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xeze [42]
2 years ago
13

Based on the side lengths given (a, b, and o, which triangles are right triangles?​

Mathematics
1 answer:
Cloud [144]2 years ago
6 0

Answer:

2 & 3

Step-by-step explanation:

Pythagorean Theorem is a^2+b^2=c^2.

If the values given in each option satisfy the theorem, the sides will make a right triangle.

<h3>For Option One:</h3>

4^2+6^2=8^2\\=> 4^2=16\\=> 6^2=36\\=>8^2 =64\\16+36=64\\\boxed{52\neq 64}

The sides would not make a right triangle.

<h3>For Option Two:</h3>

6^2+8^2=10^2\\=> 6^2 = 36\\=> 8^2=64\\=> 10^2=100\\36+64=100\\\boxed{100=100}

The sides would make a right triangle.

<h3>For Option Three:</h3>

5^2+6^2=\sqrt{61}^2\\ => 5^2=25\\=>6^2=36\\=>\sqrt{61}^2=61\\ 25+36=61\\\boxed {61=61}

The sides would make a right triangle.

<h3>For Option Four:</h3>

6^2+9^2=12^2\\=> 6^2=36\\=>9^2=81\\=>12^2=144\\36+81=144\\\boxed{117\neq 144}

The sides would not make a right triangle.

The correct answer should be options two and three.

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Mama L [17]

Answer:

-20 < 4 - 2x (subtract 4 from both sides)

-24 < -2x (divide each side by -2)

12> x  (when you divide by a negative number, the inequality flips)

x< 12 ( I always put it so x is first)

so the answer is C

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2 years ago
Write A expression for increased by 23
Akimi4 [234]

Answer:

5+23

Step-by-step explanation:

increased by is another word for add

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3 years ago
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Which of the following is the statement of the triangle inequality theorem?
kupik [55]

we know that

<u>The triangle inequality theorem</u> states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Let

a,b,c------> the length sides of a triangle

The theorem states that three conditions must be met

<u>case 1)</u>

a+b > c

<u>case 2)</u>

a+c > b

<u>case3)</u>

c+b > a

therefore

<u>the answer is the option</u>

B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

5 0
3 years ago
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A survey is being conducted in a county where 62% of the voters are Democrats and 38% are Republican. (a) What is the probabilit
Inessa05 [86]

Answer:

0.3844 = 38.44% probability that two independently surveyed voters would both be Democrats

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either the voter is a Democrat, or he is not. The probability of the voter being a Democrat is independent of other voters. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

62% of the voters are Democrats

This means that p = 0.62

(a) What is the probability that two independently surveyed voters would both be Democrats?

This is P(X = 2) when n = 2. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{2,2}.(0.62)^{2}.(0.38)^{0} = 0.3844

0.3844 = 38.44% probability that two independently surveyed voters would both be Democrats

3 0
3 years ago
What is the slope of a line that is perpendicular to the
alexgriva [62]

Answer:

The slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

Step-by-step explanation:

From the line equation, let us take two points

  • (0, 2)
  • (4, 1)

Finding the slope between two points

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)

m=\frac{1-2}{4-0}

m=-\frac{1}{4}

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be:

-\frac{1}{-\frac{1}{4}}=4

Thus, the slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

5 0
3 years ago
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