relationship between two values in an algebraic expression that are not equal.

In the given question

8(n - 3) < 4(n + 7)

Expand the bracket

8n - 24 < 4n + 28

8n - 4n < 28 + 24

n < 13

The solution set to make the inequality equal is {-∞, 13}

Learn more on inequality here;

https://brainly.com/question/25275758

#SPJ1

The missing statements/ reasons are:

     Statement                                         Reason

LN bisects ∠MLO                                    Given

LM ≅ LO                                                  Given

∠MLN ≅ ∠NLO                                  Def of angle bisector

LN ≅ LN                                                 Common side

ΔLMN ≅ ΔLON                         SAS postulate of triangle congruence

In this question, we have been given some information about triangles LMN and LON.

We need to prove ΔLMN ≅ ΔLON

LN bisects ∠MLO                    ....................(Given)

LM ≅ LO                                   ...................(Given)

∠MLN ≅ ∠NLO                         ...................(Def of angle bisector)

LN ≅ LN                                    ....................(Common side)

ΔLMN ≅ ΔLON                         ...................(SAS congruence postulate)

Therefore, the missing statements/ reasons are:

     Statement                                         Reason

LN bisects ∠MLO                                    Given

LM ≅ LO                                                  Given

∠MLN ≅ ∠NLO                                  Def of angle bisector

LN ≅ LN                                                 Common side

ΔLMN ≅ ΔLON                         SAS postulate of triangle congruence

Learn more about SAS postulate here:

https://brainly.com/question/13814326

#SPJ1

9 feet is the same as = 2.74 m

Given

1 ft≈ 0.305 m

To find out 9 feet is the same as how many meters:

To convert a foot measurement to a meter measurement, multiply the length by the conversion ratio.

Since one foot is equal to 0.3048 meters, you can use this simple formula to convert:

meters = feet × 0.3048

= 9 * 0.3048

= 2.7432 m

The length in meters is equal to the feet multiplied by 0.3048.

Hence the answer is the 9 feet is the same as meters = 2.74m.

To learn more about conversion click here https://brainly.com/question/23718955

#SPJ9

Answer:

a = 70 degrees

b = 20 degrees

c = 20 degrees

Step-by-step explanation:

First, we can find "c":

angleBCA = 90

angleBCA = angleBCD + c

90 = 70 + c

90 - 70 = c

20 = c

Knowing "c", we can find "a".

angleADC = 90

triangleADC = 180

triangleADC = angleADC + c + a

180 = 90 + 20 + a

180 = 110 + a

180 - 110 = a

70 = a

Knowing "a", we can find "b".

angle BCA = 90

triangleACB = 180

triangleACB = angleBCA + a + b

180 = 90 + 70 + b

180 = 160 + b

180 - 60 = b

20 = b

a perfect square trinomial, namely   [tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2[/tex]

where the middle-term is just a product of "2 times the square root of the terms on both sides".

so let's start by grouping the terms with a variable, and then adding the last term for the trinomial, keeping in mind the middle-term is just that product.

[tex]x^2+6x+5\implies (x^2+6x) ~~ +5\implies (x^2+6x+\square^2) ~~ +5 \\\\\\ \stackrel{middle-term}{6x}=2(\sqrt{x^2})(\sqrt{\square^2})\implies 6x=2x\square\implies \cfrac{6x}{2x}=\square\implies 3=\square[/tex]

ahhhaaa!!! so our missing term from our group is 3, meaning we need to use 3², however, let's remember, all we're doing is borrowing from our very  good friend Mr Zero, 0, so if we add 3², we also have to also subtract 3²

[tex](x^2+6x+3^2-3^2) ~~ +5\implies (x^2+6x+3^2)-3^2 +5\implies {\Large \begin{array}{llll} (x+3)^2-4 \end{array}}[/tex]

Answer:

y = 5x/6 + 3/2

Step-by-step explanation:

First, find the slope (m):

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

m=(9-4)/(9-3)

m=5/6

y=mx+b ==> slope-intercept form equation

y = 5x/6 + b==> substitute the value of the slope for m

9 = 5(9)/6 + b ==> substitute a point (x, y) or (9, 9) into the equation

9 = 45/6 + b ==> simplify

(9 = 45/6 + b)*6 ==> multiply the equation by 6 to remove denominators

54 = 45 + 6b ==> simplify

54 - 45 = 45 - 45 + 6b ==> solve for b

9 = 6b

9/6 = 6b/6

b = 3/2

y = 5x/6 + 3/2 ==> plug in b for the slop-intercept equation

Answer:

Step-by-step explanation:

1. Convert words to math

3/4/1/8=

3/4*8/1=

24/4=

6

3. Answer: 6

Step-by-step explanation:

Its is 8 inches as 72÷9 is 8

Answer:

3x

Step-by-step explanation:

When the equation is like this and they both are being multiplied by x you can just add the coefficients

x+2x

1x+2x

3x

Hopes this helps please mark brainliest

Hello..!

