MATHEMATICS HIGH SCHOOL

True or false: The rectangular coordinates of a point are unique.

Answers

Answer 1

Answer:

The rectangular coordinates of a point are unique.

The statement is true.

Given, that coordinates of rectangle.

Properties of rectangle:

1) Opposite sides of the rectangle are equal.

2) Side length of the rectangle with rectangular coordinates can be obtained by distance formula.

Distance formula :

$D = √((y_2 - y_1)^2 + (x_2 - x_1)^2)$

Where,

( $x_1 , y_1$ ) = Coordinates of rectangle .

$(x_2, y_2)$ = Coordinates of rectangle .

Four coordinates of rectangle will be different and unique thus forming a perfect rectangle satisfying all the properties.

Therefore the statement is true.

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Answer 2

Answer: The answer is true Hope the answer is correct

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The hardcover version of a book weighs twice as much as its paperback version. The hardcover book and the paperback together weigh 4.2 pounds. Which system of equations can be used to find h, the weight of the hardcover book, and p, the weight of the paperback?

Answers

If the weight of hardcover version is double the weight of paperback version then weight of hardcover version is 2.8 pounds and the weight of paperback version is 1.4 pounds.

What is equation?

An equation is a relationship between variables in equal to form. It is evaluated to find the values of variables.

How to solve an equation?

The weight of hardcover book is h

The weight of paperback version is p.

According to question:

h=2p (weight of hardcover version is double the weight of paperback version)

h+ p= 4.2 (weight of hardcover version and weight of paperback version is equal to 4.2 pounds)

Put the value of h=2p in h+ p=4.2

2p+p=4.2

3p=4.2

p=1.4

Put the value of p=1.4 in h=2p to get the value of h

h=2p

=2*1.4

=2.8

Hence the weight of hardcover version is 2.8 pounds and the weight of paperback version is 1.4 pounds.

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Answer:

Step-by-step explanation:

on edge 2023

What is the answer to factorise 3D+12

Answers

3D + 12
3(D) + 3(4)
3(D + 4)

A manufacturer makes ball bearings out of molten steel. It takes 5.24 cubic centimeters of molten steel to make ? ball bearings that each have a diameter of 1 centimeter.

Answers

So we want to know how much ball bearings can be made with 5.24 cm^3 if one ball bearing has a diameter of 1 cm. We know that radius r=d/2=0.5cm So the volume V of one ball bearing is: V=(4/3)*pi*r^3 so V=(4/3)*3.14*(0.5)^3cm^3=0.524cm^3. Now we simply divide the volume of steel by the volume of the ball bearing: 5.24/0.524=10. So we can make 10 ball bearings from 5.24 cm^3 of steel

Answer: 10 ball bearings

Plato is annoying

Step-by-step explanation:

Ms. Howard wrote a test. Part A had true/false questions, each worth points. Part B had multiple choice questions, each worth points. She made the number of points for Part A equal the number of points for Part B. It was the least number of points for which this was possible.

Answers

Full question attached

Answer and explanation:

Since x = number of true or false questions correct

And y = number of multiple choice questions correct

And each question for x =2 points

each question for y=3 points

since she then needs a total score of more than 93 to pass, we add up total correct questions and

Inequality equation = 2x +3y >93

Final answer:

To find the least number of points for which the number of points for Part A is equal to the number of points for Part B, we need to find the least common multiple (LCM) of the values of points for true/false questions and multiple choice questions.

Explanation:

To find the least number of points for which the number of points for Part A is equal to the number of points for Part B, we need to find a common multiple of the values of points for true/false questions and multiple choice questions. Let's assume the number of points for true/false questions is x and the number of points for multiple choice questions is y. We need to find the least common multiple (LCM) of x and y. Once we find the LCM, that will be the minimum number of points for which the number of points in Part A is equal to the number of points in Part B.

For example, if the number of points for true/false questions is 4 and the number of points for multiple choice questions is 6, we can find the LCM as follows:

List the multiples of 4: 4, 8, 12, 16, 20, 24, ...
List the multiples of 6: 6, 12, 18, 24, 30, ...
Find the smallest number that appears in both lists: 12

Therefore, the least number of points for which the number of points in Part A is equal to the number of points in Part B is 12.