MATHEMATICS COLLEGE

Which of the following must be given to prove that ΔABC is similar to ΔDBA?a. Segment AD is an altitude of ΔABC.
b. Segment CB is a hypotenuse.
c. Segment CA is shorter than segment BA.
d. Angle C is congruent to itself.

Answers

Answer 1

Answer:

Answer:

The correct answer is option A.

Step-by-step explanation:

For the given triangles to be similar the segment AD must be an altitude of ΔABC.

We can provide a theorem for the same:

If we draw an altitude from the right angle of any right triangle, then the two triangles formed are similar to the original triangle.

Also all the three triangles are similar to each other.

Like here, in the triangle ABC, we draw an altitude from A to the side BC, thus forming 2 triangles; ΔDBA and ΔDAC. These both will be similar to ΔABC.

So, by the theorem it is proven that ΔABC is similar to ΔDBA.

Therefore, option A is correct.

Answer 2

Answer: this answer is a (A) segment AD is an altitude at angle ABC

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Answers

Answer:

3 1/2

Step-by-step explanation:

|-7| - |-3 1/2| = 3 1/2

The Little League baseball club in town holds open registration. During one weekend they registered 432 baseball players. If 12 players are assigned to a team, then how many teams will the league need to form?

Answers

432(divided by) 12
36 teams

Final answer:

To form teams, divide the total number of players by the number of players per team. In this case, 36 teams are needed.

Explanation:

To find out how many teams will be formed, we divide the total number of players by the number of players assigned to a team. In this case, there are 432 players and 12 players per team. So, we divide 432 by 12:

Number of teams = 432 ÷ 12 = 36 teams

Therefore, the league will need to form 36 teams to accommodate all the players.

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Select the correct answer. Solve the following equation by completing the square. 1/4x^2 + x + 1/4 = 0

Answers

Answer:

1/4x^2 + x =-1/4

=−2±√3

Answer:

1/4x^2 + x =-1/4

=−2±√3

----------------

Step-by-step explanation:

Sum of series 1 +1/3 +1/3².... is?

Answers

Answer:

The sum of the series is 3/2

Step-by-step explanation:

Given

1 + 1/3 + 1/3^2 + ....

Required

The sum of the series

This implies that we calculate the sum to infinity.

We have:

$a = 1$ -- The first term

First, calculate the common ratio (r)

$r = (1)/(3^2) / (1)/(3)$

Change to product

$r = (1)/(3^2) * (3)/(1)$

Solve

$r = (1)/(3)$

The sum of the series is then calculated as:

$S_(\infty) = (a)/(1 - r)$

$S_(\infty) = (1)/(1 - 1/3)$

Solve the denominator

$S_(\infty) = (1)/(2/3)$

Express as product

$S_(\infty) = 1 * (3)/(2)$

$S_(\infty) = (3)/(2)$

Solve the inequality of 6(x-7)>-6

Answers

Answer:

x> 6

Step-by-step explanation:

6(x-7)>-6

Divide by 6

6(x-7)/6>-6/6

x-7 > -1

Add 7 to each side

x-7+7 > -1+7

x> 6

Answer:

Step-by-step explanation:

6 (x-7)>-6

6x - 42 >-6

6x >-6 +42

6x>36

x>36:6

x>6

When a sample size is greater than 10, the standard deviation of the sample is an accurate predictor of the population standard deviation. A. True B. False