a.
x = 40
c.
x = 20
b.
x = 10
d.
x = 15

Answer:

14.86 knots.

Step-by-step explanation:

Given that:

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2[tex]\times[/tex] 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 [tex]\times[/tex] 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled [tex]\triangle AOB[/tex].

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units[/tex]

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = [tex]\dfrac{Total\ distance}{Total\ time}[/tex]

[tex]\Rightarrow \dfrac{74.28}{5} = 14.86\ knots[/tex]

Answer:

Here You Go! I'm not really sure about this one but i tried.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To prove this we should first make a little representation to get an idea of how will proceed to work .

To solve it we should use vectors so the first step is to identify this vectors :

NOW LET'S IDENTIFY THEIR COORDINATES :

We get :

We notice that the opposite ones have the same coordinates so the edges are parallel .

If we want to check more we can calculate the lenghts :

So AB=DC

So AD=BC

SO ABCD IS A PARALLELOGRAM

Answer:

D is the correct answer

Step-by-step explanation:

according to the graph you can see that D should be correct.

Good luck! ^_^

Answer:

If they are opposite.

Answer:

Step-by-step explanation:

a.  

L

=

329.9

c

m

2

;

S

=

373.9

c

m

2

.

b.  

L

=

659.7

c

m

2

;

S

=

483.8

c

m

2

.

c.  

L

=

659.7

c

m

2

;

S

=

813.6

c

m

2

.

d.  

L

=

329.9

c

m

2

;

S

=

483.8

c

m

2

.

Surface Area of a Cone:

In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.

The height of the cone is the length of a line segment that joins the base to the vertex of the cone.

The radius of the cone is the same as the radius of the base.

Surface area of a cone

(a) Lateral Surface Area

If  

l

and  

r

are the slant height and radius of a cone then its lateral surface area is given by the formula-

L

=

π

r

l

where  

L

is the lateral surface area of the cone

(b) Total surface area

It is the sum of the area of the circular base and the lateral surface area of the cone.

S

=

L

+

π

r

2

S

=

π

r

l

+

π

r

2

Where  

S

is the total surface area of the cone

Answer and Explanation:

Given that the radius and slant height of a right cone is  

7

c

m

and  

15

c

m

respectively

r

=

7

c

m

l

=

15

c

m

So the lateral surface area of the cone-

L

=

π

r

l

L

=

π

(

7

)

(

15

)

L

=

105

π

L

=

105

(

3.14159

)

L

=

329.866

L

≈

329.9

c

m

2

And the total surface area of the cone-

S

=

L

+

π

r

2

S

=

329.9

+

π

(

7

)

2

S

=

329.9

+

49

(

3.14159

)

S

=

329.9

+

153.937

S

=

483.83

c

m

2

So the lateral area and total area of a right cone are  

329.9

c

m

2

and  

483.8

c

m

2

respectively.

Answer:

Step-by-step explanation:

Step-by-step explanation:

a.  

L

=

329.9

c

m

2

;

S

=

373.9

c

m

2

.

b.  

L

=

659.7

c

m

2

;

S

=

483.8

c

m

2

.

c.  

L

=

659.7

c

m

2

;

S

=

813.6

c

m

2

.

d.  

L

=

329.9

c

m

2

;

S

=

483.8

c

m

2

.

Surface Area of a Cone:

In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.

The height of the cone is the length of a line segment that joins the base to the vertex of the cone.

The radius of the cone is the same as the radius of the base.

Surface area of a cone

(a) Lateral Surface Area

If  

l

and  

r

are the slant height and radius of a cone then its lateral surface area is given by the formula-

L

=

π

r

l

where  

L

is the lateral surface area of the cone

(b) Total surface area

It is the sum of the area of the circular base and the lateral surface area of the cone.

S

=

L

+

π

r

2

S

=

π

r

l

+

π

r

2

Where  

S

is the total surface area of the cone

Answer and Explanation:

Given that the radius and slant height of a right cone is  

7

c

m

and  

15

c

m

respectively

r

=

7

c

m

l

=

15

c

m

So the lateral surface area of the cone-

L

=

π

r

l

L

=

π

(

7

)

(

15

)

L

=

105

π

L

=

105

(

3.14159

)

L

=

329.866

L

≈

329.9

c

m

2

And the total surface area of the cone-

S

=

L

+

π

r

2

S

=

329.9

+

π

(

7

)

2

S

=

329.9

+

49

(

3.14159

)

S

=

329.9

+

153.937

S

=

483.83

c

m

2

So the lateral area and total area of a right cone are  

329.9

c

m

2

and  

483.8

c

m

2

respectively.

Answer:

x = 1

Step-by-step explanation:

This is a 30-60-90 triangle, which means that if the long leg is the square root of 3, the hypotenuse is 1.

