Miguel bought a bicycle at a 30% discount. he paid $122.50. what percent of the original price did Miguel pay​


Answer 1
Answer: 70%

100% - 30% = 70%

The price is not needed
Answer 2

Final answer:

Miguel paid 70% of the original price for the bicycle. The original price was calculated as approximately $175 by dividing the price Miguel paid ($122.50) by 70% (the remaining percentage after the 30% discount).


Miguel paid $122.50 for a bicycle which was discounted by 30%. So, the $122.50 represents the 70% of the original price (because 100% - 30% = 70%). To find out what 100% (the original price) is, we need to perform a calculation where we divide the price paid by Miguel ($122.50) by 70% (in decimal format, that's 0.70).

The formula would structure as below:

Original Price = Price Paid / Percentage of Original Price Paid

Substituting in the values provided, the equation would be:

Original Price = $122.50 / 0.70

Following through with this calculation, we find that the original price of the bicycle was approximately $175. Therefore, Miguel paid 70% of the original price, as that's the remaining percentage after the 30% discount.

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The line AB has midpoint (2,5).A has coordinates (1, 2).Find the coordinates of B.

The length of a rectangle is 16 meters and the width is 3 meters. Find the area.



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What is the sum of the polynomials?(8x^2 - 9y^2 - 4x) + (x^2 - 3y^2 - 7x)

* 7x^2 - 6y^2 + 3x
* 9x^2 - 6y^2 + 3x
* 9x^2 - 12y^2 + 3x
* 9x^2 - 12y^2 - 11x


The sum of the polynomials is 4x² - 12y² - 11x. The correct answer is an option (D) 4x² - 12y² - 11x.

What is a polynomial?

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The polynomials are given as follows:

(8x² - 9y² - 4x) + (x² - 3y² - 7x)

By combining like terms, we can add the polynomials:

(8x² - 9y² - 4x) + (x² - 3y² - 7x)

= 8x² - 4x² - 9y² - 3y² - 4x - 7x

= 4x² - 12y² - 11x

Therefore, the sum of the polynomials is 4x² - 12y² - 11x.

Hence, the correct answer is option (D) 4x² - 12y² - 11x.

Learn more about the polynomial here:




Option D

Step-by-step explanation:

(8x^2-9y^2-4x) +(x^2-3y^2-7x)



The dot plot below shows the hourly rate of some babysitters in a city:A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollars per hour. There are 3 dots above 4 dollars, 2 dots above 5 dollars, 4 dots above 6 dollars, and 1 dot above 7 dollars. The title of the line plot is Babysitting Rates.

Which statement best describes the shape of the data?

It is symmetric and has a peak at $7.00.
It is not symmetric and has a peak at $6.00.
It is a cluster from $1.00 to $7.00 and has gaps.
It is a cluster from $1.00 to $7.00 and has no gaps.



  It is not symmetric and has a peak at $6.00

Step-by-step explanation:

Drawn in text in a vertical fashion, we might show it as ...

  4 | ooo

  5 | oo

  6 | oooo

  7 | o

The data is clearly not symmetric, has a range from 4 to 7, and has a peak at 6. The appropriate description is ...

  It is not symmetric and has a peak at $6.00

How to solve trigonometric functions such as

sin 2x sin x + cos x= 0


Use the double angle identity:

sin(2x) = 2 sin(x) cos(x)

Now rewrite

sin(2x) sin(x) + cos(x) = 0


2 sin²(x) cos(x) + cos(x) = 0

Factor out cos(x) :

cos(x) (2 sin²(x) + 1) = 0

Consider the two cases,

cos(x) = 0   OR   2 sin²(x) + 1 = 0

Solve for cos(x) and sin²(x) :

cos(x) = 0   OR   sin²(x) = -1/2

Squaring a real number always gives a non-negative number, so the second case doesn't offer any real solutions. We're left with

cos(x) = 0

Cosine is zero for odd multiples of π/2, so we have

x = (2n + 1) π/2

where n is any integer.

What is f ( 1/3)? When the function is f(x) =-3x+7



f(1/3) = 6

Step-by-step explanation:

f(x) =-3x+7

Let x = 1/3

f(1/3) =-3*1/3+7

        = -1 +7

       = 6


f(1/3) = 6

Step-by-step explanation:

The function is:

● f(x) = -3x+7

Replace x by 1/3 to khow the value of f(1/3)

● f(1/3) = -3×(1/3) +7 = -1 +7 = 6

which polynomials are in standard form? A. t^4-1 B. -2t^2+3t+4 C. 4t-7 D. None of The Above Choose all answers that apply



B. -2t^2+3t+4

Step-by-step explanation:

The standard form as

ax^2 + bx + c

Option B meets that requirement, even though it has a '-' in front

Final answer:

All the given polynomials, A. t^4-1, B. -2t^2+3t+4 and C. 4t-7 are in standard form since their terms are written in descending order of their degrees.


In mathematical terms, a polynomial is in standard form if its terms are written in descending order of their degree, i.e. the power of the variable. This means the term with the highest power should be listed first, followed by the term with the next highest power, and so on. Let's look at the options:

  • Option A: t^4-1 is in standard form because t^4 is the highest degree term and it is listed first.
  • Option B: -2t^2+3t+4 is also in standard form as the terms are arranged in descending order of degree: 2 (in t^2), 1 (in t) and then 0 (in 4).
  • Option C: 4t-7 is in standard form as well, with the degree of the term 4t being 1 and the degree of -7 being 0.

So, in conclusion, the polynomials in standard form from the provided options are A. t^4-1,  B. -2t^2+3t+4 and C. 4t-7.

Learn more about Standard Form of Polynomial here: