Lucy goes to a restaurant and the subtotal on the bill was x dollars. A tax of 4% is applied to the bill. Lucy decides to leave a tip of 22% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Lucy paid.

9514 1404 393

Answer:

  n = 99

Step-by-step explanation:

The sum of logarithms is the log of a product. Here, the sum of terms is ...

  log(2/1) +log(3/2) +log(4/3) + ... +log((n+1)/n)

  = log((2/1)(3/2)(4/3)×...×((n+1)/n)) = log(n+1)

So, the question reduces to ...

  log(n+1) = 2

Taking antilogs, we have ...

  n +1 = 10^2 = 100

  n = 99

The value of n that makes the sum 2 is 99.

Answer:

The location of the new cell phone tower is [tex](h,k) = (3,4)[/tex], and the equation of the circle is [tex]x^{2}+y^{2} -6\cdot x - 8\cdot y = 0[/tex].

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

[tex]x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]A[/tex], [tex]B[/tex], [tex]C[/tex] - Circunference constants.

Given the number of variable, we need the location of three distinct points:

[tex](x_{1},y_{1}) = (6,0)[/tex]

[tex]36 +6\cdot A + C = 0[/tex]

[tex](x_{2},y_{2}) = (8,4)[/tex]

[tex]80 + 8\cdot A + 4\cdot B + C = 0[/tex]

[tex](x_{3},y_{3}) = (3,9)[/tex]

[tex]90 + 3\cdot A + 9\cdot B + C = 0[/tex]

Then, we have the following system of linear equations:

[tex]6\cdot A + C = -36[/tex] (2)

[tex]8\cdot A +4\cdot B + C = -80[/tex] (3)

[tex]3\cdot A + 9\cdot B + C = -90[/tex] (4)

The solution of this system is:

[tex]A = -6[/tex], [tex]B = -8[/tex], [tex]C = 0[/tex]

By comparing the general form with the standard form of the equation of the circunference is:

[tex]A = -2\cdot h[/tex] (5)

[tex]B = -2\cdot k[/tex] (6)

[tex]C = h^{2}+k^{2}-r^{2}[/tex] (7)

Where:

[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.

[tex]r[/tex] - Radius of the circle.

If we know that [tex]A = -6[/tex], [tex]B = -8[/tex] and [tex]C = 0[/tex], then coordinates of the center of the circle and its radius are, respectively:

[tex]h = -\frac{A}{2}[/tex]

[tex]k = -\frac{B}{2}[/tex]

[tex]r = \sqrt{h^{2}+k^{2}-C}[/tex]

[tex]h = 3[/tex], [tex]k = 4[/tex], [tex]r = 5[/tex]

The location of the new cell phone tower is [tex](h,k) = (3,4)[/tex], and the equation of the circle is [tex]x^{2}+y^{2} -6\cdot x - 8\cdot y = 0[/tex].

Answer:

[tex] lenght= 6 {x}^{2} + 4x - 3[/tex]

Step-by-step explanation:

[tex]lenght = \frac{area}{width} \\ \\ = \frac{36 {x}^{3} + 24 {x}^{2} - 18x }{6x} \\ \\ = \frac{6x(6 {x}^{2} + 4x - 3) }{6x} \\ \\ lenght= 6 {x}^{2} + 4x - 3[/tex]

Answer:

5 15/48

Step-by-step explanation:

5 times 3 is 15,  8 times 6 is 56, and 5 times 1 is 5....you can not simplify 15/48 so the final answer is 5 15/48

Answer:

10^2+24^2

Step-by-step explanation:

got 100% on the quiz

Answer: 2

Step-by-step explanation:

Choose left most point

count up to the horizontal line where the 2nd point is-- up 4

count over to the point -- right 2

slope is rise/ run

4/2 = 2

Answer:

0.5

Step-by-step explanation:

Subtract 2.5 from 3

Answer:

(0, 3 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

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

Here (x₁, y₁ ) = (- 4, 8) and (x₂, y₂ ) = (4, - 2) , then

midpoint = ( [tex]\frac{-4+4}{2}[/tex], [tex]\frac{8-2}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex], [tex]\frac{6}{2}[/tex] ) = (0, 3 )

Answer:

30x-10

Step-by-step explanation:

6(5x−2)+2

Distribute:

=(6)(5x)+(6)(−2)+2

=30x+−12+2

Combine Like Terms:

=30x+−12+2

=(30x)+(−12+2)

=30x+−10

Answer:

=30x−10

Answer: $70/week

Step-by-step explanation:

E = 10w

w = 7 (1 time per day for 7 days = 7)

E = 10(7)

E = $70/week

Answer:

4

Step-by-step explanation:

Answer:

B I think

Step-by-step explanation:

hope this helps

Answer:

B

Step-by-step explanation:

Volume = π x r^2 x h

Hope that helps!

