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Sophie [7]
2 years ago
8

A conjecture and the two-column proof used to prove the conjecture are shown. Given: segment A B is congruent to segment B D, se

gment B D is congruent to segment C E, and segment C E is congruent to segment A C. Prove: triangle A B C is an isosceles triangle. Segment A D with endpoints D and A moving from left to right. Segment A D is diagonally down to the left from point A. B is the midpoint of segment A D. Segment A E shares endpoint at point A with segment A D. Segment A E is diagonally down to the right from point A. C is the midpoint of segment A E. Segment B C is horizontal between segment A D and segment A E. Drag an expression or phrase to each box to complete the proof. Statement Reason 1. AB¯¯¯¯¯≅BD¯¯¯¯¯ Given 2. BD¯¯¯¯¯≅CE¯¯¯¯¯ Given 3. Transitive Property of Congruence 4. Given 5. AB¯¯¯¯¯≅AC¯¯¯¯¯ 6. △ABC is an isosceles triangle.

Mathematics
2 answers:
rusak2 [61]2 years ago
5 0

Answer:

3.Transitive Property Of Congruence

daser333 [38]2 years ago
4 0

Answer:

Step-by-step explanation:

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The price that a company charged for a basketball hoop is given by the equation 50 - 5x^2 where x is the number of hoops that ar
DiKsa [7]

Answer: The correct option is first, the number of basketball hoops did the company previously produce to make the same profit is 1.3 million hoops.

Explanation:

Let the number of basketball hoops did the company previously produce to make the same profit be x.

Total Revenue = Price * Quantity

The total revenue in million dollars is,

\text{Total Revenue}=(50-5x^2)x

\text{Total Revenue}=50x-5x^3

The total cost in million dollars is,

Total Cost = One unit cost * Quantity

\text{Total Cost}=30x

Profit = Total Revenue - Total Cost

\text{Profit}=50x-5x^3-30x

The profit is 15 million.

15=20x-5x^3

5x^3-20x+15=0\\x^2-4x+3=0\\(x-1)(x^2+x-3)=0

The value of x is 1 and \frac{-1\pm \sqrt{13}}{2}.

The production is always positive therefore the value of x either 1 or 1.3. Since 1 million is not available in the options therefore the the correct optin is 1.3 million hoops.

4 0
2 years ago
Read 2 more answers
Rate at which risk of down syndrome is changing is approximated by function r(x) = 0.004641x2 − 0.3012x + 4.9 (20 ≤ x ≤ 45) wher
romanna [79]
The rate of change of the risk of down syndrome (in percentage of births per year) is
r(x) = 0.004641x² - 0.3012x + 4.9,   20≤ x ≤ 45
where
x = maternal age at delivery.

The function giving risk as a percentage of births when maternal age is x is the integral of r(x). That is,
f(x) = 0.001547x³ - 0.1506x² +4.9x + c

When x = 30, f = 0.14%. Therefore
0.001547(30³) - 0.1506(30²) + 4.9(30) + c = 0.14 
41.769 - 135.54 + 147 + c = 0.14
c = -53.089

Answer:
f(x) = 0.001547x³ - 0.1506x² + 4.9x - 53.089,   20 ≤ x ≤ 45

The function is graphed as shown below.

7 0
2 years ago
Select the correct answer. What is the greatest common factor of this expression? 12m + 18m2 A. 6m B. 6 C. 2m D. 2
ohaa [14]
A. No matter what M is, it will correspond to the squared version of 18m
7 0
2 years ago
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A school principal has to choose randomly among the six best students in each grade to be the school captain every month. For th
Viefleur [7K]

Since there are 6 students out of which one needs to be selected, the principal chose two die on which there are six numbers each numbered from 1 , 2, 3, 4, 5, 6.

Since there are two dice, the total possible outcome is 36.

Hence, the probability of getting one number each is 1/36

Hence, the principal used a fair method because each result is an equally likely possible outcome.

Option B is correct.

5 0
2 years ago
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The multiplication law is potentially helpful when we are interested in computing the probability of a. mutually exclusive event
Korvikt [17]

Answer:

b )  the intersection of two events

Step-by-step explanation:

Gary and Steve are both hosting . There are 50 buttons total, 15 buttons are blue and 27 buttons are red. Gary puts all of the buttons into a bag. Steve and Gary both want to wear red buttons.What is the probability ? To solve this problem, you need to understand the Multiplication Rule of Probability.This probability  means to find the probability of the intersection of two events, multiply the two probabilities.

Probability of two events occurring that is called intersection of two events. There are two different set of events , called independent and dependent events.

Independent events  event is not affected by a previous event.

A dependent event is when one event influences the outcome of another event . To find the intersection of two events, whether they are independent or dependent, multiply the two probabilities together.

3 0
2 years ago
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