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3 years ago

A convex figure has three sides what is the sum of its exterior angles

Mathematics

1 answer:

SashulF [63]3 years ago

4 0

A convex figure with three sides is triangle. The sum of the measures of all interior angles of the triangle is 180°.

Let $\alpha, \beta, \gamma$ be interior angles of this triangle. Then

$\alpha+\beta+\gamma=180^{\circ}.$

Find exterior angles of this triangle:

1. $180^{\circ}-\alpha$ is exterior angle adjacent to the interior angle $\alpha.$

2. $180^{\circ}-\beta$ is exterior angle adjacent to the interior angle $\beta.$

3. $180^{\circ}-\gamma$ is exterior angle adjacent to the interior angle $\gamma.$

The sum of the measures of all exterior angles is

$180^{\circ}-\alpha+180^{\circ}-\beta+180^{\circ}-\gamma=540^{\circ}-(\alpha+\beta+\gamma)=540^{\circ}-180^{\circ}=360^{\circ}.$

Answer: 360°

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Jamie purchased a DVD that was on sale for 15% off. The sales tax in her county is 5%. Let y represent the original price of the

xxTIMURxx [149]

Answer:

Q1) Final cost = y*0.85*1.05

Q2) Perimeter = 0.1*x - 16

Q3) One over five ( m - 100)

Step-by-step explanation:

We are given three question as follows:

Q1) Jamie purchased a DVD that was on sale for 15% off. The sales tax in her county is 5%. Let y represent the original price of the DVD. Write an expression that can be used to determine the final cost of the DVD.

Solution:

Note: The effect of each percentage on original price is as follows, where y is the original price of the DVD:

Discount of 15 % = Price reduced by 0.15*y

Sales Tax of 5% = Price increased by 0.05*y

- The resulting prices from each percentage is:

Amount left after discount = y - 0.15*y = 0.85*y

Amount after tax = y + 0.05*y = 1.05*y

- The factors of each affect are:

Factor of discount = 0.85

Factor of Tax = 1.05

Hence, The factors are multiplied by the original cost to get the combined effect as follows:

Answer: Final cost = y*0.85*1.05

Q2) Write an expression for the perimeter of the triangle shown below: A triangle is shown with side lengths labeled 0.5*x + 9, 3x, and - 3.4*x - 25.

Solution:

The perimeter of the triangle is the sum of all 3 sides given:

Perimeter = (0.5*x + 9) + (3x) + ( -3.4*x - 25 )

Perimeter = (0.5*x + 3x - 3.4x) + ( 9 - 25 )

Answer: Perimeter = 0.1*x - 16

Q3) Which expression is equivalent to one over five*m − 20?

Solution:

- Re-write expression:

(1 / 5)*m - 20

Take LCM of the denominator:

(m - 100) / 5

Answer: One over five ( m - 100)

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3 years ago

Read 2 more answers

How many gallons of a 20% acid solution should be mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solut

Alexeev081 [22]

Answer:

30 gallons of 20% acid solution should be mixed.

Step-by-step explanation:

Let x gallons of a 20% acid solution was mixed with 30 gallons of a 40% solution, to obtain a mixture of 30% acid solution.

Therefore, final volume of the solution will be (x + 30) gallons.

Now concept to solve this question is

20%.(x) + 40%.(30) = 30%.(x + 30)

0.20(x) + 0.40(30) = 0.30(x + 30)

0.20x + 12 = 0.30x + 9

0.30x - 0.20x = 12 - 9

.10x = 3

x = $\frac{3}{0.1}$

x = 30 gallons

Therefore, 30 gallons of the 20% acid solution should be mixed.

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3 years ago

−4−5+4+(−5)minus, 4, minus, 5, plus, 4, plus, left parenthesis, minus, 5, right parenthesis.

Tema [17]

Answer: -10

Step-by-step explanation: For this problem we will solve the numbers in order.

-4 - 5 + 4 + (-5)

First subtract -4 - 5, which will give you -9. Then add -9 to 4, which will give you -5. Lastly add -5 plus -5, which will give you an answer of -10.

3 0

3 years ago

Don’t understand this can someone help

pentagon [3]

1...
you need to find unknown measures in 1.ques. by using corresponding parts of similar triangle property..
THAT IS...
XY/PQ = YZ/QR =ZX/PR....
PUT VALUES IN THIS N SOLVE....

2....
use the property that ratio of corresponding sides of similar figures are equal....

HOPE IT HELPS YOU '_'

8 0

3 years ago

Read 2 more answers

The total charge for a taxi ride in nyc includes an initial fee of $3.75 plus $1.25 for every 1/2 mile traveled. Yhe taxi ride c

AnnZ [28]

Answer:

12.50 - 3.75 = 8.75

$8.75 / $1.25 * (1/2) (per mile) = 3.5 miles

1. Mile .5 (fee and 1st mile)

$3.75 + $1.25 = $5.00

2. Miles .5 - 3.5 (additional 3 miles)

$1.25 * (3*2) = $7.50

Total: $5.00 + 7.50 = $12.50

Step-by-step explanation:

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3 years ago