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3 years ago

Pls answer this question with steps (proof).

Mathematics

1 answer:

Tems11 [23]3 years ago

6 0

Answer:

Step-by-step explanation:

Since triangle BCE is a right angle triangle, we would determine angle BEC by applying the tangent trigonometric ratio. Therefore,

Tan BEC = 6/3 = 2

Angle BEC = Tan^-1(2)

Angle BEC = 63.4°

The sum of the angles on a straight line is 180°. This means that

Angle AED + angle DEC + angle BEC = 180

Angle AED = 180 - (45 + 63.4) = 71.6°

Angle ADE = angle AED = 71.6°

Angle CDE + angle ADE = 180(sum of angles on a straight line)

Angle CDE = 180 - 71.6 = 108.4°

To get line EC, we would apply Pythagoras theorem. Therefore

EC² = 3² + 6² = 45

EC = √45 = 6.71 cm

The sum of the angles in a triangle is 180°

Therefore,

Angle ECD = 180 - (45 + 108.4) = 26.6°

By applying sine rule,

6.71/sin108.4 = ED/sin26.6 = DC/Sin45

6.71/sin108.4 = ED/sin26.6

Cross multiplying, it becomes

6.71sin26.6 = EDsin108.4

ED = 6.71sin26.6/sin108.4

ED = 3.00608/0.949 = 3.18cm

The area of a triangle is

Area = 1/2abSinC

Therefore, area of triangle EDC = 1/2 ×

ED × EC × SinDEC

Area = 1/2 × 6.71 × 3.18 × sin45

Area = 1/2 × 6.71 × 3.18 × 0.707

Area = 7.54 cm²

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3 years ago

If the typical balance on Lucy's credit card is $650 and the interest rate (APR) on her credit card is 18%, how much in interest

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<h3>Further explanation </h3>

Given:

The typical balance on Lucy's credit card is $650.
The interest rate (APR) on her credit card is 18%.

Question:

How much in interest would you expect Lucy to be charged in a typical month?

The Process:

This problem includes the type of determining simple interest.

$\boxed{ \ I = P \times r \times t \ }$

where,

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P = principal (initial amount)
r = annual interest rate
t = time (in years)

This time we will find out how much in interest we would expect to be charged in a typical month.

The data is as follows:

P = 650
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Let us calculate how much in interest we would expect to be charged in a typical month.

$\boxed{ \ = 650 \times \frac{18}{100} \times \frac{1}{12} \ }$

$\boxed{ \ = 65 \times \frac{3}{10} \times \frac{1}{2} \ }$

$\boxed{ \ = \frac{195}{10} \times \frac{1}{2} \ }$

$\boxed{ \ = \frac{97.5}{10} \ }$

$\boxed{ \ = \frac{975}{100} \ }$

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3 years ago

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elena-14-01-66 [18.8K]

Answer:

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Step-by-step explanation:

we have

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we know that

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Solve the system by graphing

using a graphing tool

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see the attached figure

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