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3 years ago

In triangle ABC, angle C is a right angle and BC=5. If measure of angle B = 30 degrees, find AC

2 answers:

5 0

Answer = d

using the 30 - 60 - 90 triangle theorem

side across from the angle

across from angle 30 is x
across from angle 60 is x rad. 3
across from 90 is 2x

BC is across from angle 60
so BC is the x rad 3
set the given measurement equal to it

x sqrt 3 = 5
÷ sqrt 3 ÷ sqrt 3
x = (5/ sqrt 3)
multiply top and bottom by the radical to get rid of the radical in the bottom

x = (5/ sqrt 3) × (sqrt 3/sqrt 3)
x = 5 sqrt 3/ 3

since side BC is x
BC = 5 sqrt 3/ 3

* Drawing the triangle diagram would help*

steposvetlana [31]3 years ago

4 0

Answer:

Step-by-step explanation:

._.

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3 years ago

Four-fifths of a number decreased by two is eighteen

hodyreva [135]

Pls mark me brainiless

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3 years ago

How to find the point slope form with the slope of 3 and the point of -2/6

Levart [38]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:y-6 = 3(x + 2)$

____________________________________

$\large \tt Solution \: :$

Equation of line in point - slope form :

$\qquad \tt \rightarrow \:y-y_1 = m(x - x_1)$

$\tt \:m = slope=3$

$\tt y_1 = y \: \: coordinate \: \: of \: \: point = 6$

$\tt \:x_1 = x \: \: coordinate \: \: of \: \: point = - 2$

Here :

$\qquad \tt \rightarrow \:y - 6 = 3(x - ( - 2))$

$\qquad \tt \rightarrow \:y - 6 = 3(x + 2)$

5 0

2 years ago

Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28.

ycow [4]

Answer: The tenth term is 76

=======================================================

Explanation:

We use this arithmetic sequence formula to get the nth term

$a_n = a_1 + d(n-1)$

Plug in $a_1 = 4, \ d = 8, \ n = 10$ and you should get the following:

$a_n = a_1 + d(n-1)\\\\a_{10} = 4 + 8(10-1)\\\\a_{10} = 4 + 8(9)\\\\a_{10} = \textbf{76}\\\\$

The tenth term is <u>76</u>

---------

We can verify this by listing out the terms one by one. Start at 4, add on 8 each time, until you generate the 10th term. A table like the one shown below is a good way to keep track of all the terms.

$\begin{array}{c|c}\boldsymbol{n} & \boldsymbol{a_n}\\1 & 4\\2 & 12\\3 & 20\\4 & 28\\5 & 36\\6 & 44\\7 & 52\\8 & 60\\9 & 68\\10 & \textbf{76}\\\end{array}$

---------

In short, the error is with the "10" in the expression 4+10(8). The student should have used 9 instead. This is because of the n-1 term in $a_n = a_1 + d(n-1)$ which shifts everything one spot to the left.

7 0

2 years ago

A certain radioactive material decays in such a way that the mass in kilograms remaining after t years is given by the function

Angelina_Jolie [31]

The mass of radioactive material remaining after 50 years would be 48.79 kilograms

<h3>How to determine the amount</h3>

It is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.

Given the radioactive decay formula as

m(t)=120e−0.018t

Where

t= 50 years

m(t) is the remaining amount

Substitute the value of t

$m(t) = 120e^-^0^.^0^1^8^(^5^0^)$

$m(t) = 120e^-^0^.^9$

Find the exponential value

m(t) = 48.788399

m(t) = 48.79 kilograms to 2 decimal places

Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms

Learn more about half-life here:

brainly.com/question/26148784

#SPJ1

7 0

2 years ago