The main mast of s sailboat is supported by a rope that extends from the top of the mast to the deck. If the mast is 23 feet tall and the rope attaches to the deck 15 feet away from the base of the mast, how long is the rope? ​

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Answer:

  D. 12

Step-by-step explanation:

There are a number of ways to find the area of this rectangle. Perhaps the most straightforward is to find the lengths of the sides and multiply those. The distance formula is useful.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

Using the two upper-left points, we find the length of that side to be ...

  d = √((3 -0)^2 +(3 -0)^2) = √(9 +9) = √18 = 3√2

Similarly, the length of the lower-left side is ...

  d = √((-2 -0)^2 +(-2 -0)^2) = √(4+4) = √8 = 2√2

Then the area of the rectangle is ...

  A = LW

  A = (3√2)(2√2) = 3·2·(√2)^2 = 3·2·2 = 12

The area of rectangle ABCD is 12.

_____

Other methods include subtracting the area of the corner triangles from the area of the bounding square:

  5^2 -2(1/2)(3·3) -2(1/2)(2·2) = 25 -9 -4 = 12

3 plus tax

Step-by-step explanation:

Answer:

9.75 mph

Step-by-step explanation:

3 1/4 ÷ 1/3 = 9 3/4

Answer:

Less than 4 I guess??

This part I have scribbled so I can answer

no x Ehud ihehiexbhhenxkjwbhxnwbxhuebxbuebxh

Answer:

D

Step-by-step explanation:

Answer:

You are 8 hours apart and it would be 6am for them

Step-by-step explanation:

You guys are 8 hours apart because thats the hour difference, so you add 8 to 10pm getting 6am

Answer:

You are 8 hours apart

Step-by-step explanation:

If it was 10pm for you it would be 6 am for him

Answer:

height of b = 280

Step-by-step explanation:

candle b has a height of 280 - 5t, when it comes out of the mold then t=0 so the initial height of b is 280

candle b's height drops by 5 every hour (that's what the -5t part means)

candle a started at 216 and dropped to 192 in 3 hours, so it dropped by 24 in 3 hours so it drops 8 each hour

so candle b starts out taller (280 v. 216) and candle b burns slower (a at 8 per hour and b at 5 per hour), so b will never 'catch up' with a... candle a will be burned out while candle b is still burning

Answer: X= 1 2 3 4  Y= 5 8 11  14

Step-by-step explanation: i tried my best

Answer:

2/5

Step-by-step explanation:

Answer:

10 : 4, 15 : 6, 20 : 8,

Step-by-step explanation:

increase the first number by 5 then add two to the second number

8 square feet will be needed. 3x2= 6 + 2x1= 2= 8 square feet

Answer:

obtuse triangle

Step-by-step explanation:

Answer:

It is a obtuse scalene triangle.

Step-by-step explanation:

Equilateral: all three sides are equal

Isosceles: two sides are equal

Scalene: no sides are equal to each other

If a squared + b squared = c squared it is a right triangle

If a squared + b squared is less than c squared it is a obtuse triangle.

If a squared + b squared is more than c squared it is a acute triangle.

Answer:

letter D

Step-by-step explanation:

2

x

2

−

5

x

−

12

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like

a

x

2

+

b

x

+

c

, we need to think of 2 numbers such that:

N

1

⋅

N

2

=

a

⋅

c

=

2

⋅

−

12

=

−

24

and,

N

1

+

N

2

=

b

=

−

5

After trying out a few numbers we get:

N

1

=

−

8

and

N

2

=

3

3

⋅

(

−

8

)

=

−

24

, and

3

+

(

−

8

)

=

−

5

2

x

2

−

5

x

−

12

=

2

x

2

−

8

x

+

3

x

−

12

=

2

x

(

x

−

4

)

+

3

(

x

−

4

)

(

x

−

4

)

is a common factor to each of the terms

=

(

2

x

+

3

)

(

x

−

4

)

Answer:

a see below for explanation

Step-by-step explanation:

2x^2 + 8x - 3x - 12

2x^2 +5x - 12

Answer:

Base of 5mm, Height of 6mm, Width of 7mm214mm^2

Base of 4mm, Height of 4mm, Width of 10mm192mm^2

Base of 5mm, Height of 6mm, Width of 7mm214mm^2

Base of 6mm, Height of 3mm, Width of 2mm72mm^2

7mmLittle over 1/4 Inch0.27559 Inches

The total surface area is 124 square millimeters.