-Sabrina

Answer:

1. A, C, and E

2. 13.5

3. -3

4. $3.39

5. 9 1/4 miles

Step-by-step explanation:

Answer:

the answer is x=5

Step-by-step explanation:

hoped I helped:)

Answer:

x = 5

Step-by-step explanation:

6(5) - 3 = 3(5) + 12

30 - 3 = 15 + 12

27 = 27

Answer: Since x2=6, the width of the rectangle is x-6.

Explanation: factor x^2-4x-12.

given that length=x+2 and area of rectangle = length * width

all you have to do is find the width

there are several way to do this, here is one:

Since one factor of x^2-4x-12 is x+2, x1=-2 is a solution to x62-4x-12=0 so in order to find the other solution, you can use the sum and product properties.

x1*x2= -12 with x1=-2, so x2=6.

Since x2=6, the width of the rectangle is x-6.

Answer:it’s F

Step-by-step explanation:

It’s F

Answer:

x = 38°

Step-by-step explanation:

in the given question,

the two angles are complementary, because sum of their measures = 90°

so,

=》52° + x = 90°

=》x = 90° - 52°

=》x = 38°

Answer:

x = 38

Step-by-step explanation:

I first took the measure of a right angle (90 degrees) Then, I subtracted 52 degrees from 90. After that I added 52 and 38 to check. The answer was 38.

Answer:

Angle 3

Step-by-step explanation:

They are both interior angles as well as on the other sides of the transverse

Answer:

500

Step-by-step explanation:

g (10) = 20(x+15)

= 20 (10+15)

= 20 (25)

= 500

Answer:

Step-by-step explanation:

Find an ordered pair that satisfies the equation 5x + y = 3.  

There are infinitely many ordered pairs that satisfy this equation.

If we were to choose y = 0, then 5x = 3, and x = 3/5, leading to the ordered pair (3/5, 0).

If we were to choose x = 1, then 5(1) + y = 3, or y = -2.  The ordered pair would be (1, -2).

And so on.

Answer:

x= -7 and x= -3

Step-by-step explanation:

(x+7)(x+3)=0 (Think about the numbers that will add to 10 and multiply to 21)

x= -7 and x= -3

Answer:

x = −3 or x = −7

Step-by-step explanation:

Let's solve your equation step-by-step.

x^2 +  10x + 21 = 0

Step 1: Factor left side of equation.

(x+3) (x+7) = 0

Step 2: Set factors equal to 0.

x + 3 = 0 or x + 7 = 0

x = −3 or x = −7

I hope this helps you with your assignment and have a fantastic day! :D

Answer: reflection

Translation

Rotation

Rotation

Step-by-step explanation:

Step-by-step explanation:

Length of cube (L) = 1 ft

Volume of the cube

= L³

= 1³

= 1 ft³

Hope it will help :)❤

Answer:

D) 1

Step-by-step explanation:

D)1

to find the area follow the formula length * width * height

l * w * h

substitute the numbers

1 * 1 * 1

= 1

Answer:

there is no solution, meaning the lines would be parallel

Step-by-step explanation:

i hope this helps :)

Answer:

9/81

Step-by-step explanation:

Too long for me to explain it

Answer:

It's B

... because if you evaluate it it'll be 9x - 6xy, and 2xy + 2x^2

-6xy and 2xy are like terms

Answer:

The slope is -2/-3

Step-by-step explanation:

Look at the X-axis and go up to the point

Answer:

4/-2

Four over -2

Is your slope.

Your y-intercept is -1

Step-by-step explanation:

The correctly arranged binary numbers from smallest to largest is; B) 001100110011, 010101010101, 011001100110, 101010101010

Binary numbers are numbers that are made of only 1 and 0. Now, let us look at the options;

A) 001100110011, 011001100110, 010101010101, 101010101010; This is not well arranged from smallest to biggest because the 2nd and 3rd numbers both have 12 terms but the 2nd term is larger because it starts with 011 while the 3rd term starts with 010 which is not meant to be.

B) 001100110011, 010101010101, 011001100110, 101010101010; Thus is well arranged because unlike the option A above, this one has the second and third term correctly positioned and also the 4th term is the biggest.

Options C & D are not properly arranged for the resaons given in options A and B.

Read more about Binary Numbers at; https://brainly.com/question/8649831

Answer: -6, -10.

The question is asking you to make the coordinates negative and then multiply the negative numbers by 2, thus, -6, -10.

The coordinate of (x, y) is (-3/2, -5/2) if the -2(x, y) → (3, 5) option second is correct.

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

We have:

-2(x, y)  →  (3, 5)

The coordinate (x, y) changes after multiplication by factor 2

New coordinate = (3, 5)

-2x = 3

x = -3/2

-2y = 5

y = -5/2

Thus, the coordinate of (x, y) is (-3/2, -5/2) if the -2(x, y) → (3, 5) option second is correct.

Learn more about the ordered double here:

https://brainly.com/question/10757890

#SPJ2

Answer:

Step-by-step explanation:

    64^(1/3)       in English it is 64 to the one third power