2x . (x² - 5x + 6) - 3x . (x² + 2x -1)

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:

Step-by-step explanation:

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

Answer:

A whole number first term to render as fifth term a value larger than 10000, should be at least 121

Step-by-step explanation:

The formula is given as recursive since it involves the previous number of the sequence, and defined as:

[tex]a_n=a_{n-1}*3+6[/tex]

we also know that the first term is 4

Then in this case, the first five terms are:

[tex]a_1=4\\a_2=4*3+6=18\\a_3=18*3+6=60\\a_4=60*3+6=186\\a_5=186*3+6=564\\[/tex]

So if we want to find the first term in the case that the fifth one is greater than 10,000 using this recursive formula, now we have to start backwards, and say that the fifth term is "> 10000" and what the fourth one is.

Notice that if you have this definition for the nth term, we can obtain from it, what the previous term is to find the general rule:

[tex]a_n=a_{n-1}*3+6\\a_n-6=a_{n-1}*3\\\frac{a_n-6}{3} = a_{n-1}\\a_{n-1}=\frac{a_n}{3} -2[/tex]

So the rule is to subtract 6 from he term, and divide the subtraction by 3. Then working backwards:

[tex]a_5>10000\\\frac{a_5}{3} -2>\frac{10000}{3} -2\\a_4>=\frac{10000}{3} -2\\\frac{a_4}{3} -2>\frac{\frac{10000}{3}-2}{3}-2 =\frac{10000}{9}-\frac{8}{3} \\a_3>\frac{10000}{9}-\frac{8}{3} \\\frac{a_3}{3} -2>\frac{\frac{10000}{9}-\frac{8}{3} }{3} -2=\frac{10000}{27} -\frac{8}{9} -2=\frac{10000}{27} -\frac{26}{9}\\a_2=\frac{10000}{27} -\frac{26}{9}\\\frac{a_2}{3} -2>\frac{\frac{10000}{27} -\frac{26}{9}}{3} -2=\frac{10000}{81} -\frac{80}{27} \\a_1>\frac{10000}{81} -\frac{80}{27}\approx 120.49[/tex]

therefore, the starting first term should be at least about 121 to give a fifth term larger than 10,000

Answer:

50 %

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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:

Step-by-step explanation:

Yes because it can kill people going into that sea or ocean for various activities and also for the living creatures existing in that ocean or sea.

If the gulf oil leak had been processed oil, it would have been worse than a regular oil disaster since processed oils have a longer shelf life.

The Gulf Coast is a region in the extreme south of the United States that runs along the northern shore of the Gulf of Mexico.

When a substantial amount of oil is combined with vast bodies of water, such as the sea or oceans, an oil spill occurs.

Because oil is denser than water, it floats on top of the water and does not mix with it. On top of the water, it produces a layer.

The difference between processed and regular oil is that processed oil is heated to extremely high temperatures, causing oxidation and the creation of free radicals,

Hence refined oil has a longer shelf life, it's a better option.

To learn more about the gulf coast refer to the link;

https://brainly.com/question/1146516

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:

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:

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:

In this equation, the value of x is 9.

Step-by-step explanation:

-4(6x + 3) = -12(x + 10)

Distribute -4 to (6x + 3) and distribute -12 to (x + 10).

-24x - 12 = -12x - 120

Add 12x on both sides of the equation.

-12x - 12 = -120

Add 12 on both sides of the equation.

-12x = -108

Divide -12 on both sides of the equation.

x = 9

The value of x in this equation is 9.

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: 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:

(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: 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: 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:

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:

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:

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

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.

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:

x = 9

Step-by-step explanation:

-2x = 18 - 4x

-2x + 4x = 18

2x = 18

x = 18/2

x = 9

Answer:

x=9

Step-by-step explanation:

-2x = 18 -4x

+4x        +4x

2x  = 18

÷2    ÷2

x=9

Answer:

12

Step-by-step explanation:

because the more the root the faster the plant grows

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:

If they are opposite.

Answer:

solution,

Area of trapezoid:

[tex] \frac{a + b}{2} \times h \\ = \frac{2 + 4}{2} \times 2 \\ = \frac{6}{2} \times 2 \\ = 6 \: {units}^{2} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

The statement is true

Step-by-step explanation:

We have been given an equation of hyperbola

In the given equation of hyperbola center is located at h at -1 and k at 2. so:

C:(h,k) = (-1,2)

Coordinated of the foci of the hyperbola are given as:

Foci: (h, k ± c)

Substitute the values of h and k into the coordinated of foci of hyperbola.

Foci: (-1, 2 ± c)

Where c can be found by using the given formula

c = √(a²+b²)

c = √(16+144)

c = 4√10

So the the coordinates of the foci are:

Foci: (-1, 2 - 4√10) and (-1, 2 + 4√10)

Thus, the statement given is true