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Zina [86]
2 years ago
14

Given L(-4, 3) and M(-7, -2), what is the length of segment LM?

Mathematics
1 answer:
kati45 [8]2 years ago
4 0

Answer:

d = \sqrt{34}

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 II</u>

  • Distance Formula: d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Step-by-step explanation:

<u>Step 1: Define</u>

Point L (-4, 3)

Point M (-7, -2)

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>.

  1. Substitute [DF]:                    d = \sqrt{(-7+4)^2+(-2-3)^2}
  2. Add/Subtract:                       d = \sqrt{(-3)^2+(-5)^2}
  3. Exponents:                           d = \sqrt{9+25}
  4. Add:                                      d = \sqrt{34}
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Step-by-step explanation:

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Here's the question. ​
OleMash [197]

Answer:

The value of T₂₀ - T₁₅ is <u>-20</u>.

Step-by-step explanation:

<u>Given</u> :

  • >> If for an A.P, d = -4

<u>To</u><u> </u><u>Find</u> :

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<u>Using Formula</u> :

General term of an A.P.

\star{\small{\underline{\boxed{\sf{\red{ T_n = a  + (n - 1)d}}}}}}

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Firstly finding the A.P of T₂₀ by substituting the values in the formula :

{\dashrightarrow{\pmb{\sf{ T_n = a  + (n - 1)d}}}}

{\dashrightarrow{\sf{ T_{20} = a  + (20 - 1) d}}}

{\dashrightarrow{\sf{ T_{20} = a  + (19)d}}}

{\dashrightarrow{\sf{ T_{20} = a  + 19  \times d}}}

{\dashrightarrow{\sf{ T_{20} = a  + 19d}}}

{\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a  + 19d}}}}}}

Hence, the value of T₂₀ is a + 19d.

\rule{190}1

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

{\dashrightarrow{\pmb{\sf{ T_n = a  + (n - 1)d}}}}

{\dashrightarrow{\sf{ T_{15}= a  + (15 - 1) d}}}

{\dashrightarrow{\sf{ T_{15}= a  + (14) d}}}

{\dashrightarrow{\sf{ T_{15}= a  + 14 \times d}}}

{\dashrightarrow{\sf{ T_{15}= a  + 14d}}}

{\star{\underline{\boxed{\sf \pink{ T_{15}= a  + 14d}}}}}

Hence, the value of T₁₅ is a + 14d

\rule{190}1

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{\dashrightarrow{\pmb{\sf{T_{20} -  T_{15}}}}}

{\dashrightarrow{\sf{(a + 19d) -  (a + 14d)}}}

{\dashrightarrow{\sf{a + 19d -  a  -  14d}}}

{\dashrightarrow{\sf{a - a + 19d -  14d}}}

{\dashrightarrow{\sf{0+ 19d -  14d}}}

{\dashrightarrow{\sf{19d -  14d}}}

{\dashrightarrow{\sf{5 \times  - 4}}}

{\dashrightarrow{\sf{ - 20}}}

{\star \: \underline{\boxed{\sf{\pink{T_{20} -  T_{15} =  - 20}}}}}

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\underline{\rule{220pt}{3.5pt}}

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