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Nikolay [14]
2 years ago
8

To the nearest tenth, find the perimeter of ABC with vertices A (-2,-2) B (0,5) and C (3,1)

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
5 0

the perimeter will then just be the sum of the distances of A, B and C, namely AB + BC + CA.


\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquadB(\stackrel{x_2}{0}~,~\stackrel{y_2}{5})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\AB=\sqrt{[0-(-2)]^2+[5-(-2)]^2}\implies AB=\sqrt{(0+2)^2+(5+2)^2}\\\\\\AB=\sqrt{4+49}\implies \boxed{AB=\sqrt{53}}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\B(\stackrel{x_2}{0}~,~\stackrel{y_2}{5})\qquad C(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\\\\\\BC=\sqrt{(3-0)^2+(1-5)^2}\implies BC=\sqrt{3^2+(-4)^2}


\bf BC=\sqrt{9+16}\implies \boxed{BC=5}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\C(\stackrel{x_2}{3}~,~\stackrel{y_2}{1})\qquad A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\\\\\\CA=\sqrt{(-2-3)^2+(-2-1)^2}\implies CA=\sqrt{(-5)^2+(-3)^2}\\\\\\CA=\sqrt{25+9}\implies \boxed{CA=\sqrt{34}}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\~\hfill \stackrel{AB+BC+CA}{\approx 18.11}~\hfill

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Answer:

m=1

Step-by-step explanation:

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lukranit [14]
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3 0
2 years ago
How do you solve 58 and 1/3÷6 and 2/3
strojnjashka [21]

Answer:

35/4, or 8 3/4 as a mixed number

Step-by-step explanation:

First, change 58 1/3 into an improper fraction by multiplying the whole number and denominator, then adding the numerator. 58 x 3 equals 174, + 1 equals 175. So, 58 1/3 as an improper fraction is 175/3. Next, change 6 2/3 into an improper fraction. 6 times 3 equals 18, plus 2 equals 20. So, it's 20/3. So, here are your two fractions:

175/3 & 20/3

To divide fractions, I like to use a method called Keep Change Flip. Basically, you keep the first fractions the same, then change the sign. The division sign changes into a multiplication symbol. Now, your equation should look like this: 175/3 x 20/3. Next, flip the fraction from 20/3 into 3/20. This is what your equation should look like now: 175/3 x 3/20. Now you can multiply the fractions together. Before you do so, you can cross reduce to make it easier. What is a number that both 3 and 3 can be divided by? The correct answer is 3. 3/3= 1, so the equation is now 175/1 x 1/20. However, you can continue to cross reduce. You can also divide 175 and 20 by 5, so the equation changes into this: 35/1 x 1/20. Multiply numerator by numerator, denominator by denominator. So, the answer is 35/4, or 8 3/4 as a mixed number. Hope this helped!

5 0
3 years ago
Suppose your boss wants you to obtain a sample to estimate a population mean. Based on previous analyses, you estimate that 49 i
VashaNatasha [74]

Answer:

the minimum sample size n = 11.03

Step-by-step explanation:

Given that:

approximate value of the population standard deviation \sigma = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error = Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}

38 = \dfrac{2.576 \times 49}{\sqrt{n}}

\sqrt{n} = \dfrac{2.576 \times 49}{38}

\sqrt{n} = \dfrac{126.224}{38}

\sqrt{n} = 3.321684211

n= (3.321684211)^2

n ≅ 11.03

Thus; the minimum sample size n = 11.03

5 0
2 years ago
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