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3 years ago

Find the Length of AC. Round answers to the nearest hundredth (2 decimal places)

Mathematics

1 answer:

lara31 [8.8K]3 years ago

5 0

Answer:

32.78

Step-by-step explanation:

Assuming that we have two right triangles joined together, with one having adjacent side a, with a side of 12 ft opposite reference angle 30°, and the other one having adjacent side b, with a side of 12 ft opposite reference angle 45°. Thus, a + b = length of AC.

Let's find a and b.

Finding a:

Reference angle = 30°

Opp = 12 ft

Adj = a

Using trigonometric ratio formula, we have:

tan(30) = 12/a

Multiply both sides by a

a*tan(30) = 12

Divide both sides by tan(30)

a = 12/tan(30)

a = 20.78 (nearest hundredth)

Finding b:

Reference angle = 45°

Opp = 12 ft

Adj = b

Using trigonometric ratio formula, we have:

tan(45) = 12/b

Multiply both sides by a

b*tan(45) = 12

Divide both sides by tan(45)

b = 12/tan(45)

a = 12

Length of AC = 20.78 + 12 = 32.78

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The population of bacteria in a culture doubles every 14 hours. How long will it take for

Snezhnost [94]

Answer: 22 hours 11 minutes

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

$P=P_o\cdot e^{(kt)}\\\\\text{Since the initial population is doubled in 14 hours, then:}\\2P_o=P_o\cdot e^{k\cdot 14}\\2=e^{14k}\\ln\ 2=ln\ e^{14k}\\ln\ 2=14k\\\\\dfrac{ln\ 2}{14}=k\\\\0.0495=k\\\\\\\text{Now that the k-value has been determined, we can find the time when the}\\\text{population is tripled:}\\3P_o=P_o\cdot e^{0.0495t}\\3=e^{0.0495t}\\ln\ 3=ln\ e^{0.0495t}\\ln\ 3=0.0495t\\\\\dfrac{ln\ 3}{0.0495}=5\\\\22.19=t\\\\22\ hrs +0.19\ hrs$

$22\ hours + \bigg[\dfrac{19}{100}=\dfrac{x}{60}\bigg]\\\\22\ hours + 11\ minutes$

4 0

3 years ago

Find the inverse function of y=8x.

Zarrin [17]

Answer:

x/8

Step-by-step explanation:

how I see the problem I just put the 1 over the 8 because you can't really do anything else with the problem

4 0

3 years ago

Please help!! dont answer if you're not going to explain! need help with my geometry!

FinnZ [79.3K]

Step-by-step explanation:

Statement:

2-) ∠BAC = ∠EDC

<em>Reason:</em>

Angles opposite to equal sides of a triangle are equal (Alternate Interior Angles Theorem)

Statement:

3-) AC = CD

<em>Reason:</em>

CPCTC ("Corresponding Parts of Congruent Triangles are Congruent")

Statement:

4-) ∠BCA = ∠DCE

<em>Reason:</em>

Vertical Angles Theorem (states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent)

Statement:

5-) triangle ABC = triangle DEC

ASA Postulate

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. (The included side is the side between the vertices of the two angles.)

<h2>22</h2><h3>Answer: B</h3><h3 /><h2>23</h2><h3>Answer: D</h3><h3 /><h2>24</h2><h3>Answer: A</h3><h3 /><h2>25</h2><h3>Answer: C</h3>

6 0

3 years ago

The Third Side Is Called The base if an isosceles triangle has perimeter 345 cm and base length 85 cm what is the length of each

maks197457 [2]

Answer:

Length of each leg = 130 cm.

Step-by-step explanation:

Given that there is an isosceles triangle which has perimeter 345 cm.

Base length =85 cm.

Since other two sides are equal, let the equal size = x

Perimeter = sum of all 3 sides of a triangle

= 85+x+x = 85+2x

But perimeter = 345 (given)

So equate x term perimeter with actual

85+2x = 345

Subtract 85

2x = 260

Divide by 2

x =130 cm.

Hence answer is 130 cm.

6 0

3 years ago

Read 2 more answers

What are equivelent ratios<br>give an example please then help me with problem 24

postnew [5]

4:5 8:10 12:15 that some eqivelent ratios

3 0

3 years ago