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3 years ago

I was sick for a week and never got tought this stuff can you help

Mathematics

1 answer:

Crank3 years ago

8 0

1. We know that Sum of Three Angles in a Triangle is 180

⇒ m∠1 + 75 + 40 = 180

Option B is the Answer

2. We know that Sum of Three Angles in a Triangle is 180

⇒ ∠1 + 30 + 20 = 180

⇒ ∠1 + 50 = 180

⇒ ∠1 = 180 - 50

⇒∠1 = 130

3. We know that Sum of Three Angles in a Triangle is 180

⇒ ∠1 + 75 + 35 = 180

⇒ ∠1 + 110 = 180

⇒ ∠1 = 180 - 110

⇒ ∠1 = 70

4. We know that Sum of Three Angles in a Triangle is 180

⇒ ∠1 + 60 + 60 = 180

⇒ ∠1 + 120 = 180

⇒ ∠1 = 180 - 120

⇒ ∠1 = 60

5. We know that Sum of Three Angles in a Triangle is 180

We can notice that the Given Triangle is a Right Angled Triangle

We know that One Angle in Right Angled Triangle is 90

⇒ ∠2 + 90 + 30 = 180

⇒ ∠2 + 120 = 180

⇒ ∠2 = 180 - 120

⇒ ∠2 = 60

6. We know that Sum of Three Angles in a Triangle is 180

We can notice that the Given Triangle is a Right Angled Triangle

We know that One Angle in Right Angled Triangle is 90

⇒ ∠2 + 90 + 40 = 180

⇒ ∠2 + 130 = 180

⇒ ∠2 = 180 - 130

⇒ ∠2 = 50

7. We know that Sum of Three Angles in a Triangle is 180

We can notice that the Given Triangle is a Right Angled Triangle

We know that One Angle in Right Angled Triangle is 90

⇒ ∠2 + 90 + 45 = 180

⇒ ∠2 + 135 = 180

⇒ ∠2 = 180 - 135

⇒ ∠2 = 45

8. We know that the Exterior Angle of one Vertex of a Triangle is the Sum of Other two vertices interior angles.

⇒ ∠3 = 80 + 60

⇒ ∠3 = 140

9. We know that the Exterior Angle of one Vertex of a Triangle is the Sum of Other two vertices interior angles.

⇒ ∠3 = 40 + 35

⇒ ∠3 = 75

10. We know that the Exterior Angle of one Vertex of a Triangle is the Sum of Other two vertices interior angles.

⇒ ∠3 = 75 + 65

⇒ ∠3 = 140

11. We know that Sum of Three Angles in a Triangle is 180

⇒ x + x + 108 = 180

⇒ 2x + 108 = 180

⇒ 2x = 180 - 108

⇒ 2x = 72

⇒ x = 36

12. We know that Sum of Three Angles in a Triangle is 180

⇒ 60 + 60 + 3x = 180

⇒ 3x + 120 = 180

⇒ 3x = 180 - 120

⇒ 3x = 60

⇒ x = 20

13. We know that Sum of Three Angles in a Triangle is 180

We can notice that the Given Triangle is a Right Angled Triangle

We know that One Angle in Right Angled Triangle is 90

⇒ (5x + 3) + 47 + 90 = 180

⇒ 5x + 140 = 180

⇒ 5x = 180 - 140

⇒ 5x = 40

⇒ x = 8

14. We can notice that the Given Diagram is a Right angled Triangle :

⇒ ∠1 + 90 + 45 = 180

⇒ ∠1 + 135 = 180

⇒ ∠1 = 180 - 135

⇒ ∠1 = 45

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The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people.

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Using an exponential function, the inequality is given as follows:

$9400(0.857)^t < 6000$

The solution is t > 2.9, hence the tax status will change within the next 3 years.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

$A(t) = A(0)(1 - r)^t$

$A(t) = 9400(1 - 0.143)^t$

$A(t) = 9400(0.857)^t$

The tax status will change when:

$A(t) < 6000$

Hence the inequality is:

$9400(0.857)^t < 6000$

Then:

$(0.857)^t < \frac{6000}{9400}$

$\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}$

$t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}$

Since both logs are negative:

$t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}$

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

More can be learned about exponential functions at brainly.com/question/25537936

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