The sum of three consecutive even integers is 288. find the three integers.

Answer:

Hence,

[tex]S_5=1162.5[/tex]

Step-by-step explanation:

We are asked to evaluate:

[tex]S_5[/tex]

We are given a geometric series.

( since each term of the series are in geometric progression as each term is half of the previous term of the series.

i.e. we have a common ratio of 1/2 )

Also, we know that sum of n terms in geometric progression is given by:

[tex]S_n=a(\dfrac{1-r^n}{1-r})[/tex]

where r is the common ratio.

a is the first term of the series.

Here we have:

[tex]a=600\ ,\ r=\dfrac{1}{2}[/tex]

Hence,

[tex]S_5=600(\dfrac{1-(\dfrac{1}{2})^5}{1-\dfrac{1}{2}})\\\\\\S_5=600(\dfrac{2^5-1}{2^4}})\\\\\\S_5=600(\dfrac{31}{16})\\\\\\S_5=1162.5[/tex]

The sum of the first five terms of the geometric progression 600 + 300 + 150 + …  is 1162.5.

A geometric progression is the series of numbers where the ratio of the two consecutive numbers is always the same.

As it is given to us the sequence 600, 300, 150 is a geometric progression. Therefore, the first term of the progression is 600, while the ratio between the two terms are,

[tex]r = \dfrac{300}{600} = \dfrac{1}{2}[/tex]

Now,  we know that the sum of the geometric sequence of the first 5 terms can be written as where the value of the n is 5,

[tex]S=a\dfrac{(1-r^n)}{(1-r)}[/tex]

[tex]S=600\dfrac{(1-(\dfrac{1}{2})^n)}{(1-(\dfrac{1}{2}))}[/tex]

[tex]S = 1162.5[/tex]

Hence, the sum of the first five terms of the geometric progression 600 + 300 + 150 + …  is 1162.5.

Learn more about Geometric Progression:

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circumference = PI x D

 using 3.14 for PI

2.9 x 3.14 = 9.106 = 9.11 meters of chicken wire are needed.

Answer:

12

Step-by-step explanation:

Answer: The object and its image have opposite orientations

Step-by-step explanation:

A reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to produce the image, such that the figure and its image have opposite orientations.

Since, it preserves distance.

Therefore, the points of the image have the same distance from the line as the points of pre-image on the opposite side of the line.

Hence, the right option is "the object and its image have opposite orientations".

Answer:

x=0,  x=3

Step-by-step explanation:

The solution to the system of equations is x = 6 and y = 84.

The given equations are:

-13x = 90 - 2y

-6x = 48 - 2y

To find the values of x and y, we can solve the system of equations. We can start by multiplying the second equation by -2 to eliminate the y variable. This gives us:

12x = -96 + 4y

Now we have two equations:

-13x = 90 - 2y

12x = -96 + 4y

We can add the two equations together:

-13x + 12x = 90 - 2y + (-96 + 4y)

-x = -6

Then, we can divide both sides of the equation by -1 to solve for x:

x = 6

Substituting the value of x back into one of the original equations, we can solve for y. Let's use the first equation:

-13(6) = 90 - 2y

-78 = 90 - 2y

-2y = -168

y = 84

Therefore, the solution to the system of equations is x = 6 and y = 84.

1 1/3 + 1 1/6

 add the 1 +1 = 2

add 1/3 + 1/6 ( find common denominator, which in this case is 6)

 so 1/3 becomes 2/6

2/6 + 1/6 = 3/6 which reduces to 1/2

 they ate  2 1/2 pints total

Step-by-step explanation:

[tex]x + 2y \leq 4[/tex]

To graph this inequality we replace <= symbol with = sign

[tex]x + 2y =4[/tex]

subtract x on both sides

[tex]2y =-x+4[/tex]

divide both sides by 2

[tex]y= \frac{-1}{2} x +2[/tex]

Graph the equation using a table

LEts assume some number for x  and find out y

x                           [tex]y= \frac{-1}{2} x +2[/tex]

-2                           3

0                             2

2                             1

Now graph the equation using points (-2,3)  (0,2)(2,1)

use solid line for graphing

Now use test point (0,0) for shading

[tex]x + 2y \leq 4[/tex]

[tex]0 + 2(0) \leq 4[/tex]

[tex]0 \leq 4[/tex]     true

So  we shade the region that contains (0,0)

the graph is attached below

The expression (13x+9k)+(17x+6k) simplifies to 30x + 15k. This is done by adding the coefficients of the like terms which in this case are 13x with 17x, and 9k with 6k.

The expression (13x+9k)+(17x+6k) is a mathematical expression in algebra with two variables, x and k. The goal here is to simplify the expression by combining like terms. In mathematics, 'like terms' refer to the terms that have the same variables and powers. The coefficients of the like terms can be different.

Now to simplify this expression, we add the coefficients of the like terms. The like terms here are 13x and 17x, and also 9k and 6k.

Add 13x and 17x, you get 30x. And when you add 9k and 6k, you get 15k.

So, the simplified version of the given expression (13x+9k)+(17x+6k) is 30x + 15k.

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Answer:

Vertex=(-4,3)

Focus=(-4, 2)

Directrix: y=4

Step-by-step explanation:

Given the equation

[tex]x^2+8x+4y+4=0[/tex]

we have to find the vertex, focus, and directrix of parabola.

[tex]x^2+8x+4y+4=0[/tex]

[tex]y=\frac{-x^2}{4}-2x-1[/tex]

[tex]h=\frac{-b}{2a}=\frac{2}{2(\frac{-1}{4})}=-4[/tex]

Now, k can be calculated by putting x=4 and y=k in given equation

[tex]k=-1-\frac{16}{4}-2(-4)=-1-4+8=3[/tex]

The vertex is (h,k) i.e (-4,3)

[tex]y=\frac{-x^2}{4}-2x-1[/tex]

[tex]y=\frac{1}{4}(-x^2-8x-4)[/tex]

[tex]=\frac{1}{4}(-x^2-8x-16+16-4)[/tex]

[tex]y=\frac{1}{4}(-(x+4)^4+12)[/tex]

[tex]y=\frac{-1}{4}(x+4)^2+3[/tex]

which is required vertex form [tex]4p(y-k)=(x-h)^2[/tex]

gives p=-1

Focus=(-4, 3+(-1))=(-4,2)

Now directrix can be calculated as

y=3-p=3-(-1)=4

we know that

The simple interest formula is equal to

[tex]I=Prt[/tex]

where

I represents simple interest

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]

[tex]I=Prt[/tex]

Solve for P

[tex]P=I/(rt)[/tex]

substitute the values

[tex]P=40/(0.10*5)=\$80[/tex]

therefore

the answer is

[tex]\$80[/tex]

Answer:

(2x+3)(x+2)

Step-by-step explanation:

i hope this helps

2/3x = 4/15 =

 x = 4/15 / 2/3 =   4/15 x 3/2 = 12/30 = 2/5

x = 2/5

all i know is x=25 its hard for me to explain.

If the volume of the substance of 4.9 liters is from x rounded to the nearest tenth of a liter, that means 4.85 <= x < 4.95 then this does NOT leads to x > 5. Therefore the substance does not need to be sent to the lab.