1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ipn [44]
3 years ago
11

Dinah went out to eat at a restaurant. She wants to leave the waitress a tip of 18%. She can determine the amount she should pay

by adding the total amount of the bill (b) to 18% of b + 18% ×b. Which expression shows another way that dinah can calculate the total amount she will pay, Including tip? Help me plssss

Mathematics
2 answers:
hoa [83]3 years ago
6 0

Answer:

C. 1.18b

Step-by-step explanation:

Hi! Ace here!

In order to do this, we have to convert 18% into a decimal.

The decimal form of it is .18.

So we have to do

b+.18b

Combine like terms:

1.18b

I hope this helped

zvonat [6]3 years ago
6 0

Answer:

1.18b

Step-by-step explanation:

Remember: percentage = decimal × 100

total = b + 18% x b

Factor out b:

total = b x (1 + 18%) = b x (1 + 0.18)

total = b x 1.18 = 1.18b

You might be interested in
I really need it to be sold in imaginary numbers
Yuliya22 [10]
Solving a 5th grade polynomial

We want to find the answer of the following polynomial:

x^5+3x^4+3x^3+19x^2-54x-72=0

We can see that the last term is -72

We want to find all the possible numbers that can divide it. Those are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

We want to factor this polynomial in order to find all the possible x-values. In order to factor it we will have to find some binomials that can divide it using the set of divisors of -72.

We know that if

(x - z) is a divisor of this polynomial then z might be a divisor of the last term -72.

We will verify which is a divisor using synthetic division. If it is a divisor then we can factor using it:

Let's begin with

(x-z) = (x - 1)

We want to divide

\frac{(x^5+3x^4+3x^3+19x^2-54x-72)}{x-1}

Using synthetic division we have that if the remainder is 0 it will be a factor

We can find the remainder by replacing x = z in the polynomial, when it is divided by (x - z). It is to say, that if we want to know if (x -1) is a factor of the polynomial we just need to replace x by 1, and see the result:

If the result is 0 it is a factor

If it is different to 0 it is not a factor

Replacing x = 1

If we replace x = 1, we will have that:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ 1^5+3\cdot1^4+3\cdot1^3+19\cdot1^2-54\cdot1-72 \\ =1+3+3+19-54-72 \\ =-100 \end{gathered}

Then the remainder is not 0, then (x - 1) is not a factor.

Similarly we are going to apply this until we find factors:

(x - z) = (x + 1)

We replace x by -1:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ (-1)^5+3\cdot(-1)^4+3\cdot(-1)^3+19\cdot(-1)^2-54\cdot(-1)-72 \\ =-1+3-3+19+54-72 \\ =0 \end{gathered}

Then, (x + 1) is a factor.

Using synthetic division we have that:

Then:

x^5+3x^4+3x^3+19x^2-54x-72=(x+1)(x^4+2x^3+x^2+18x-72)

Now, we want to factor the 4th grade polynomial.

Let's remember our possibilities:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

Since we verified ±1, let's try with ±2 as we did before.

(x - z) = (x - 2)

We want to divide:

\frac{x^4+2x^3+x^2+18x-72}{x-2}

We replace x by z = 2:

\begin{gathered} x^4+2x^3+x^2+18x-72 \\ \downarrow \\ 2^4+2\cdot2^3+2^2+18\cdot2-72 \\ =16+16+4+36-72 \\ =0 \end{gathered}

Then (x - 2) is a factor. Let's do the synthetic division:

Then,

x^4+2x^3+x^2+18x-72=(x-2)(x^3+4x^2+9x+36)

Then, our original polynomial is:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =\mleft(x+1\mright)\mleft(x^4+2x^3+x^2+18x-72\mright) \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \end{gathered}

Now, let's prove if (x +2) is a factor, using the new 3th grade polynomial.

(x - z) = (x + 2)

We replace x by z = -2:

\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-2)^3+4(-2)^2+9(-2)+36 \\ =-8+16-18+36 \\ =26 \end{gathered}

Since the remainder is not 0, (x +2) is not a factor.

All the possible cases are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

let's prove with +4

(x - z) = (x + 4)

We want to divide:

\frac{x^3+4x^2+9x+36}{x+4}

Let's replace x by z = -4 in order to find the remainder:

\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-4)^3+4(-4)^2+9(-4)+36 \\ =-64+64-36+36 \\ =0 \end{gathered}

Then (x + 4) is a factor. Let's do the synthetic division:

Then,

x^3+4x^2+9x+36=(x+4)(x^2+9)

Since

x² + 9 cannot be factor, we have completed our factoring:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \\ =(x-1)(x-2)(x+4)(x^2+9) \end{gathered}

Now, we have the following expression:

(x-1)(x-2)(x+4)(x^2+9)=0

Then, we have five posibilities:

(x - 1) = 0

or (x - 2) = 0

or (x + 4) = 0

or (x² + 9) = 0

Then, we have five solutions;

x - 1 = 0 → x₁ = 1

x - 2 = 0 → x₂ = 2

x + 4 = 0 → x₃ = -4

x² + 9 = 0 → x² = -9 → x = ±√-9 = ±√9√-1 = ±3i

→ x₄ = 3i

→ x₅ = -3i

<h2><em>Answer- the solutions of the polynomial are: x₁ = 1, x₂ = 2, x₃ = -4, x₄ = 3i and x₅ = -3i</em></h2>

7 0
1 year ago
1. The diameter of a sphere is 21.6 cm. The volume of the sphere is __
sveta [45]
Detailed Answers:

Volume of a Sphere (V) = 4/3 πr^3

1. Diameter (d) = 21.6 cm
Radius (r) = 21.6/2 = 10.8 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (10.8)^3
= 4/3 * 22/7 * 1259.712
= 88/21 * 1259.712
=> 5278.79

Volume (V) = 5278.79 cm^3

2. Diameter (d) = 16 cm
Radius (r) = 16/2 = 8 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (8)^3
= 4/3 * 22/7 * 512
= 88/21 * 512
=> 2145.52

Volume (V) = 2145.52 cm^3

3. Diameter (d) = 24 cm
Radius (r) = 24/2 = 12 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (12)^3
= 4/3 * 22/7 * 1728
= 88/21 * 1728
=> 7241.14

Volume (V) = 7241.14 cm^3

4. Diameter (d) = 6 cm
Radius (r) = 6/2 = 3 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 88/21 * 27
=> 113.14

Volume (V) = 113.14 cm^3
6 0
1 year ago
Read 2 more answers
Which is bigger 0.17 or 0.165
Bogdan [553]
0.17 is bigger because you compare the values of the number in each place. There is no whole number, the tenths place is equal. Then in the hundredths place you have a 6 and a 7. 6<7 so therefore 0.17> 0.165. To help yourself out u can add a 0 at the end to then more easily compare .170 to .165
5 0
3 years ago
Find the median and mean of the data set below:<br> 13, 6, 47,0
Readme [11.4K]

Answer:

Mean=16.5

Median=9.5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help .................
alexandr1967 [171]
The formula to solve the area of a circle is 3.14 (pi) times the radius (1/2 of the circumference) so 3.14 x 8 = 25.12 so your answer is 25.1
4 0
3 years ago
Other questions:
  • Thproduct of 12 and a number is 7
    10·1 answer
  • Approximate the value of the square root 100 to the nearest hundredth
    8·1 answer
  • A computer company uses the function f(h) = 50h + 75 to calculate the total repair bill, f(h), for h number of hours worked. Fin
    14·2 answers
  • What is the total weight in pounds of the books in duanes backpack
    10·1 answer
  • What is the sum of the addition of the two characters 7 + 7 when added​
    12·1 answer
  • If the scale factor of figure a to figure b is 7:2 find the perimeter of figure a whenever the perimeter of figure b is 35
    6·2 answers
  • PLZ HELP!!! :D
    10·2 answers
  • Fast I’m taking a test plz help
    7·2 answers
  • Using completing the square method in quadratic equation 5x²+ 11x + 2=0​
    7·1 answer
  • Can someone plz help me ?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!