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Leona [35]
3 years ago
15

What is AE ? Enter your answer in the box. units Two segments A D and B C intersect at point E to form two triangles A B E and D

C E. Side A B is parallel to side D C. A E is labeled 2 x plus 10. E D is labeled x plus 3. A B is 10 units long. D C is 4 units long

Mathematics
1 answer:
spin [16.1K]3 years ago
5 0

Answer:

The length of AE is 20 units.

Step-by-step explanation:

Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.

we have to find the length of AE

AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD  

In ΔABE and ΔDCE

∠EAB=∠EDC      (∵Alternate angles)

∠EBA=∠ECD      (∵Alternate angles)

By AA similarity, ΔABE ≈ ΔDCE

therefore, \frac{AE}{ED}=\frac{AB}{CD}

⇒ \frac{2x+10}{x+3}=\frac{10}{4}

⇒ 8x+40=10x+30

⇒ x=5

Hence, AE=2x+10=2(5)+10=20 units

The length of AE is 20 units.

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Kruka [31]

This question is incomplete.

Complete Question

Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

Answer:

280 tons of wood.

Step-by-step explanation:

From the above question:

To make 1 ship = we require 40 tons of wood.

1 ship = can accommodate 300 sailors.

Step 1

If :

300 sailors = 1 ship

2100 sailors = y ships

Cross Multiply

300 × y ships = 1 ship × 2100 sailors

y ships = 2100 / 300

y ships = 7

Hence, 2100 sailors can occupy 7 ships.

Step 2

We are told in the question that:

Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

If:

1 ship = 40 tons of wood

Since 7 ships can accommodate 2100 sailors,

7 ships =

7 × 40 tons of wood = 280 tons of wood.

Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.

6 0
3 years ago
Solve the equation below for x. <br> 500 = 25e ^ (2x)
Zigmanuir [339]

Answer:

x = i π n + log(20)/2 for n element Z

Step-by-step explanation:

Solve for x:

500 = 25 e^(2 x)

500 = 25 e^(2 x) is equivalent to 25 e^(2 x) = 500:

25 e^(2 x) = 500

Divide both sides by 25:

e^(2 x) = 20

Take the natural logarithm of both sides:

2 x = 2 i π n + log(20) for n element Z

Divide both sides by 2:

Answer: x = i π n + log(20)/2 for n element Z

7 0
3 years ago
How many weeks when the amount of money Hannah owed her friend was 18$
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I believe it’s 3.5 but I could totally be wrong I’m not much help at all
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2 years ago
WILL AWARD BRAINLIEST
julia-pushkina [17]

Answer: a= c+11

Step-by-step explanation:

a has 9 more than b which has 2less than c

7 0
3 years ago
I need help with this, I’ll give brainliest!
Ivanshal [37]

Answer:

A

Step-by-step explanation:

Only graph A satisfies the domains provided

8 0
3 years ago
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