Please help me In a geometric series, each term is 21% less than the previous term. What is the value of r for this
geometric series?
0.79
0.21
1
1.21
1.21

Answer:

Step-by-step explanation:

From what I understand, you are trying to solve for a.

So,

d=g+2ac

d-g=2ac

(d-g)/2c=a

So,

a = (d-g) / 2c

Answer:

Explicit : [tex]a_n=3(2)^{n-1}[/tex]

Recursive: a₁ = 1

                  [tex]a_n=a_{n-1}(2)[/tex]

Step-by-step explanation:

We have to write the recursive formula for the geometric sequence with second term 2 and third term 12.

Geometric sequence will be in the form of,

a, ar, ar², ar³,...........

Here, r = common ratio

a = first term of the sequence

Here, ar = 6 ------(1)

And ar² = 12 ------(2)

By dividing equation (2) by (1),

[tex]\frac{ar^2}{ar}=\frac{12}{6}[/tex]

r = 2

From equation (1),

a(2) = 6

a = 3

Recursive formula of a geometric sequence is given by,

a₁ = a

[tex]a_n=a_{n-1}(r)[/tex]

Therefore, for the given sequence,

a₁ = 1

[tex]a_n=a_{n-1}(2)[/tex]

Similarly, explicit formula of the geometric sequence is given by,

[tex]a_n=a_1(r)^{n-1}[/tex]

[tex]a_n=3(2)^{n-1}[/tex]

Answer:Hence, x = 5, y = 0 is the required solution.

Step-by-step explanation:

Answer:

There is only one solution

Step-by-step explanation:

Answer:

4.8%

Step-by-step explanation:

Answer:4.8

Step-by-step explanation:

Trust

Answer:

64 square units

Step-by-step explanation:

if you spilt up the polygon you can find the area of the square and triangle making up the square.

length * width = Area;   6 * 8 = 48 sq units for the square part

1/2 * base * height = Area;   1/2 * 4 * 8 = 16 sq units for the triangle part

then add the two areas together for the area of the entire polygon:

48 + 16 = 64 sq units

Answer:

The probability that none of the balls selected is red ²⁴/₉₁

Step-by-step explanation:

Given;

number of red balls, R = 5

number of white balls, W = 4

number of blue balls, B = 6

Total number of balls, = 5 + 4 + 6 = 15

Probability of selecting 3 none red balls = P(WWW) or  P(BBB) or P(WWB) or  P(WBW) or P(BWW) or P(BBW) or P(BWB) or P(WBB)

[tex]P = (\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{4}{15} \times \frac{3}{14} \times \frac{6}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{3}{13} ) + \\\\(\frac{6}{15} \times \frac{4}{14} \times \frac{3}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{6}{15} \times \frac{4}{14} \times \frac{5}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{5}{13} )[/tex]

[tex]P = \frac{24}{2730} + \frac{120}{2730} + \frac{72}{2730} +\frac{72}{2730} + \frac{72}{2730} + \frac{120}{2730} + \frac{120}{2730} + \frac{120}{2730} \\\\P = \frac{720}{2730} \\\\P = \frac{24}{91} \\\\[/tex]

Therefore, the probability that none of the balls selected is red ²⁴/₉₁

c is the answer

Answer:

Step-by-step explanation:

Answer:

The sides of the equilateral triangle are 11.7 m.

Step-by-step explanation:

Let's find the area of the isosceles triangle:

[tex] A_{i} = \frac{bh}{2} [/tex]

Where:

b: is the base = 12 m

h: is the height

We can find the height by using Pitagoras:

[tex] x^{2} = \frac{b^{2}}{2} + h^{2} [/tex]    

Where:

x is the hypotenuse = side of the triangle = 10 m

[tex] h = \sqrt{x^{2} - \frac{b^{2}}{2}} = \sqrt{(10)^{2} - 6^{2}} = 8 m [/tex]

Then, the area is:

[tex] A_{i} = \frac{12*8}{2} = 48 m^{2} [/tex]

Now, since the area of the isosceles triangle is equal to the area of the equilateral triangle:

[tex] A_{e} = A_{i} = 48 m^{2} [/tex]

[tex] A_{e} = \frac{bh}{2} [/tex]

The height of the equilateral triangle is given by:

[tex] b^{2} = \frac{b^{2}}{2} + h^{2} [/tex]    

[tex] h = \sqrt{b^{2} - \frac{b^{2}}{2}} = \frac{b}{\sqrt{2}} [/tex]

Hence, the sides are:

[tex] A_{e} = \frac{1}{2}b\frac{b}{\sqrt{2}} = \frac{b^{2}}{2\sqrt{2}} [/tex]            

[tex] b = \sqrt{A*2\sqrt{2}} = \sqrt{48*2\sqrt{2}} = 11.7 m [/tex]      

Therefore, the sides of the equilateral triangle are 11.7 m.

I hope it helps you!      

Answer:

The sides must be  around     10.53 m

Step-by-step explanation:

You can calculate the area of isosceles  dividing into 2 equal right triangles

Once you know that the area of the isosceles is 48 m²,solve for the side of the equilateral triangle

Formula for the Area:    (A= area    a = side)

A = (√3* a² ) / 4

48= (√3* a² ) / 4

Multiply both sides by 4

192 =√3* a²

Divide both sides by√3               (   √3 = 1.732050....)

110.851303 =   a²

Square root on both sides

10 .5385...( 10.53 )  = a

Answer:

It is already in an increasing order

1. 4x - 8 Highest

2. 3x - 2

3. 2x + 1

4. 1x - 0 Lowest

Step-by-step explanation:

1. 56

2. 25

3. 9

4. 1

Welcome to the concept of the maths.

Here, we can see, that Linear equation always have highest power or degree of its variable as '1' ,

thus here, y = 3/x has degree as -1 and y = x^2 +5 has degree 2 ,

hence,

The equations that are NOT linear are

2.) y = 3/x and 5.) y = x^2 + 5

Answer:

72.3

Step-by-step explanation:

So, to find the average you need to add all the numbers together and divide it by the amount of numbers there are, if that makes sense.

so in your question: 100 + 90 + 80 + 89 + 75 + 0= 434

and there are 6 numbers that you had to add together, so you divide 434 by 6, which is 72.3 so that's the answer! It's quite easy once you understand how to do it :)

Answer:f(x)=-16(x-1)^2+22

Step-by-step explanation:

The equation for the trajectory of ball in the air is h(t) = -16t² + 32t + 6.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

It can also be said as the slope of the tangent for the  function at a given point.

Given that,

The maximum height reached by the ball  after 1 sec is 22 ft above ground.

And, the height at which it is thrown is 6 ft above the ground.

Which implies at 0 sec the height is 6 ft.

The quadratic function for the height can be written as,

h(t) = at² + bt + c

Substitute t = 0 to gat,

f(0) = a × 0² + b × 0 + c

=> c = 6

Now, for maximum height,

h'(t) = 0

=> 2at + b = 0

At maximum height t = 1

Then, the above expression becomes,

2a × 1 + b = 0

=> a = -b/2

Substitute t = 1 in h(t) = at² + bt + c to get,

22 = a + b + c

=> 22 = -b/2 + b + 6

=> b/2 = 16

=> b = 32

Then, a = -b/2

            = -32/2

            =-16

Thus substituting the corresponding values the equation can be written as h(t) = -16t² + 32t + 6.

Hence, the required equation for the path of the ball in the air is  h(t) = -16t² + 32t + 6.

To know more about differentiation click on,

https://brainly.com/question/24898810

#SPJ2

Answer:

They donated 6%.

Step-by-step explanation:

The total sales were $9800.

The amount donated is $588.

We want to know what percent of 9800 is 588.

Let's make an equation.

what percent of 9800 is 588

x/100 • 9800 = 588

Divide by 9800.

x/100 = 0.06

Multiply by 100.

x = 6

They donated 6%.

Hope this helps!

Answer:

i think its second pythagreom therom

Step-by-step explanation:

because

Answer:

72km/h

Step-by-step explanation:

the formula of changing metres per second to km/h is 18/5 and kilometre per hour into metres per second is 5/8 in hope it helps.

Answer:

Q = (9, 4 )

Step-by-step explanation:

Use the midpoint formula and equate to the coordinates of the midpoint.

M = ([tex]\frac{x_{1}+x_{2} }{2}[/tex] ) , ([tex]\frac{y_{1}+y_{2} }{2}[/tex] )

let the coordinates of Q = (x, y ) , R = (- 7, 0 ) , then

[tex]\frac{x-7}{2}[/tex] = 1 ( multiply both sides by 2 )

x - 7 = 2 ( add 7 to both sides )

x = 9

and

[tex]\frac{y+0}{2}[/tex] = 2 ( multiply both sides by 2 )

y = 4

Thus Q = (9, 4 )

Answer:

Distribute

Subtract   two from both sides of the equation

Simplify

and that's your solution

which should be t=4

Step-by-step explanation:

Answer:

-3 and 0 are like terms because both of them are numbers

Answer:

26

Step-by-step explanation:

Answer:

The answer is 0.0085 So I'm guessing less than one.

Given:

The figure of a right triangle.

To find:

The value of x.

Solution:

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

In the given right triangle,

Hypotenuse = 15

Perpendicular = 12.5

Now,

[tex]\sin x^\circ=\dfrac{12.5}{15}[/tex]

[tex]\sin x^\circ=0.83333[/tex]

[tex]x^\circ=\sin^{-1}0.83333[/tex]

[tex]x^\circ =56.442345^\circ[/tex]

[tex]x\approx 56[/tex]

Therefore, the equation used to find x is [tex]\sin x^\circ=\dfrac{12.5}{15}[/tex] and the value of x is 56.

Answer:

10 makes this equation true

Step-by-step explanation:

2x -4 = 16 /+4

2x= 20 /÷2

x= 10

Test

2(10) - 4 = 16

20 - 4 = 16 Correct

Answer:

top 8, middle 7, 16, bottom 13

Answer:

149500

Step-by-step explanation:

since there's 8 goats, each goat would be 1040000/8, which is 130000 per goat.

marketing at a 15% increase means the new percentage would be 115%, which could be represented by 1.15.

130000 * 1.15 = 149500 / goat

Answer:

(2x + 1)(x + 5).

Step-by-step explanation:

`y=2x^2+11x+5`

2 * 5 = 10

1 * 10 = 10 and  1 + 10 = 11 so we write:

y = 2^2 + 10x + x + 5

y = 2x(x + 5) + 1(x + 5)

= (2x + 1)(x + 5).

Step-by-step explanation:

12a-9a>-12+6

3a>-6/:3

a>-2

Answer:

a is the answer for this question