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2 years ago

(05.02 LC) Given triangle ABC, which equation could be used to find the measure of ∠C?

Mathematics

1 answer:

Sidana [21]2 years ago

6 0

Answer:

D. sin m∠C = 2 square root of 5 all over 5

Step-by-step explanation:

The triangle ABC is a right angled triangle. The angle ∠C is where we are asked to find. The side AB measures 6 , AC measures 3 and the side BC measures 3√5.

The longest side of a right angle triangle is the hypotenuse, that means the side with length 3√5 is the hypotenuse.

Therefore side BC is the hypotenuse side and we are asked to find the angle C. AB is the opposite side while AC is the adjacent side.

Using

sin C = opposite/hypotenuse = 6/3√5 = 2/√5 = 2√5/5

cos C = adjacent/hypotenuse = 3/3√5 = 1/√5

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Which of the following disasters is typically not covered by property

Dima020 [189]

Answer: C

Step-by-step explanation: Typically flood insurance is not included. You can however individually buy flood insurance.

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3 years ago

hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

1 year ago

1)Make an area model(Table) or a tree diagram to model all the possible combinations in this situation. 2)What is the theoretica

Ann [662]

Answer:

Example:

A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag.

a) Construct a probability tree of the problem.

b) Calculate the probability that Paul picks:

i) two black balls

ii) a black ball in his second draw

Solution:

tree diagram

a) Check that the probabilities in the last column add up to 1.

b) i) To find the probability of getting two black balls, first locate the B branch and then follow the second B branch. Since these are independent events we can multiply the probability of each branch.

ii) There are two outcomes where the second ball can be black.

Either (B, B) or (W, B)

From the probability tree diagram, we get:

P(second ball black)

= P(B, B) or P(W, B)

= P(B, B) + P(W, B)

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3 years ago

Consuela earns a salary of 40000$ per year plus commission of 1000$ for each car she sells. Write and solve an equation that sho

iVinArrow [24]

40000+1000x=60000
-40000. -40000

1000x=20000
x=20

6 0

3 years ago

Help me!!!!!!!!!!!!!

sukhopar [10]

Answer: 17

Step-by-step explanation:

2 x2 is 4 4+13 is 17

3 0

3 years ago