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Naddik [55]
3 years ago
15

Which theorem or postulate proves that △ABC and △DEF are similar?

Mathematics
2 answers:
GaryK [48]3 years ago
5 0
For similarity measures of corresponding angles should be equal so we would use AA similarity postulate
Svetlanka [38]3 years ago
4 0

Answer:

AA similarity postulate holds here.

Step-by-step explanation:

As in right angled ΔCAB and ΔFDE we are given two angles each and with the help of property that in a triangle the sum of all the angles of a triangle is equal to 180° w can find out the measure of third angle.

In ΔCAB we have:

∠A=90° and ∠B=37°.

The measure of third angle i.e. ∠C will be:

∠A+∠B+∠C=180°

90°+37°+∠C=180°

∠C=180°-127°

⇒  m∠C=53°

Similarly in ΔFDE we get:

m∠E=37° ( since we are given ∠F=53° and ∠D=90°)

Hence clearly all the corresponding  angles in both the triangles are equal.

Hence AAA similarity holds.

Hence, both the triangles are similar.

Hence, first option is true.

AA similarity postulate

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babunello [35]

Read the question carefully: it costs 4 tokens to park in a garage for an hour.

We will apply the unitary method to solve this question

It costs 4 tokens to park in a garage for 1 hour

Find how many hours can park in a garage for 1 token

If it costs 4 token to park in a garage for 1 hour

Then it will cost 1 token to park in a garage for 1/4 hour

Step2:

With 20 token we can park in a garage for (1/4) * 20

= 5 hours

So, we can park for 5 hours with 20 tokens.

Another method

If we take twenty tokens and divide them into groups of four, we will find that we are left with five groups of tokens. Each group of tokens represents an hour of parking time. This will give us five groups, or five hours, total.

So, we can park for 5 hours with 20 tokens
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3 years ago
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Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual
irina [24]
Using how tall it is over how wide
=>tall/wide
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Convert everything into the same units so 55ft to inches
There are 12in in 1ft
55ft * 12in/1ft
The ft cross out leaving in
55*12in= 660 in

So
15in/1.5in = x/660in
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17. x^2 + 2x + 1
valentina_108 [34]

Answer:

E. This polynomial could be factored by using grouping or the perfect squares methods.

Step-by-step explanation:

x^2 + 2x + 1

There is no greatest common factor

This is a perfect square

a^2 + 2ab+ b^2 = ( x+1)^2

We can factor this  by grouping

x^2 + 2x + 1

(x^2 +x) + (x+1)

x( x+1)  + x+1

Factor out x+1

( x+1)  ( x+1)

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3 years ago
Please help solve for x..
aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

x^{100}-4^x \cdot x^{98}-x^2+4^x=0

Factor out -1:

\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0

Divide both sides by -1:

\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0

Rearrange the terms:

\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0

\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:

\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0

Factor the first two terms and the last two terms separately:

\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0

Factor out the common term (x^{98}-1) :

\implies (4^x-x^2)(x^{98}-1)=0

<u>Zero Product Property</u>:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}

Therefore, the solutions to the given equation are: x = 1 or x = -1

Learn more here:

brainly.com/question/27751281

brainly.com/question/21186424

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