pays $0.72\$0.72 $0.72 dollar sign, 0, point, 72 in sales tax. The sales tax rate is 6%6\% 6% 6, percent . What is the original price of the bracelet, before tax?

80........................

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

Step-by-step explanation:

We have, Sorin hits a cricket ball straight up into the air. After 1.5 s, the ball is falling straight down with a speed of 6.5 m/s.

We want to find the initial vertical velocity of the ball.

The relation between initial speed, final speed, acceleration and time is given by using first equation of kinematics. Let v₀ is the initial speed. So,

[tex]v=v_o +at[/tex]

Here, v = -6.5 m/s, t = 1.5 s and a = -g

[tex]v_o=v-at\\\\v_o=v+gt\\\\v_o=-6.5+9.8\times 1.5\\\\v_o=8.2\ m/s[/tex]

So, the initial velocity of the ball is 8.2 m/s and the formula used is (1).

Answer:

b) 16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121

Step-by-step explanation:

[tex] \Sigma_{k=1}^{16} (k - 5)^2 \\

= (1- 5)^2 + (2- 5)^2 + (3- 5)^2 + \\ (4- 5)^2 + (5- 5)^2 + (6- 5)^2 \\+ (7- 5)^2 + (8- 5)^2 + (9- 5)^2 \\+ (10- 5)^2 + (11- 5)^2 + (12- 5)^2 \\+ (13- 5)^2 + (14- 5)^2 + (15- 5)^2\\ + (16- 5)^2 \\\\

=(-4)^2 + (-3)^2 + (-2)^2 + (-1)^2 + (0)^2 \\+ (1)^2 + (2)^2 + (3)^2 + (4)^2 + (5)^2 \\+ (6)^2 + (7)^2 + (8)^2 + (9)^2 + (10)^2 + \\ (11)^2 \\\\

=16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 \\+ 36 + 49+ 64 + 81 + 100 + 121[/tex]

Answer:

The answer would be {y|y>0}

Step-by-step explanation:

hope this helps

40π

You dont need paper hw since we're in quarantine

Answer:40

Step-by-step explanation:

Answer:

The correct answer is 11 ft.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.

Subtract x from each side:

x+4-x=2x-7-x

4=x-7.

Add 7 to both sides:

4+7=x-7+7

11=x

Answer:

11

Step-by-step explanation:

On edge

Answer:

Find the area of the shape

First the two triangles

3 x 4 = 12 so the area of both triangles is twelve

Now it is only 1 big rectangle left

The side lengths can be added 3 + 4 + 5 = 12

12 x 11 = 132

132+12=144

144 is the surface area/area

If you have any questions please ask

Step-by-step explanation:

30x and 12 have a common factor of 6.   So yes, this might have been the result of distributing the 6 in

6(5x - 2)

Answer:

30x - 12 = 2(15x - 6)

30x - 12 = 3(10x - 4)

30x - 12 = 6(5x - 2)

Step-by-step explanation:

30 and 12 have these factors in common: 2, 3, 6

There are three possible answers.

30x - 12 = 2(15x - 6)

30x - 12 = 3(10x - 4)

30x - 12 = 6(5x - 2)

Answer:

(0, 8)

Step-by-step explanation:

i just got this question

Answer:

(-9,0)

Step-by-step explanation:

To find the x intercept, set y=0 and solve for x

f(x) = (x-8) (x+9)

0 = (x-8) (x+9)

Using the zero product property

x-8 =0    x+9=0

x=8    x=-9

(8,0)    (-9,0) are the x intercepts

Answer:

The shape of a cone

Step-by-step explanation:

If we rotate the right triangle for 360 degrees around one leg, we will have a shape of a cone (a conical shape).

the leg we choose to rotate around will be the height of the cone.

The other leg will be the radius of the cone's base.

And the hypotenusa of the right triangle will be the slant height of the cone.

Answer:

[tex]6x + 42[/tex]

Step-by-step explanation:

Apply the distributive property:

[tex]6x + 6 \times 7[/tex]

Multiply 6 by 7

[tex]6x + 42[/tex]

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

Answer:

38

Step-by-step explanation:

3 x {10 +1} +5.

PEMDAS

Parentheses first

3 x {11} +5.

Then multiply and divide

33+5

38

Answer:

38

Step-by-step explanation:

3 x {10 +1} +5             Following PEMDAS, solve in the parentheses

3 x 11 + 5                   Multiply 3 x 11

33 + 5                       Add

38

Answer:

4 times

Step-by-step explanation:

Answer:

4.8333333 or 4 5/6 times

Step-by-step explanation:

29/6 = 4.83333333

Answer: x = 2

Step-by-step explanation:

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

Answer:

Traci could say draw 2 long parellel sides one on top of another. Then draw 2 smaller sides to connect the long sides.

Step-by-step explanation:

Answer:

You will get $3 back

mark me as brainliest pls

Step-by-step explanation:

$25 times 8%= 2

25+2=27

30-27=3

Answer:

$3

Step-by-step explanation:

25*.08=2

25+2=27

30-27=3

Answer:

4x^2−4x+7

Step-by-step explanation:

Let's simplify step-by-step.

4x^2−10x+9+6x−2

=4x^2+−10x+9+6x+−2

Combine Like Terms:

=4x^2+−10x+9+6x+−2

=(4x^2)+(−10x+6x)+(9+−2)

=4x^2+−4x+7

Answer:

=4x^2−4x+7

Answer:

A

Step-by-step explanation:

Answer:

Angle 2

Step-by-step explanation:

They are 90 degrees when added together

Answer:

<2

Step-by-step explanation:

Complementary angles add to 90 degrees ( form right angles)

<1 and <2 add to 90 degrees so they are complementary angles

Answer:

m = 17

Step-by-step explanation:

[tex]4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}[/tex]

Answer:

73,139.67

Step-by-step explanation:

Answer:

5.3

Step-by-step explanation:

Answer:

The answer is 5.3

Step-by-step explanation:

5.3x3-2= 13.9 but when you round its 14

Answer:

the right answer is : A

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

im smort

Answer:

area=250.12. perimeter=3380

Step-by-step explanation:

Answer:

1.45

Step-by-step explanation:

1. divide both sides of the equation by 20 to get rid of the 2o on the right side

[tex]\frac{29}{20}[/tex]= p x [tex]\frac{20}{20}[/tex]

now u end up with 1.45=p

hope it helped

Answer:

work is shown and pictured

Answer: The volume is 480 in^3

Step-by-step explanation:

v= lwh

v= 12 * 5 * 8

v= 480 in^3

Answer:

Volume of the rectangular prism = [tex]480in.^{3}[/tex]

Step-by-step explanation:

Formula for the volume of a rectangular prism= Ah, where A= base area

                                                                                               & h= height

Base area(A)= Length×Width

                    = 12in.×8in.

                    = [tex]96in.^{2}[/tex]

Since height=5in.,

Volume= [tex]96in.^{2}[/tex]×5in.

            = [tex]480in.^{3}[/tex]

Hope this helps!!!

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