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LiRa [457]
3 years ago
11

find the area of an equilateral triangle whose side measures 7 units. find the area to the nearest tenth of square unit

Mathematics
1 answer:
Eddi Din [679]3 years ago
8 0

\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}~~
\begin{cases}
s=side's~length\\[-0.5em]
\hrulefill\\
s=7
\end{cases}\implies A=\cfrac{7^2\sqrt{3}}{4}\implies A=\cfrac{49\sqrt{3}}{4}
\\\\\\
A\approx 21.21762239271874684571\implies A = \stackrel{rounded~up}{21.2}

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A number is called squarefree if it is not divisible by the square of a positive integer greater than one. find the number of sq
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Count the number of positive integers less than 100 that do not contain any perfect square factors greater than 1.

Possible perfect squares are the squares of integers 2-9.
In fact, only squares of primes need be considered, since for example, 6^2=36 actually contains factors 2^2 and 3^2.
Tabulate the number (in [ ])of integers containing factors of 
2^2=4: 4,8,12,16,...96 [24]
3^2=9: 9,18,....99  [11] 
5^2=25: 25,50,75  [3]
7^2=49:  49,98 [2]

So the total number of integers from 1 to 99
N=24+11+3+2=40
=>
Number of positive square-free integers below 100 = 99-40 = 59
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3 years ago
Find the discriminant and determine the nature of the roots to the quadratic equation
Katen [24]
№17
x^{2} +6x-7=0 \\ D=6 ^{2} -4*(-7)=36+28=64=8 ^{2}  \\  \\  x_{1} = \frac{-6+8}{2} =1 \\  \\  x_{2} = \frac{-6-8}{2} =-7
Answer: x₁ = 1
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№18
2 x^{2} -3x+4=3 \\ 2 x^{2} -3x+4-3=0 \\ 2 x^{2} -3x+1=0 \\  \\ D= -3 ^{2} -4*2=9-8=1 \\  \\  x_{1} = \frac{3+1}{2*2} = \frac{4}{4} =1 \\  \\  x_{2} = \frac{3-1}{2*2} = \frac{2}{4} =0.5
Answer: x₁ = 1
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№19
2 x^{2} -4x-5=0 \\  D=-4 ^{2} -4*2*(-5)=16+40=56 \\  \\  x_{1}= \frac{4+ \sqrt{56} }{2*2}  = \frac{4}{4} + \sqrt{ \frac{56}{16} } =1+ \sqrt{3.5}  \\  \\  x_{2} = \frac{4- \sqrt{56} }{2*2} = \frac{4}{4} -  \sqrt{ \frac{56}{16} } =1- \sqrt{3.5} 

Answer: x₁ = 1 + √3.5
               x₂ = 1 - √3.5

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4 years ago
Find the equation of the line that has a slope of 14 and passes through the point (-3, 12)
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Answer:

Step-by-step explanation:

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