If anyone understands proofs, could you walk me through this? I really don't get them. Any help would be appreciated!

Answers

Answer 1

Answer: Just a note before I get started: The specific theorem/postulate/definition will be given in quotes. Everything else will be explanation of why we will use itLets get started :D
b. We can use the "definition of a square" because it states that it a square, every side is congruent. We can use this because we already know that the shape is a square due to a.

c. We can use "definition of a square" again for the same reason as b.

e. We know that the hypotenuses (hypoteni?) of both triangles are congruent, and they both share a side, so we can use the "Hypotenuse Leg Theorem"

f. Because we know that the triangles are congruent, we can use the "Base Angle Theorem" to say that the angles are congruent.

h. Because they share the same side, we can use the "Linear Pair Theorem" to say that they are supplementary angles

Hope this helped! Sorry if its a bit late. :D

Answer 2

Answer: In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms.

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Lisa is seven times as old as her brother. She will be four times as old as her brother in three years. Represent the above situation in mathematical form.

Answers

Answer:

Let B = the brothers age now

Let L = Lisa's age now

Then today:

L = 7B

And three years from now, Lisa's current age plus 3 equals 4 times the brothers age plus 3 represented by the following formula

L+3 = 4(B+3)

Now we can substitute the value of L in the first formula for L in the second formula

7B + 3 = 4(B+3)

So the answer is C

Step-by-step explanation:

Find 4 consecutive even integers whose sum is 156?

Answers

x+(x+1)+(x+2)+(x+3)=156
4x+6=156
4x=150
x=37.5 (not an integer)
If x=37 you get 37+38+39+40=154 and if x=38 you get 38+39+40+41=158[/tex]

Answer: The integers are 36, 38, 40, and 42

Step-by-step explanation:

156/2=78

Find even integers by dividing that by two. 39.

So the two middle integers are 38 and 40.

You can go from there.

Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other fundamental identities.

Answers

1 ) 1 + tan² t = sec² t
1 + sin² t / cos² t = 1 / cos² t
( This is because we know that tan x = sin x / cos x and csc x = 1 / cos x )
Then we will multiply both sides of an equation by cos² t
1 * cos² t + sin² t * cos² t / cos² t = 1
cos² t + sin² t = 1 ( and we know that it is the identity - true )
2 ) 1 + cot ² t = csc² t
1 + cos² t / sin² t = 1 / sin² t / · sin² t ( multiply both sides by sin² t )
sin² t + cos² t = 1 ( true )

Multiply: (6x - 1)(6x +1)

Answers

i’m not positive but i think it’s 36x^2 -1

Answer:

36x^2 -1

Step-by-step explanation:

6x times 6x= 36x^2

6x times 1= 6x

-1 times 6x= -6x

-1 times 1= -1

so, ...

36x^2+6x+(-6x)+(-1) = 36x^2 -1

Miguel ordered a party tray of sandwiches for a birthday party. during the party, the guests left of the sandwiches. the next day, miguel shared the leftover sandwiches with his family who ate of the remaining sandwiches. which fraction represents the portion of the entire tray miguel's family ate?