All categories

3 years ago

In the accompanying diagram of circle O, chords AB and CD intersect at E. If AE = 3, EB = 4, CE = x, and ED = x + 1, find. CE.

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

CE = 3

Step-by-step explanation:

Given:

AE = 3

EB = 4

CE = x

ED = x + 1

Required:

Solution:

First we need to determine the value of x by generating am equation as follows:

CE × ED = AE × EB (Interacting Chords Theorem)

Substitute

x × (x + 1) = 3 × 4

x² + x = 12

Subtract 12 from each side

x² + x - 12 = 12 - 12

x² + x - 12 = 0

Factorize to find the value of x

x² + 4x - 3x - 12 = 0

x(x + 4) -3(x + 4) = 0

(x - 3)(x + 4) = 0

x - 3 = 0

x = 3

x + 4 = 0

x = -4

Let's use the positive value of x

CE = x = 3

You might be interested in

Can you help me 4(b–1)²–9

Tamiku [17]

Answer:

(b-1)²-9

= 4[(b - 1)(b - 1)] - 9

= 4[b² - b - b + 1] - 9

= 4(b² - 2b + 1) - 9

= 4b² - 8b + 4 - 9

= 4b² - 8b - 5

Hope this helps!

7 0

2 years ago

Shirt cost $20 each and ties cost $12 each. Write an expression for the cost of s shirts and t ties

Ierofanga [76]

20s+12t= is your expression.

6 0

3 years ago

Read 2 more answers

Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina

Leona [35]

Answer:

Ann would need 3 h to complete the remainder of the Job.

Step-by-step explanation:

Step 1.

The "speed" that each girl has to do the work is determined as:

Tina: $\frac{1}{12h}$ , it means that Tina complete one twelveth of the job each hour.
Ann: $\frac{1}{8h}$ , it means the Ann completes one eighth of the job each hour.

Step 2.

The amount of work done by Tina in 9 hours, is obtain multiplying by the "speed" calculated in step 1:

Amount of work done= $8 h*\frac{1}{12h} = \frac{2}{3}$ . It means that Tina completes two thirds of the work in 9 h.

Step 3.

The remaining job is calculated as $1-\frac{2}{3}=\frac{1}{3}$ . It means that still remains is one third of the job to be completed.

Step 4.

The time required for Ann to complete the job is calculated dividing the remaining of the job by the "speed" of Ann to do the job.

$\frac{\frac{1}{3}}{\frac{1}{9h}}=3h$ . It means that Ann would complete the job in another 3 hours.

3 0

3 years ago

Identify the sequence as arithmetic, geometric, both, or neither. 7 9 11 13

Lisa [10]

Arithmetic and the sequence is adding 2

6 0

3 years ago

The radius of a circle is 13 feet. What is the length of an arc that subtends an angle of

Irina-Kira [14]

Answer:

The length of the arc is 221π/18 ft or 38.55 ft

Step-by-step explanation:

Given

Subtended angle, θ = 17π/18

Radius, r = 13 ft

Required

Length of the arc.

When an angle is given in radians, the length of the arc is calculated using the formula below

Length = rθ

By substituting

Length = 13 * 17π/18

Length = 221π/18

The answer can be left in this form.

But for simplification purpose, I'll solve further.

Taking π as 3.14

Length = 221 * 3.14/18

Length = 693.94/18

Length = 38.552222

Length = 38.55 ft (Approximated).

Hence, the length of the arc is 221π/18 ft or 38.55 ft

8 0

3 years ago