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Andrej [43]
2 years ago
11

Can someone please help me with this ?

Mathematics
1 answer:
serg [7]2 years ago
8 0

Answer:

Area = 25 cm²

Diagonal = 10.6cm

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What is the missing reason in the proof? (Reason 9)
den301095 [7]

Answer:

transitive property

Step-by-step explanation:

Generally proofs flow naturally from one step to the next.  Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.

From statement 8, note that 90^{o}=m\angle{ABD}

For statement 9, the proof asserts that m\angle{ABC}=m\angle{ABD}

What changed between line 8 and 9?  The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.

So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?

Recall from statement 3, that m\angle{ABC}=90^{o}.

The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).


Recall that the transitive property states:

\text{If }a=b\text{ and }b=c, \text{then }a=c

There are three parts,

1. the first part needs a=b

2. the second part needs b=c

3. the third part produces a=c

Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.

Statement 8 is like the second part, and statement 9 is like the third part.

Replacing "a" with m\angle{ABC}, replacing "b" with 90^{o}, and replacing "c" with m\angle{ABD}, we can update the transitive property and see how it applies to our situation:

Original transitive property:  \text{If }a=b\text{ and }b=c, \text{then }a=c

Updated transitive property:  \text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}

In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true.  The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.

7 0
1 year ago
A circular cardboard piece is needed for the base of a volcano model. The volcano is 46 centimeters tall and has a volume of 800
Alenkinab [10]
For this case we can model the problem as a cylinder.
 The volume of a cylinder is given by:
 V = Ab * h

 Where,
 Ab: base area
 h: cylinder height
 Substituting values in the equation we have:
 800 = Ab * 46

 From here, we can clear the area of the base
 Answer:
 
An equation that can be used to find the area of the circular base is:
 
800 = Ab * 46
7 0
3 years ago
Read 2 more answers
Which statement describes the expression 9(8 + 25)?
Norma-Jean [14]
2 because you do what is in parenthesis first :)
3 0
2 years ago
Read 2 more answers
What is the area of this tile?
8_murik_8 [283]

Answer:

The area is 480 inches

10 × 8 = 80

80 × 6 = 480

8 0
3 years ago
Find the following dates in the units given:
11Alexandr11 [23.1K]

Answer and step-by-step explanation:

a.  4 litres in 5 minutes (litres per minute)

4 litres per 5 minutes means 4/5 litres per 1 min = 0.8 litres per minutes

b. 12 litres in 45 minutes = 12/3 litres in 45/3 minutes = 4 litres per 15 minutes

60 minutes = 4*15 minutes

4 * 4 = 16 litres per hour

c. 800 kilowatt hours in 2 months

1 year = 12 months = 2*6 months

kilowatt per year = 800 * 6 = 4800 kilowatt per year

Hope this helped :3

3 0
3 years ago
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