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2 years ago

If ∠ABE = 100° and ∠EDC = 100°, are the two triangles, ΔABE and ΔEDC similar? If so, by what criterion?

Mathematics

2 answers:

ipn [44]2 years ago

6 0

Answer:

a) yes, by AA criterion

Step-by-step explanation:

If two angles in a triangle are congruent to two angles in another triangle then the two triangles are congruent. ∠ABE ≈ ∠EDC since they have the same measure. ∠BEA ≈ ∠CED since they are vertical angles. Since two angles are congruent, then you can conclude yes, by AA criterion

Arturiano [62]2 years ago

3 0

Answer:

No, not possible to tell that the two triangles, ΔABE and ΔEDC are similar

Step-by-step explanation:

Similarity criterion:

1. AAA similarity : two triangles are similar if all three angles in the first

triangle equal the corresponding angle in the second triangle

2. AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.

3. SSS similarity : If the corresponding sides of the two triangles are

proportional, then the two triangles are similar.

4. SAS similarity : In two triangles, if two sets of corresponding sides

are proportional and the included angles are equal then the two

triangles are similar.

Now in the two triangles ABE and EDC :

∠ABE = 100°

∠EDC = 100°

∠ABE = ∠EDC

But only one congruent angle does not not prove that the two triangles are similar.

Hence, NOTHING CAN BE SAID ABOUT THE nature of the triangle.

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Answer:

Step-by-step explanation:

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2 years ago

What is the y value of the vertex 4x^2+8x-8

Oksana_A [137]

Answer:

The y-value of the vertex is $-12$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$f(x)=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

In this problem we have

$f(x)=4x^{2}+8x-8$ -----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+8=4x^{2}+8x$

Factor the leading coefficient

$f(x)+8=4(x^{2}+2x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+8+4=4(x^{2}+2x+1)$

$f(x)+12=4(x^{2}+2x+1)$

Rewrite as perfect squares

$f(x)+12=4(x+1)^{2}$

$f(x)=4(x+1)^{2}-12$

The vertex is the point $(-1,-12)$

The y-value of the vertex is $-12$

5 0

3 years ago

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Please help! Identify each decimal number as either rational or irrational.

labwork [276]

Answer:

A Rational number is a number that can be written as a ratio in fraction form.

An Irrational number is a number that, when in decimal form, does not terminate or repeat.

Step-by-step explanation:

1.485 can be written as 1 485/1000 - it is rational

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333.051422218... continues on and does not repeat - it is irrational

0.2268715 can be written as 2268715/10000000 - it is rational

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3 years ago

Write the equation of the line that is parallel to y= 3x -7 and goes through point (4,2).

My name is Ann [436]

Answer:

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Step-by-step explanation:

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6 0

3 years ago

20 POINTS PLEAE HELP!!!!!!!!!!!!!!!

Alina [70]

His first payment is $100, thus a₁ = 100.

the next "term", month will be 1.1 times more than the one before, namely r = 1.1, the common ratio.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=100\\
r=1.1\\
n=20
\end{cases}$

$\bf \sum\limits_{i=1}^{20}~100(1.1)^{i-1}\qquad \qquad\qquad \qquad S_{20}=100\left( \cfrac{1-1.1^{20}}{1-1.1} \right)
\\\\\\
S_{20}=100\left( \cfrac{1-\stackrel{\approx}{6.727499949}}{-0.1} \right)\implies S_{20}\approx 100(57.27499949)
\\\\\\
S_{20}\approx 5727.4999493256$

is the serie divergent or convergent?

well, to make it short, when the common ratio is 0 < | r | < 1, namely a fraction between 0 and 1, only then the serie is convergent, namely it reaches a fixed value, now in this case, 1.1 is a value larger than anything between 0 and 1, so no dice.

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3 years ago

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