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MakcuM [25]
3 years ago
9

What are the coordinates of the point that is one half the distance between A(−3, −5) and B(2, 7)?

Mathematics
1 answer:
Olenka [21]3 years ago
3 0

Answer:

(\frac{-1}{2},1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Midpoint Formula: (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Step-by-step explanation:

<u>Step 1: Define</u>

A (-3, -5)

B (2, 7)

<u>Step 2: Find midpoint</u>

  1. Substitute:                    (\frac{-3+2}{2},\frac{-5+7}{2})
  2. Add:                              (\frac{-1}{2},\frac{2}{2})
  3. Divide:                          (\frac{-1}{2},1)
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Common difference d = 36-35 = 1

Nth term of arithmetic sequence is:

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n_{th}= 35+(n-1)(1)

n_{th} = 34+n

To find the 100th term, substitute n = 100

n_{100} = 34 +100

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Correct option is B

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A mother has two children whose ages differ by 5 years. The sum of the squares of their ages is 97. The square of the​ mother's
svetoff [14.1K]

Answer:

41 years old.

Step-by-step explanation:

Let x represent age of younger child.

We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be x+5.

The sum of the squares of their ages is 97. We can represent this information in an equation as:

x^2+(x+5)^2=97

Let us solve for x.

x^2+x^2+10x+25=97

2x^2+10x+25-97=0

2x^2+10x-72=0

Divide both sides by 2:

x^2+5x-36=0

x^2+9x-4x-36=0

x(x+9)-4(x+9)=0

(x+9)(x-4)=0

(x+9)=0 ; (x-4)=0

x=-9 ; x=4

Since age cannot be negative, therefore, age of younger child is 4 years.

Age of older child would be x+5\Rightarrow4+5=9

Therefore, the age of older child would be 9 years.

We have been given that the square of the​ mother's age can be found by writing the squares of the​ children's ages one after the other as a​ four-digit number.

Square of 4: 4^2=16

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Square of mother's age: 1681

To find mother's age, we need to take positive square root of 1681 as:

\sqrt{1681}=41

Therefore, the mother is 41 years old.

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