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Anton
11 days ago
6

do you agree that the equation (x-4)²=9 can be solved both by factoring and extracting square roots? ​

Mathematics
1 answer:
Zina [3.9K]11 days ago
7 0

Given parameters:

  Equation:

          (x-4)²=9

Problem: Solve the equation by both factoring and extracting the square root.

Solution:

    Starting equation:

                  (x-4)²=9

         Subtracting 9 from both sides brings us to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  This fits the concept of the difference of squares;

          x² - y² = (x + y)(x-y)

                     

Let x  = x-4 and y = -3

  Then input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 1) = 0

S thus,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

<pBy extracting the square roots;

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; however, this is not the sole solution

Thus, direct extraction of the square root is not the method for complete solutions.

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Adam can earn money recycling aluminium cans .each can weighs 15g and he can get paid 50p per kg . If Adam earns £15 , how many
Leona [4166]

There are 0.015 kilograms in 15 grams. Since each can weighs 0.015 kg and the payment rate is 50p per kilogram, 0.015 multiplied by 66 amounts to 1 kilogram! Therefore, 66 cans are needed to generate one kilogram. As a result, earning £15 would mean that with 2 kg equating to one dollar, then 15 multiplied by 2 equals 30. Consequently, 66 times 30 gives 1980!

66 relates to each kilogram, and 30 indicates how many 50p are required for one dollar!

Thus, to obtain £15, Adam has to recycle a total of 1980 cans!


7 0
10 days ago
True or False: Like the edges of a filled-in area, the endpoints of a polygon do not need to conform to snap points.
PIT_PIT [3919]

Answer:

The response is "False."

Explanation:

In geometry, an area refers to the space that an object occupies. A filled area consists of lines that connect to create an "edge."

These connecting lines help define the shape or area of the object and are known as "snap points." Keep in mind that "polygons" are made up of line segments that connect at their endpoints to form a closed shape. Consequently, it must adhere to "snap points."

This clarifies the response.

8 0
11 days ago
Suppose your parents are traveling on a work-related trip for a whole week. They left you P10,000 as allowance for the week to b
zzz [4022]

Answer:

This is how the money should be divided:

Each of my two younger siblings receives P3,000.

I will take P4,000.

The reasoning for this allocation stems from the principle that the eldest and youngest siblings should not receive equal portions when dividing assets.

Step-by-step explanation:

This division approach is the only sensible method to distribute P10,000 among myself and my younger siblings while ensuring no fractions are involved, maintaining whole peso amounts. Any other method would result in leftover change.

8 0
2 days ago
Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?
PIT_PIT [3919]

Answer:

A scale transformation that contracts and is subsequently followed by a reflection.

Step-by-step explanation:

A contraction with a scale factor less than 1, followed by a reflection, constitutes the combination of similarity transformations that maps polygon ABCD to polygon A'B'C'D.

4 0
10 days ago
Read 2 more answers
Angie baked 100 cookies and 20 brownies. She wants to  split them into equal groups  for the big sale. Each group must have the
zzz [4022]
Avoid repeating the question as it can be perplexing.

Given 100 cookies and 20 brownies,
What is the highest number you can divide them equally by?

To find the greatest common factor,
Factor them:
100 = 2*2*5*5
20 = 2*2*5
Thus, the greatest common factor, which is shared between them, is 2*2*5 or 20.

Calculating further, 100/20=5
20/20=1

This means there are 20 groups, each containing 5 cookies and 1 brownie.


20 groups
7 0
2 days ago
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