To find the surface area of any kind of prism we use the general formula. The total surface area of a prism is the sum of lateral surface area and area of two flat bases.

The total surface area of a Prism = (2 × Base Area) + (Base perimeter × Length).

Here, area of base is Area=2(Base×Height)

= 2(6×4)

= 12 square millimeters

Now, Base perimeter × Length= (5+5+6)×7

= 16×7

= 112 square millimeters

Total area = 12+112

= 124 square millimeters

Therefore, the total surface area is 124 square millimeters.

To learn more about the surface area of a prism visit:

https://brainly.com/question/28016184.

#SPJ2

Answer:

30

Step-by-step explanation:

formula :15÷100×200

Answer:

23

Step-by-step explanation:

The number of car are in the y-intercept line so just add each one of the for every different bar.

3 + 4 + 5 + 6 + 3 + 2 = 23

So there are 23 vehicles in total.

The number of vehicles are at Nam's Gas Station is 23

Since The number of cars are in the y-intercept line

So here the no of vehicles should be

= 3 + 4 + 5 + 6 + 3 + 2

= 23

Here we added according to the given graph

Therefore, we can conclude that The number of vehicles are at Nam's Gas Station is 23

Learn more about the graph here: https://brainly.com/question/10587623

Answer:

x=all real numbers

y=all real numbers

Step-by-step explanation:

x=-5y-1

-3(-5y-1)-15y=3

15y+3-15y=3

3=3

therefore the answer is all real numbers

The volume of a cube with a side length of 7 inches is 343 cubic inches.

To find the volume of a cube with a side length of 7 inches, we can use the formula [tex]V = s^3[/tex], where V represents the volume and s represents the side length.

Substituting the given side length into the formula, we have:

[tex]V = 7^3[/tex]

To simplify the expression, we raise 7 to the power of 3, which means multiplying 7 by itself three times:

V = 7 * 7 * 7

V = 343 cubic inches

Therefore, the volume of a cube with a side length of 7 inches is 343 cubic inches.

The complete question is

The formula V = s3 gives the volume V of a cube with side length s. The volume of a cube that has a side length of 7 inches is equal to ____.

Learn more about volume;

https://brainly.com/question/1578538

#SPJ4

Answer:

Step-by-step explanation:

Since it is a regular hexagon, the length of its sides are equal. And same as the distance across its flats.

So that;

NR ≅ OP (property of a regular polygon)

PM ≅ RM (half of the distance across flats of a polygon)

NM ≅ OM (half of the distance across flats of a polygon)

<NMR ≅ <PMO (vertically opposite angles)

<NRM ≅ <OPM (alternate angle property)

<RNM ≅ <POM (alternate angle property)

This therefore proves that: ΔNRM = ΔOPM

Answer:

Mode of the given frequency is 6 as it is occurring frequently

Answer:

5/9

5 to 9

5:9

hope this helps <3

Answer:

5/9,

5:9,

and 5 to 9

Step-by-step explanation: i am pretty sure it is 1

Answer:

x^2-3x+36

Step-by-step explanation:

Answer:

breakdown the initial figure into 2 rectangle

and add their area

Answer:

B: 3

Step-by-step explanation:

2x

x=3 3times2= 6

6+4 =10

Hope this helps

Answer:

16

Step-by-step explanation:

180 is a straight line.

x is among that line so you must subtract the angles you know from 180.

180-54-38= 16

Given:

The figure of a triangular prism.

To find:

The surface area of the triangular prism.

Solution:

We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.

Triangles have base 3 ft and height 2 ft.

Area of a triangle is

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

[tex]A_1=\dfrac{1}{2}\times (3)\times (2)[/tex]

[tex]A_1=3[/tex]

Area of congruent triangles are congruent. So,

[tex]A_1=A_2=3\text{ sq. units}[/tex]

Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.

Area of a rectangle is

[tex]Area=Length\times width[/tex]

[tex]A_3=10\times 3[/tex]

[tex]A_3=30[/tex]

Dimensions of all three rectangles are same, therefore there areas are equal.

[tex]A_3=A_4=A_5=30[/tex]

Now, the total surface area of the prism is

[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]

[tex]A=3+3+30+30+30[/tex]

[tex]A=96[/tex]

Therefore, the total surface area of the prism is 96 sq. ft.