In this triangle, the product of sin B and tan C is _ , and the product of sin C and tan B is ___.

Answers

Answer 1

Answer: In this triangle, the product of sin B and tan C is c/a or cos B, and the product of sin C and tan B is b/a cos C. We determine these as follows:

sin B tan C = b/a (c/b) = c/a

sin C tan B = c/a (b/c) = b/a

Hope this answers the question. Have a nice day.

Answer 2

Answer:

Answer

part 1 = c/a

part 2 = b/a

Sine is the ratio of opposite to hypotenuse respect to as agiven angle while tangent is the ratio of opposite to adjacent lengths of agiven angle.

Part 1

Sine = opposite/hypotenuse

SinB = b/a

Tangent = opposite/adjacent

TanC = c/b

SinB × TanC = b/a×c/b

= c/a

Part 2

SinC = c/a

TanB = b/c

SinC×TanB= c/a×b/c

=b/a

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Answers

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Chris has a collection of 20 baseball cards and Kyle has collection of 40 baseball cards. Chris is adding 3 baseball cards per month to his collection while Kyle is adding one baseball card per month to his collection. After how many months will Chris and Kyle have the same number of baseball cards?

Answers

Answer:

11 months

Step-by-step explanation:

The initial number of baseball cards that Chris has is 20.

This is like the first term of a sequence.

If Chris is adding 3 baseball cards per month, then there will be a constant difference of 3.

The number of baseball cards after $n$ months is given by the formula;

$C_n=20+(n-1)3$

$\Rightarrow C_n=20+3n-3$

$\Rightarrow C_n=3n+17$ where $n\ge1$

Similarly, Kyle initially has 40 baseball cards and adds one base ball card per month to his collection;

The number of his baseball cards after $n$ months is given by the formula;

$K_n=40+(n-1)1$

$K_n=40+n-1$

$\Rightarrow K_n=n+39$

To determine the number of months that will pass before Kyle and Chris have the same number of base ball cards, we equate both equations to get;

$\Rightarrow 3n+17=n+39$

We group like terms to get;

$3n-n=39-17$

$\Rightarrow 2n=22$

$\Rightarrow n=11$

Therefore Chris and Kyle will have the same number of baseball cards after 11 months.

Final answer:

By setting equal the linear expressions for how many baseball cards Chris and Kyle have after a given number of months, we find that it will take 10 months for them to have the same number.

Explanation:

The question is essentially asking how long it will take for Chris and Kyle to have the same number of baseball cards. It's a problem about linear expressions, rooted in mathematics. Chris starts with 20 baseball cards and adds 3 per month. We can express this as C = 20 + 3m, where m is the number of months. Kyle starts with 40 baseball cards and adds 1 per month. We express this as K = 40 + m.

We want to find out when Chris and Kyle will have the same number of cards, so we set C = K, which results in 20 + 3m = 40 + m. By solving this equation, we can condense it to 2m = 20 or m = 10. Therefore, it will take 10 months for Chris and Kyle to have the same number of baseball cards.

Learn more about Linear Equations here:

brainly.com/question/32634451

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Which of the following numbers is a whole number a.3/5 b.0.5 c.15% d.47

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D....................................................................................................................

Which of the following describes the domain of the function?

Answers

I think it's A but I'm not sure. The domain of a relation is simply the input, or x-values of the relation

One student makes 20 origami figures that they want to give to 9 friends. Which of the following best describes how the origami can be most evenly divided between the friends.

Answers

Answer:

give each friend 2 origami figures

Step-by-step explanation:

Solve the logarithmic equation. be sure to reject any value that is not in the domain of the original logarithmic expressions. give the exact answer. log8(5x + 8) = log8(5x + 5)