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tatiyna
3 years ago
11

What estimate can you make for 2/3 and 1/6?

Mathematics
2 answers:
Leona [35]3 years ago
8 0
2/3= About 66% give or take a few decimals
1/6=About 16% also give or take a few decimals
OverLord2011 [107]3 years ago
3 0
The answer should be 5/6

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An equation in the form ax2+bx+c=0 is solved by the quadratic formula. The solution to the equation is shown below.x=−7±√ "572"
jolli1 [7]

Answer:

B: a = 1, b= 7, c = -2

Step-by-step explanation:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0

Given:

x=\dfrac{-7\pm\sqrt{57}}{2}

Comparing the terms of the given x-value with those of the quadratic formula:

\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}=\dfrac{-7\pm\sqrt{57}}{2}

Therefore:

  • 2a=2 \implies a=1
  • b = 7
  • b^2-4ac=57

Using the found values of a and b to solve for c:

\implies b^2-4ac=57

\implies (7)^2-4(1)c=57

\implies 49-4c=57

\implies -4c=57-49

\implies -4c=8

\implies c=-2

In summary:   a = 1,  b = 7,  c = -2

\implies x^2+7x-2=0

Therefore, <u>option B</u> is the correct solution.

5 0
2 years ago
Read 2 more answers
Given that 'n' is a natural number. Prove that the equation below is true using mathematical induction.
LenaWriter [7]

<h3>To ProvE :- </h3>

  • 1 + 3 + 5 + ..... + (2n - 1) = n²

<u>Method</u><u> </u><u>:</u><u>-</u>

If P(n) is a statement such that ,

  1. P(n) is true for n = 1
  2. P(n) is true for n = k + 1 , when it's true for n = k ( k is a natural number ) , then the statement is true for all natural numbers .

\sf\to \textsf{ Let P(n) :  1 + 3 + 5 + $\dots$ +(2n-1) = n$^{\sf 2}$ }

Step 1 : <u>Put </u><u>n </u><u>=</u><u> </u><u>1</u><u> </u><u>:</u><u>-</u><u> </u>

\sf\longrightarrow LHS = \boxed{\sf 1 } \\

\sf\longrightarrow RHS = n^2 = 1^2 = \boxed{\sf 1 }

Step 2 : <u>Assume </u><u>that </u><u>P(</u><u>n)</u><u> </u><u>is </u><u>true </u><u>for </u><u>n </u><u>=</u><u> </u><u>k </u><u>:</u><u>-</u>

\sf\longrightarrow 1 + 3 + 5 + \dots + (2k - 1 ) = k^2

  • Add (2k +1) to both sides .

\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1)=k^2+(2k+1)

  • RHS is in the form of ( a + b)² = a²+b²+2ab .

\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1)= (k +1)^2

  • Adding and subtracting 1 to LHS .

\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1) + 1 -1  = (k +1)^2 \\

\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+2) - 1 = (k +1)^2

  • Take out 2 as common .

\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+\{2(k+1)-1\}= (k +1)^2

  • P(n) is true for n = k + 1 .

Hence by the principal of Mathematical Induction we can say that P(n) is true for all natural numbers 'n' .

<em>*</em><em>*</em><em>Edits</em><em> are</em><em> welcomed</em><em>*</em><em>*</em>

8 0
2 years ago
Read 2 more answers
Ten people reported the number of hours they worked last week.
taurus [48]
First arrange them in ascending order:-

17 20 24 25 30 32 35 38 40 42
The median  = mean of middle 2 numbers = (30+32)/2 = 31
Lower quartile = 24 and upper quartile =  38
Inter quartile range = 38 - 24  = 14

Its the first choice.
4 0
3 years ago
Read 2 more answers
If anyone knows the answer to this question please let me know! thanks
Bond [772]

Answer:

D. 10 units

Step-by-step explanation:

Use pythagorean theorem

a^2 + b^2 = c^2\\6^2+8^2= c^2

36+64=c^2\\100=c^2\\\\\\sqrt{100}  =\sqrt{x^2} \\10=c

7 0
3 years ago
PLS HELP with this problem !!!
Sophie [7]

Answer:

god

Step-by-step explanation:

5 0
3 years ago
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