Answer:

X=1

Step-by-step explanation:

Answer:

(2,1)

Step-by-step explanation:

The point (2,1) is the only point that is not included in the shaded region so I would assume that it's not a solution to the system.

Answer:

Area of ΔDEF = 12 in²

Step-by-step explanation:

Since they are similar, we have to find the scale factor

Scale Factor = [tex]\frac{Side OfDilated Triangle}{Side of Original Triangle}[/tex]

Scale Factor = 4/2

Scale Factor = 2

This means The area of ΔABC is 2 times the area of ΔDEF

So,

ΔABC = 2(ΔDEF)

Where Area of ΔABC = 24 in²

24 = 2(ΔDEF)

Dividing both sides by 2

=> Area of ΔDEF = 12 in²

Answer:

Circle Circumference: 5

Triangle: 8

Circle Area: 3

Regular Polygon: 7

Parallelogram:6

Equilateral triangle: 1

Trapezoid:4

Rectangle:2

Step-by-step explanation:

I don't know how I would do a step by step explanation

answer: the denominator of the improper fraction is the sum of the numerator and the product of denominator and the whole number of the mixed fraction.

Answer:

It is the same denominator of the fraction.

Step-by-step explanation:

[tex]1\frac{1}{5} = \frac{x}{y}[/tex]

[tex]1\frac{1}{5} = \\1=\frac{5}{5}\\\frac{1}{5} = \frac{1}{5}\\\frac{5}{5} +\frac{1}{5} =\frac{6}{5}[/tex]

Answer:

[tex] \boxed{\sf (8x + y)(2x + 3y)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {(5x + 2y)}^{2} - {( 3x - y)}^{2} \\ \\ \sf Factor \: the \: difference \: of \: two \: squares. \\ \sf {(5x + 2y)}^{2} - (3x - y)^{2} = ((5x + 2y) + (3x - y)) \\ \sf ((5x + 2y) - (3x - y)) : \\ \sf \implies ((5x + 2y) + (3x - y))((5x + 2y) - (3x - y)) \\ \\ \sf Grouping \: like \: terms, \: 5x + 2y + 3x - y = \\ \sf (5x +3x) + (2y - y) : \\ \sf \implies \boxed{ \sf( (5x +3x) + (2y - y))}((5x + 2y) - (3x - y) \\ \\ \sf 5x + 3x = 8x : \\ \sf \implies (\boxed{ \sf 8x} + (2y - y))((5x + 2y) - (3x - y)) \\ \\ \sf 2y - y = y : \\ \sf \implies (8x + \boxed{ \sf y})((5x + 2y) - (3x - y)) \\ \\ \sf - (3x-y)=y-3x: \\ \sf \implies (8x + y)(5x + 2y + \boxed{ \sf y - 3x}) \\ \\ \sf Grouping \: like \: terms, \: 5x + 2y + y - 3x = \\ \sf (5x - 3x)(2y + y) : \\ \sf \implies (8x + y) + \boxed{ \sf ((5x - 3x)(2y + y))} \\ \\ \sf 5x - 3x = 2x : \\ \sf \implies (8x + y)( \boxed{ \sf 2x} + (2y + y)) \\ \\ \sf 2y + y = 3y : \\ \sf \implies (8x + y)(2x + \boxed{ \sf 3y})[/tex]

Answer:

(8x+y)(2x+3y)

Step-by-step explanation:

see attached

Answer:

n = √2/8

Step-by-step explanation:

1/4 × √ 2 = 2n

√2/4 = 2n

√2 = 4×2n

8n = √2

n = √2/8

The value of n in

[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]

is n = √2 / 8

The given equation is:

[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]

Multiply through by 4

[tex] \sqrt{2} = 4(2n)[/tex]

This can be further simplified as

[tex] \sqrt{2} = 8n[/tex]

[tex] \frac{ \sqrt{2} }{8} = \frac{8n}{8} [/tex]

The like terms cancel out

[tex]n = \frac{ \sqrt{2} }{8} [/tex]

Therefore, the value of n in

[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]

is

[tex]n = \frac{ \sqrt{2} }{8} [/tex]

Learn more here: https://brainly.com/question/2956399

Answer:

733.04

Step-by-step explanation:

Cylinder:

V=3.14x5x5x7

=549.78

Cone:

V=3.14x5x5x7/3

=183.26

TOTAL:

549.78+183.26=733.04

Hey there! :)

Answer:

Choice 3: David's equation is correct because their spending will be multiplied by the number of months and then subtracted from their savings.

Step-by-step explanation:

In the question, $12,350 is given as the initial value and '240x' is the monthly spending in terms of x.. When writing the equation, we must subtract 240x because the money is being spent.

The correct equation for this situation would be:

y = 12,350 - (240x).

Thus, David's Equation is correct.

