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2 years ago

Could anyone help me with this? Thanks in advance x

Mathematics

1 answer:

alexira [117]2 years ago

5 0

Answer:

find b: since the triangle is right angle triangle apply the Pythagorean theorem

c²+b²=d²

b²=d²-c²

b²=16²-12²

b²=256-144

b²=112

the sum of the angle of the triangle=180

( in top Δ abd ) sin Ф=opp/hyp

sinФ=b/d=4√7/16= √7/4 radian

convert to degrees : √7/4 *180/π= 37.91 almost 38 degrees

<h2>which makes A= 38 degrees ( adjacent angles are equal when they have common side and do not overlap)</h2>

find a=?? apply law of cosine

a²= d^2 + c^2 − 2dc cosA

a²=16² + 12²-2(16)(12)cos38

a =√(16² + 12²-2(16)(12)cos38)

<h2>a=9.87 rounded to the nearest hundredth</h2>

(i hope it is right )

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Now each angle of the triangle is 60°, it means the triangle is equilateral.

The base of the triangle is given as 12. So, the length of each side will be 12.

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Read 2 more answers

Demarcus and his brother are saving up some money to take a trip together. to open a joint savings account, demarcus deposited a

Anastaziya [24]

a. Demarcus' method is (d + d + 7) = 111/3

b. His brother's method is 3d + 3d + 3 × 7 = 111

c. The banker's method is 3(2d + 7) = 111

<h3>How to complete each person's method</h3>

Each pperson's method is the solution to a linear equation

<h3>What is a linear equation?</h3>

A linear equation is an equation in which the highest power of the unknown is 1.

<h3>a. How to complete Demarcus' method?</h3>

Since the equation is given by 3(d + d + 7) = 111 and demarcus was solving the equation and his first step was to divide both sides by 3, we have that

3(d + d + 7) = 111

(d + d + 7) = 111/3

d + d + 7 = 37

2d + 7 = 37

2d = 37 - 7

2d = 30

d = 30/2

d = 15

So, Demarcus' method is (d + d + 7) = 111/3

<h3>b. How to complete his brother's method?</h3>

Since the equation is given by 3(d + d + 7) = 111 and his brother started solving the equation by using the distributive property,we have that

3(d + d + 7) = 111

3d + 3d + 3 × 7 = 111

3d + 3d + 21 = 111

6d + 21 = 111

6d = 111 - 21

6d = 90

d = 90/6

d = 15

So, his brother's method is 3d + 3d + 3 × 7 = 111

<h3>c. How to complete the banker's method?</h3>

Since the equation is given by 3(d + d + 7) = 111 and their banker started solving the equation by combining like terms, we have that

3(d + d + 7) = 111

3(2d + 7) = 111

6d + 21 = 111

6d = 111 - 21

6d = 90

d = 90/6

d = 15

So, the banker's method is 3(2d + 7) = 111

Learn more about linear equation here:

brainly.com/question/26260688

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