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4 years ago

Find the value of x. Part 1c

Mathematics

2 answers:

aniked [119]4 years ago

6 0

Answer: x = 11

<u>Step-by-step explanation:</u>

a) bottom triangle, bottom right angle: Using Linear Pair Postulate, 180° - 114° = 66°

b) bottom triangle, top angle: Congruent sides implies congruent angles = 66°

c) bottom triangle, bottom left angle: Using the Triangle Sum Theorem, 66° + 66° + y = 180° --> y = 48°

d) top triangle, bottom angle: Using Complimentary Angles Theorem, 90° - 48° = 42°

Congruent sides implies congruent angles:

42° = ∠2

42 = 2x + 20

22 = 2x

11 = x

gtnhenbr [62]4 years ago

4 0

Answer:

x=11

Step-by-step explanation:

Please see attached image.

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The game commission observes the fish population in a stream and notices that the number of trout increases by a factor of 1.5 e

just olya [345]

Answer:

A - $f(t)=80(1.5)^t$

B - Graph given below

C - Number of trouts in 5th week are 607.2

D - Population of trouts will exceed 500 on the 5th week.

Step-by-step explanation:

We are given that,

The number of trout increases by a factor of 1.5 each week and the initial population of the trout is observed to be 80.

Part A: So, the explicit formula representing the situation is,

$f(t)=80(1.5)^t$ , where f(t) represents the population of trouts after 't' weeks.

Part B: The graph of the function can be seen below.

It can be seen that the function is an exponential function.

Part C: It is required to find the number of trouts in the 5th week.

So, we have,

$f(5)=80(1.5)^5$

i.e. $f(5)=80\times 7.59$

i.e. f(5) = 607.2

Thus, the number of trouts in 5th week are 607.2

Part D: We are given that the trout population exceeds 500.

It is required to find the week in which this happens.

So, we have,

$50$

i.e. $(1.5)^t>\frac{500}{80}$

i.e. $(1.5)^t>6.25$

i.e. $t\log 1.5>\log 6.25$

i.e. $t\times 0.1761>0.7959$

i.e. $t>\frac{0.7959}{0.1761}$

i.e. t > 4.5

As, t represents the number of weeks. So, to nearest whole, t = 5.

Thus, the population of trouts will exceed 500 on the 5th week.

7 0

3 years ago

The graph of a line goes up and to the right when:

Afina-wow [57]

<h3><u>Answer:</u></h3>

Option: C is the correct answer.

c) the coefficient of x is positive

<h3><u>Step-by-step explanation:</u></h3>

We know that graph of a line goes up and to the right when the coefficient of x is positive.

Since we know that when a line goes up and to the right this means that the line is increasing and hence we will get a positive slope of the line and we know that the slope intercept of a line is given as:

$y=mx+c$

as m is positive this means that:

the coefficient of x is positive.

Hence, the correct answer is:

c) the coefficient of x is positive

4 0

3 years ago

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MA_775_DIABLO [31]

7. 21.39
8. 6
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8 0

3 years ago

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bekas [8.4K]

Answer:

A = 3.14 × r²

Step-by-step explanation:

A = πr²

A = 3.14 × r²

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3 years ago

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Multiplying and Dividing Radicals <br><br> Simplify the following expressions.

adelina 88 [10]

The answer is 14. your welcome :)

6 0

3 years ago

Find the value of x. Part 1c​

Find the value of x. Part 1c