Answer: h(x) = 3*(1/6)^(x + 4)

Step-by-step explanation:

if we have a function g(x), and we want to create another function h(x) such that:

h(x) is a vertical contraction/dilation of factor a.

Then h(x) = a*g(x).

h(x) is a right shift of N units (N positive):

h(x) = g(x - N)

Then:

A vertical shink of factor 1/3 means that:

h(x) = (1/3)*g(x)

And a left shift of 4 units (or a right shift of -4 units) means that

h(x) = (1/3)g(x - (-4)) = (1/3)*g(x + 4)

and we know that:

g(x) = 9*(1/6)^x

Then:

h(x) = (1/3)*9*(1/6)^(x + 4) = 3*(1/6)^(x + 4)

Answer:

Step-by-step explanation:

"Four times a number" in symbols is "4n."

Answer:

A

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

because the more the root the faster the plant grows

Answer:

13<x<39 (range of hours)

Step-by-step explanation:

2<x<6 (x is the range of days)

Since each workday is 6.5 hours, multiply everything by 6.5:

13<x<39 (the new x is the range of hours)

Answer:

57°

Step-by-step explanation:

Δ AOB has 2 equal sides as radius of the circle, this is isosceles triangle

So the angles ∠OAB= ∠OBA

∠AOB= 66° and sum of 3 angles = 180°

So  ∠OAB= (180° - 66°)/2= 57°

Answer:

Option B.

Step-by-step explanation:

The given triangle is a right angle triangle.

In a right angle triangle,

[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]

In the given triangle,

[tex]\tan (45^{\circ})=\dfrac{v}{7}[/tex]

[tex]1=\dfrac{v}{7}[/tex]

[tex]7=v[/tex]

Using Pythagoras theorem, we get

[tex]hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]u^2=v^2+7^2[/tex]

[tex]u^2=7^2+7^2[/tex]

[tex]u^2=2(7^2)[/tex]

Taking square root on both sides, we get

[tex]u=\sqrt{2(7^2)}[/tex]

[tex]u=7\sqrt{2}[/tex]

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

Given data

θ= 10°

Horizontal length is equivalent to the adjacent= 20 m

the height of the ramp is equivalent to the opposite=?

Applying SOH CAH TOA we have

using TOA

Tan θ= opp/adj

Tan 10= opp/20

opp= Tan(10)* 20

opp= 0.64836*20

opp= 12.96

Approximately the maximum height of the ramp is 12 m

Answer: A. (-3,7)

Step-by-step explanation:

No work needed, you just need to look at the coordinate plane.

Coordinate II is x as a negative and y as a positive

Answer:

D, (5,-1)

5 is in the x axis

-1 is in the y axis

This point is it the second quadent

Hope this helps ( if incorrect try a)

Answer:

1 & 2

Step-by-step explanation:

Remote interior angles are the angles inside of a triangle but not on the same straight line as the exterior angle (4)

Answer:

<1 and <2 are the remote interior angles for angle 4

Step-by-step explanation:

The remote interior angles that correspond to angle 4 are the angles that are in the triangle that are not adjacent to angle 4

<1 and <2 are the remote interior angles

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the SURFACE AREAS AND VOLUMES.

Since the given section is a Sector of a Circle with length as, 8πcm .

Thus then it's folded veltically at an axis to make a cone.

since we know that, The Curved surface area of a cone is given as formula,

C.S.A = πrl

where, r = radius and l = slant height.

also 2πr = circumference of a circle,

we get as, radius = 4 cm.

Answer:

r = 4 cm

Step-by-step explanation:

AB is actually the circumference of the circle

So,

Circumference = 8π cm

Whereas,

Circumference = 2πr

8π = 2πr

Dividing both sides by 2π

=> r = 4 cm

Answer:

Step-by-step explanation:

3/25 = 12%

3/25=0.12

Answer:

12%

.12

Step-by-step explanation:

3/25 * 4/4 = 12/100

Percent means out of 100

12%

12/100

Since it is out of 100, we can move the decimal 2 places to the left

.12

Answer: 0.22 kilolitre

Step-by-step explanation:

First, let’s find the volume of the tank. We know the volume of a cylinder is represented by the equation V=πr^2h,

Radius = 1 m

Height = 7 cm = .07 m

The tank is 0.22 cubic meters

Now that we found the volume, we will try to find how many liters are in the tank.

1 cubic meter = 1 kilolitre

So, 0.22 cu. m = 0.22 kilolitre

Answer:

50 %

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiplying a(x) and b(x) together results in a quadratic equation (a trinomial).  This trinomial looks like (a·b)(x) = (2)(x - 2)(x + 2).  Note that this is a "special product;"  (2)(x^2 - 4); there is no middle term.

Answer:(ab)x

Step-by-step explanation: