What is the value of 3(a-9) when a =6

[tex]\text{First term,} ~a = 72\\\\\text{Common ratio,}~ r = \dfrac{-36}{72} =-\dfrac 12 \\\\\text{Sum of an infinite geometric series,}\\\\S_{\infty} = \dfrac a{1 - r}\\\\\\~~~~~= \dfrac{72}{1+ \dfrac 12}\\\\\\~~~~~=\dfrac{72 }{\tfrac 32}\\\\\\~~~~~=\dfrac{72 \times 2}3\\\\\\~~~~~=48[/tex]

Series: 72 - 36 + 18 - 9 +...

[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]

Identify the following

Solve:

[tex]\rightarrow \sf S \infty \ =(72-36) \ x \ \dfrac{1}{1-\frac{1}{4} }[/tex]

[tex]\rightarrow \sf S \infty \ =48[/tex]

This series has a sum of 48.

Answer:

15

Step-by-step explanation:

- 360 degrees in a complete circle you divide it by 24

360/24=15

The initial value of the function is f(0) = 1 and the graph of the function has been attached.

We are given the function f(x) = (1/4)ˣ

1) Now, the initial value of the function is;

f(0) = (1/4)⁰ = 1

2) The initial value of the function which is the coordinate (0, 1) can be plotted on the attached graph and the point is where the graph crosses the y-axis.

3) f(1) = (1/4)¹ = 1/4

4) The points  (1, 1/4) and (-1, 4)

5) The horizontal asymptote will be a vertical line which will be the value of x when y = 0.

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Answer:

g(x) = f(x) - 4.

Step-by-step explanation:

4 down = -4

g(x) = f(x) - 4.

see the attachment...

hope it helps...!!!

Answer:

There are two solutions.

[tex]x_1 = -0.5\\x_2 = -2[/tex]

Step-by-step explanation:

Step 1

Use the formula of ax^2 + bx + c = 0 to find the coefficients.

[tex]a = 2\\b = 5\\c = 2[/tex]

Step 2

[tex]x=\frac{ (-b+/-sqrt(b^2-4ac))}{(2a)}\\x=\frac{ (-5 +/- sqrt(5^2-4*2*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(25-4*2*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(25-8*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(9))}{(2*2)}[/tex]

[tex]x = \frac{-5 +/- \sqrt{9} }{4}[/tex]

Step 3

[tex]9 = 3^2\\\sqrt{9} = \sqrt{3*3}\\\sqrt{3*3} = \sqrt{3^2}\\\sqrt{3^2} = 3[/tex]

Step 4

[tex]x_1=\frac{(-5+3)}{4} -- > x_2=\frac{(-5-3)}{4}\\x_1=\frac{(-5+3)}{4}\\x_1=\frac{-2}{4}\\x_1=-0,5[/tex]

[tex]x_2=\frac{(-5-3)}{4}\\x_2=\frac{(-8)}{4}[/tex]

[tex]x_2=-2[/tex]

Hope this helps.

Answer:

y = 3/2x + 6

Step-by-step explanation:

Equation of the given line

Perpendicular

Using Point-slope equation

Answer:

2/3

Step-by-step explanation:

The slope sits next to the x in the slope-intercept equation, y=mx+b. Slope is the m. In the equation in the problem y=2/3x-2.

The slope is 2/3.

Answer:

267.95 cubic meters

Explanation:

volume of sphere: (4/3)π(radius)³

Here given:

Volume:

insert values

simplify

final answer

Answer:

V = 267.95

Step-by-step explanation:

The equation to find the volume of a sphere is:

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

r = radius

In the diagram of the question it shows that the radius is 4 m. Plug this into the equation:

[tex]V=\frac{4}{3} (3.14) (4)^{3}[/tex]

Use a calculator to find the answer and then round to two decimal points:

V = 267.95

Hope this helps!!

The advance tickets were 35 in number and the same day ticket will be 30 in number.

To find out the number of the tickets sold we will give some notations so the notations are as follows:-

A= Cost of advance tickets=$30

S= cost of same-day ticket-=15

[tex]N_A=[/tex] Number of the advance tickets

[tex]N_S=[/tex]Number of same-day tickets.

The equations made by the given data will be:-

[tex]30N_A+15N_S=1500\\\\\\N_A+N_S=65[/tex]

By solving the above equations:-

[tex]N_S=30\ \ \ \ \ \ N_A=35[/tex]

Hence the advance tickets were 35 in number and the same day ticket will be 30 in number.

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Answer:

Step-by-step explanation:

2x + 4 + x + 23 = 180

3x + 27 = 180

3x = 153

x = 51

The probability distribution for x will be given below.

x              0              1              2              3

P(x)        0.20       0.30        0.40        0.10

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In a particular region, for families with a combined income of $80,000 or more, 20% have no children, 30% have one child, 40% have two children, and 10% have three children.

Let x be the number of children per family.

We have to construct a probability distribution for x from the given information.

x = 0, 1, 2, 3

For x = 0, the probability will be

P(x) = 20 / 100 = 0.20

For x = 1, the probability will be

P(x) = 30 / 100 = 0.30

For x = 2, the probability will be

P(x) = 40 / 100 = 0.40

For x = 2, the probability will be

P(x) = 10 / 100 = 0.10

Then the probability distribution for x will be given as

x              0              1              2              3

P(x)        0.20       0.30        0.40        0.10

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Answer:

C? Not 100% sure

Step-by-step explanation:

Answer:

559.01 i think that is rounded correctly

Step-by-step explanation:

so it did $615.99 - 9.25% = 559.010925

Hope This Is Good And Helped Sorry If i Did It Worng

Answer:

Below in bold.

Step-by-step explanation:

a) The rectangle in the middle of the net is 10 cm long.

A = 8

B = 3

C = 6

D = 10

b) Surface area

=  3*6 + 3*10 + 3*8 + 2 * 1/2 + 8 * 6

= 18 + 30 + 24 + 48

= 120 cm^2

[tex]sa = bh + ( b_{1} + b_{2} + b_{3})l[/tex]

[tex]sa = 6(8) + (6 + 8 + 3) \times 10[/tex]

[tex]sa = 48 + (17)(10)[/tex]

[tex]sa = 48 + 170[/tex]

[tex]sa = 220 \: {cm}^{2} [/tex]

Answer:

12 * Answer:
12 x 3 = 36 + 6 = 42,
Step-by-step explanation:

Step-by-step explanation:

Answer:

38.88

Step-by-step explanation:

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

The volume of the rectangular prism given its base area and its height is 264 units³.

A rectangular prism is a three-dimensional object that has six faces, 12 sides and 6 vertices.

Volume = length x width x height

base area x height

44 x 6 = 264 units³

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Answer:

Step-by-step explanation:

4a. yes: 5 = 3(2)-1    5 = 6 - 1      5 = 5

4b.  No: 1 = 3(4) + 1

      1 = 12 + 1

       1 ≠ 13

4c. No; 1 = 3 - 3

            1 ≠ 3

4d. yes; 7 = -3(5) + 22

              7 = -15 + 22

              7 = 7

4e. no; -8 = -2(-4)

             -8 ≠ 8

4f. no; 8 = -2 + 11

           8 ≠ 9

Answer:

sin(t) = 4*sqrt(5) / 21; cos(-t) = 19/21

Step-by-step explanation:

think of a right triangle with an adjacent leg a, opposite leg b, and hypotenuse c.

cos(t) = a/c = 19/21. so we can assume a=19 and c=21.

using Pythagorean's theorem, find b: b = sqrt(21^2 - 19^2) = 4*sqrt(5) or 8.944

since tan(t)> 0, b/a > 0 and a is positive so b must be positive. using this information, we know sin(t) = b/c = 8.944/21 or 4* sqrt(5) / 21

since cos x is an even function, cos(-x) = cos x so cos(-t) = cos(t) = 19/21

Answer:

26.88

Step-by-step explanation:

20%*22.40=4.48

22.40+4.48=26.88

Step-by-step explanation:

13113x+1665
_____________________________
Rewrite 13113 as 9 .  1457

Rewrite 1665 as 9 .  185
= 9 .  1457x + 9 .  185
=9(1457x + 185)

The data recorded by Ben shows the attendance log of his classmates over a given period of time.

This refers to a simple chart that resembles a histogram that is used to represent small data.

Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,

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Answer:

[tex]m <U = 80°[/tex]

Step-by-step explanation:

Before we start calculating we have to first note that the angles in a triangle always add up to 180°. Therefore in order to find the missing angle U we have to add both the angles we know, 37° and 63°, then subtract the sum from 180°

[tex]m < U = 180- (37 + 63) \\ \\ m < U = 180 - 100 \\ \\ m< U = 80[/tex]

Answer:

Given equation:

[tex]10^{5x-2}=2^{8x-3}[/tex]

Take natural logs of both sides:

[tex]\implies \ln 10^{5x-2}= \ln 2^{8x-3}[/tex]

[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]

[tex]\implies (5x-2)\ln 10=(8x-3) \ln 2[/tex]

Expand brackets:

[tex]\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2[/tex]

Collect like terms:

[tex]\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2[/tex]

Factor left sides:

[tex]\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2[/tex]

[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]

[tex]\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3[/tex]

[tex]\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay[/tex]

[tex]\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)[/tex]

Simplify:

[tex]\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)[/tex]

[tex]\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}[/tex]

[tex]\implies x=0.4232297737...[/tex]

The equation of the amount charged by Bob will be y = 7.25x.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given that:-

The equation will be generated as follow:-

6 hours  =  $  43.50

1 hours   =  $  7.25

9 hours   =  $ 65.2575

1 hours    =  $ 7.25

Let x represent the number of hours Bob works and y represent the amount he charges. The equation will be:-

y  =  7.25x dollars.

Therefore the equation of the amount charged by Bob will be y = 7.25x.

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Answer:

a5 = 122

Explanation:

Given:

Solve:

a1 = 2

a2 = -3a1+2 = -3(2)+2 = -4

a3 = -3a2 + 2 = -3(-4)+2 = 14

a4 = -3a3 + 2 = -3(14) + 2 = -40

a5 = -3a4 + 2 = -3(-40) + 2 = 122

Answer:

a₅ = 122

Step-by-step explanation:

What is a₅ for the sequence defined by:

[tex]\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_{n-1}+2\\\end{array}\right\\\\\\\hrule[/tex]

Letting n=2:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{2-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{1}+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4[/tex]

Letting n=3:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{3-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{2}+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14[/tex]

Letting n=4:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{4-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{3}+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40[/tex]

Letting n=5:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{5-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{4}+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}[/tex]

Answer:

√3 is the answer

Step-by-step explanation:

the value of tan60 is √3

The sign of a times -b/b when a = 0 and b < 0 is neutral neither negative nor positive .

An integer is a whole number (not a fractional number) that can be positive, negative, or zero

As b<0 which means b would be negative.

So, -b/b gives a negative value.

Because if any of the either numerator or denominator is negative then the resulting value also be negative.

and if zero '0' is multiplied and number whether it is positive or negative the resulting value will be zero.

So,  a* (-b/b)= 0* negative= negative zero, but zero is neither negative nor positive .

hence, the sign of a times -b/b is neutral neither negative nor positive .

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Answer:

Image attached below.

Step-by-step explanation:

Hello!

First let's isolate y:

This means that we are looking at all the values on the coordinate plane that are above the line y = -15.

The red shaded region is the solution region. Note that -15 is not a solution of y > -15 (the dotted line indicates that).