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2 years ago

Given: FB ║ CG ∠BFE and ∠C are supplementary. Prove CA ║ FE

Mathematics

1 answer:

Alina [70]2 years ago

5 0

Answer:

Step-by-step explanation:

1) $FB \parallel CG$ , $\angle BFE$ and $\angle C$ are supplementary (given)

2) $\angle ABF \cong \angle C$ (corresponding angles theorem)

3) $\angle BFE$ and $\angle ABF$ are supplementary (supplements of congruent angles are congruent)

4) $CA \parallel FE$ (converse of the same-side interior angles theorem)

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For each statement, write what would be assumed and what would be proven in a proof by contrapositive of the statement. Then wri

Anna007 [38]

Answer:

Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.

Proof by Contrapositive:

Assumed statement: Suppose that integers x and y do not have opposite parity.

Proven Statement: x and y are not a pair of consecutive integers.

Proof -

x = 2u₁ , y = 2u₂

Then

(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)

If y = 2u₁ + 1

Not possible

⇒x and y are not a pair of consecutive integers.

Hence proved.

Proof by Contradiction:

Assumed statement: Suppose x and y are not a pair of consecutive integers.

Proven Statement: Suppose x and y do not have opposite parity.

Proof -

If x and y are not a pair of consecutive integers.

⇒ either x and y are odd or even

If x and y are odd

⇒x and y have same parity

Contradiction

If x and y are even

⇒x and y have same parity

Contradiction

(b)

Proof by Contrapositive:

Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)

Proven Statement: n² is not odd (i.e n² is even)

Proof -

Let n is even

⇒n = 2m

⇒n² = (2m)² = 4m²

⇒n² is even

Hence proved.

Proof by Contradiction:

Assumed statement: Let n be an integer such that n² be odd.

Proven Statement: suppose that n is not odd (i.e n is even)

Proof -

Let n² is odd

⇒n² is even

⇒n² = 2m

⇒2 | n²

⇒2 | n

⇒n = 2x

⇒ n is even

Contradiction

8 0

3 years ago

The graph of g(x) = f(x + 2) + 3 is the graph of y = f(x) shifted

vovangra [49]

Answer:

The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?

The vertex of the graph of g is 1.5 units to the left of

the vertex of the graph of f.

The y-intercept of the graph of g is 1.5 units above the

y-intercept of the graph of f.

The graph of g is a reflection of the graph of f across

the y-axis.

The graph of g is a reflection of the graph of f across

the x-axis.

Step-by-step explanation:

8 0

2 years ago

You rent an apartment that costs $1500 per month during the first year, but the rent

belka [17]

<h3>Answer:</h3>

$\begin{cases}a_1 = 1500\\a_n = 140+a_{n-1}\end{cases}$

==============================

Explanation:

$a_1 = 1500$ means the first term is 1500, ie this is the first rent value.

To get the next term, we add on $140

$a_2 = 140+a_1 = 140+1500 = 1640$

and

$a_3= 140+a_2= 140+1640 = 1780$

and so on.

In general, the nth term $a_n$ is found by adding 140 to the term just before it $a_{n-1}$

So that's where $a_n = 140+a_{n-1}$ comes from.

5 0

2 years ago

If you know please help me

MrRa [10]

Average rate of change of the function $=\frac{75}{2}$

Solution:

Given function: $f(x)=5(2)^{x}$ from x = 1 to x = 5

Substitute x = 1 and x = 5 in f(x).

$f(1)=5(2)^{1}=10$

$f(5)=5(2)^{5}=160$

Let us find the average rate of change of the function.

Average rate of change

$$=\frac{f(b)-f(a)}{b-a}$

Here a = 1 and b = 5.

$$=\frac{f(5)-f(1)}{5-1}$

Substitute f(5) and f(1).

$$=\frac{160-10}{4}$

$$=\frac{150}{4}$

$$=\frac{75}{2}$

Average rate of change of the function $=\frac{75}{2}$

4 0

4 years ago

Tyler can swim 1/2 Mile in 1/3 hour at a constant speed how fast is Tyler swim in miles per hour

Gemiola [76]

Answer:

It’s 3/2 mph

Step-by-step explanation:

8 0

3 years ago