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Vlad1618 [11]
3 years ago
14

given that BD is both the median and altitude of triangle ABC, congruence postulate SAS is used to prove that triangle ABC is wh

at type of triangle?

Mathematics
2 answers:
stira [4]3 years ago
7 0

Answer:

Isosceles

Step-by-step explanation:

Consider triangle ABC, BD is the median and the altitude drawn to the side AC. This segment (BD) divide the triangle ABC into two triangles: ABD and CBD.

In these triangles:

  • AD=DC (because BD is the median);
  • ∠ADB=∠CDB=90° (because BD is the altitude);
  • BD is common side.

Thus, by SAS postulate, triangles ABD and CBD are conruent. Congruent triangles have congruent corresponding sides. Hence, AB=CB.

If in triangle ABC, AB=BC, then this triangle is isosceles.

Leno4ka [110]3 years ago
3 0

Answer:

Isosceles (apex)

Step-by-step explanation:

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B. is the answer all it asking you is she correct that she only has 18.25 to play with for the games.


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3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
The box plots show the math scores of students in two different classes. Based on the box plots, which statement is correct?
Allisa [31]

Based on the box plots, the statement which is correct is that: A. The median score of Class A is greater than the median score of Class B.

<h3>What is a box and whisker plot?</h3>

In Mathematics, a box plot is also referred to as box and whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Additionally, the five-number summary of any box plot (box and whisker plot) include the following:

  1. Minimum
  2. First quartile
  3. Median
  4. Third quartile
  5. Maximum

By critically observing the box plot (box and whisker plot) which represent the math scores of students in in two different classes, we can reasonably and logically deduce the following median scores;

Median score of class A = 80

Median score of class B = 75

Therefore, a median score of 80 in Class A is greater than the median score of 75 in Class B.

Read more on box plots here: brainly.com/question/14277132

#SPJ1

6 0
10 months ago
Giving brainliest to correct answer!
lisov135 [29]

Answer:

The answer is 1.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Need help with number 2 please help. Due today!!​
Blababa [14]

Answer:

Radius = 9

Step-by-step explanation:

Circumference = 2πr

2πr = 18 ×3.14

2πr = 56.5

6.28r = 56.5

r = 56.5/6.28

r = 9.04 round off , 9

3 0
3 years ago
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