[tex] \sf{x + 2x = 3x}[/tex]

It is known that in similar terms "x" is an unknown quantity and that in this problem "x" is 1 and that we only have to add it to 2:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf2 + 1 = 3[/tex]

So the result is 3x

Answer: only 1

Step-by-step explanation:

Answer: One-fifth.

Step-by-step explanation:

2/5 is two-fifths, 3/5 is three-fifths, and so on.

1/10 is one-tenth, 2/10 is two-tenths, and so on.

Altogether, Abby and Annie have 2,400 coins, using the Lowest Common Multiple of 75 and 80.

The lowest common multiple (LCM) of two or more numbers is the common multiple shared by the numbers.

LCM of 75 and 80 can be obtained by multiplying common prime factors of 75 and 80, and then raising them to their respective highest power, i.e. 2^4 × 3^1 × 5^2, which gives 1200.

For instance, 1,200 can be divided by both 75 and 80 evenly without a remainder.  And there is no other number less than 2,000 that 75 and 80 can divide evenly without a remainder.

Abby's coins = 1,200

Annie's coins = 1,200

Total coins = 2,400

Abby's 80 coins will have 15 groups (1,200/80)

Annie's 75 coins will have 16 groups (1,200/75)

Thus, using the LCM of 80 and 75, the total number of coins held by Abby and Annie is 2,400.

Learn more about the LCM at https://brainly.com/question/233244

#SPJ1

The bottle of grapefruit juice at store A is $6.63 less than the store B.

According to the question,

We have the following information:

The equation y = 1.75x represents what Lamonte would pay in dollars and cents, y, for a bottles of grapefruit juice at store A.

Cost of 17 bottles of grapefruit juice at store B = $36.38

Now, we will find the cost of 17 bottles at store A.

y = 1.75*17

y = $29.75

Now, the difference in their price = 36.38-29.75

Difference = $6.63

Hence, the bottle of grapefruit juice at store A is $6.63 less than the store B.

To know more about bottle of grapefruit juice here

https://brainly.com/question/28983587

#SPJ1

Answer: 0.39

Step-by-step explanation:

Store A

y= 1.75x

A bottle of grapefruit juice costs 1.75 at store A

Store B

36.38$/17 bottles = 2.14$ per bottle

A bottle of grapefruit juice costs 2.14$ at store B

Store B - Store A= 2.14$ - 1.75$

=0.39

Answer:

Step-by-step explanation:

percentage increase = (final - initial)/initial

increase = (672 - 480)/480

               = 192/480

               = 0.4 * 100 = 40% increase

Answer:

Page 1 of 3

1. twenty  

2. 16,49  

3. option3  

4.32  

5. 40 tickets     show your work--10= 1.00 40=4.00

Page 2 of 3

7, 14, 21, 28, 35, 42, 49, 56, 63

Page 3 of 3 (left to right)

56, 0, 21, 63, 42, 35, 14, 28, 7, 77, 84, 56, 14, 49, 63, 28, 70, 42, 21, 35, 84, 7, 77, 0, 70

Step-by-step explanation:

learn your times tables

it will help you in high school and college

The value of the car depreciates according to the scatter plot model that is attached , from the model we can infer that the model is exponential in nature.

So from the data that is plotted in the scatter plot we can see that

The graph is exponential.

We know that the depreciation is calculated by the formula as

A = A₀(1-r)ⁿ

So it is an exponential form of equation. therefore the scatter plot model will also predict an exponential equation.

A scatter plot is a type of plot or mathematical diagram that displays values for a group of data using two or more variables and Cartesian coordinates. A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.

If the points are somehow coded according to colour, shape, or size, another variable can be seen. A series of points is used to represent the data, with each point's position on the y line determined by the value of one variable and its position on the vertical axis by the value of the other.

To learn more about scatter plot visit:

https://brainly.com/question/29231735

#SPJ1

Answer:

El otro extremo dista :

12.5 decímetros

Step-by-step explanation:

1 dm = 1 decímetro = 10 cm

1 m = 1 metros = 10 decímetros = 10 dm

3.5 metros = 3.5 * 10 = 35 decímetros

125 cm = 125/10 = 12.5 decímetros

Entonces:

35 dm - 12.5 dm = 22.5 dm

Answer:

s = 14m + 458

Step-by-step explanation:

current amount = 458

14 per month

s = 14m + 458

The speed of the humming bird when converted to miles per minute is; 0.67 miles per minute

In scientific problems, sometimes, it is necessary to change units from one to another as specifically needed.

The procedure for unit conversion is;

1. Identify the unit you have.

2. Identify the unit you desire or require.

3. Identify appropriate unit conversion factor(s).

4. Cancel units and carry out the math calculations.

5. Evaluate the result.

We are given the speed as 40 miles per hour. Now, the unit of conversion factor from mph to miles per minute is;

1 mile per hour = 1/60 miles per minute

Thus;

40 miles per hour = 40 * 1/60 = 0.67 miles per minute

Read more about Unit conversions at; https://brainly.com/question/141163

#SPJ1