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ikadub [295]
3 years ago
7

Given: AB parallel to DC prove: ABE ~ DCE

Mathematics
2 answers:
slava [35]3 years ago
8 0
The reasons would be:

alternate interior angles
vertical angles
AAA (all angles are congruent)

Since we know that the two line segments are parallel, this means that BC is a transversal.  Using that knowledge with the position of ABE and DCE, we see these are alternate interior angles.

AEB and DEC are vertical angles, since they share only a vertex.

This gives us 3 congruent angles, so the triangles must be similar.
Vesna [10]3 years ago
3 0
Answer: The 3 missing statements are listed below with explanations.

2) Alternate interior angles are congruent. Since the lines are parallel these angles are congruent.

3) Vertical angles are congruent. Intersecting angles across from each other are congruent.

4) AA Similarity Theorem. If 2 angles of a triangle are congruent, then the triangles are similar.
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13
il63 [147K]

The required value after simplification of the s = -16/3. None of these are correct.

Given that,
To simplify [\frac{x^{2/3}x^{-1/2}}{x\sqrt{x^3}\sqrt[3]{x}}]^2   and to find the value of s in x^s.

<h3>What is simplification?</h3>

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Simplification,

=[\frac{x^{2/3}x^{-1/2}}{x\sqrt{x^3}\sqrt[3]{x}}]^2\\= \frac{x^{4/3}x^{-1}}{x^2x^3*{x}^{2/3}}\\= \frac{x^{1/3}}{x^{17/3}}\\=x^{-16/3}
Comparing with x^S
s = -16/3


Thus, the required value of the s = -16/3. None of these are correct.

Learn more about simplification here: brainly.com/question/12501526

#SPJ1

4 0
1 year ago
Integrate Sec (4x - 1) Tan (4x - 1) Dx ​
Delicious77 [7]

\bf \displaystyle\int~sec(4x-1)tan(4x-1)dx \\\\[-0.35em] ~\dotfill\\\\ sec(4x-1)tan(4x-1)\implies \cfrac{1}{cos(4x-1)}\cdot \cfrac{sin(4x-1)}{cos(4x-1)}\implies \cfrac{sin(4x-1)}{cos^2(4x-1)} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~\cfrac{sin(4x-1)}{cos^2(4x-1)}dx \\\\[-0.35em] ~\dotfill\\\\ u=cos(4x-1)\implies \cfrac{du}{dx}=-sin(4x-1)\cdot 4\implies \cfrac{du}{-4sin(4x-1)}=dx \\\\[-0.35em] ~\dotfill

\bf \displaystyle\int~\cfrac{~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{u^2}\cdot \cfrac{du}{-4~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{1}{4}\int\cfrac{1}{u^2}du\implies -\cfrac{1}{4}\int u^{-2}du \\\\\\ -\cfrac{1}{4}\cdot \cfrac{u^{-2+1}}{-1}\implies \cfrac{1}{4}\cdot u^{-1}\implies \cfrac{1}{4u}\implies \cfrac{1}{4cos(4x+1)}+C

5 0
3 years ago
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
algol13
Answers:
x = 24
y = 8√3
Explanation:

1) Since, the given triangle is a right triangle, and you have both an angle and the hypotenuse length, you can use some trigonometric ratios to find the variables.

2) The variables given represent:

x: adjacent-leg to angle 30°
y: opposite length to angle 30°

3) sine ratio:

sin 30° = opposite-leg / hypotenuse = y / (16√3)

⇒ y = 16√3 sin 30° = 16√3 × (1/2) = 8√3

4) cosine ratio

cos 30° = adjacent-leg / hypotenuse = x / (16√3)

⇒ x = 16√3 cos 30° = 16√3 (√3 / 2) = 16 × 3 / 2 = 24

4 0
3 years ago
What’s the ratio for 40 and 64
NARA [144]

Answer:

5/8, 5:8, or 5 to 8

Step-by-step explanation:

you have to simplify the ratio so you have to figure out what 40 and 64 have in common. tho right away you can assume that they both have 2 in common bcz they are both even so you can divide them both by two and get 20/32, and then you can do it again bcz they are both even again and get 10/16, and then you can do it again bcz they are also both even and get 5/8. now 5 is a prime number so you cant divide it any further so you stop it there. and i put three answers bcz there are three ways to write a ratio

6 0
3 years ago
Sum of 2 and 5 is divided by the difference of 9 and 4 in expression form ​
Goshia [24]

Answer:

(2 + 5) / (9 - 4)

Step-by-step explanation:

"sum of 2 and 5" = (2 + 5)

"difference of 9 and 4" = (9 - 4)

"sum of 2 and 5 is divided by the difference of 9 and 4"

= (2 + 5) / (9 - 4)

5 0
3 years ago
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