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2 years ago

Which sine ratios are correct for ∆PQR? Check all that apply

Mathematics

2 answers:

Zanzabum2 years ago

7 0

Answer:

$sin(P)=\frac{p}{q}\\ sin(R)=\frac{r}{q}$

Step-by-step explanation:

In the given graph, we have the right triangle PQR, where q is the hypothenuse and r and p are legs.

Now, if we want to the sin function of an angle, it would be like

$sin(A)=\frac{opposite}{adjacent}$

That is, the sin of an angle is the quotient between its opposite leg and its adjacent leg.

So, in this case, if we apply this defintion to P and R angles, we have

$sin(P)=\frac{p}{q}\\ sin(R)=\frac{r}{q}$

Therefore, the right choices are the second and the last option.

$sin(P)=\frac{p}{q}\\ sin(R)=\frac{r}{q}$

nataly862011 [7]2 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

sinP = $\frac{opposite}{hypotenuse}$ = $\frac{QR}{PR}$ = $\frac{p}{q}$

sinR = $\frac{PQ}{PR}$ = $\frac{r}{q}$

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For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean $210x^6y^4$

We can deduce that this term will be located somewhere in the middle. So I will calculate $k= 5; k=6 \text{ and } k =7$ .

For $k=5$

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just $x^{n-k} y^k$

For $k=6$

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0

2 years ago

Which expression is equivalent to sin7pi/6?

elena-14-01-66 [18.8K]

For this case we must find an expression equivalent to:

$Sin (\frac {7 \pi} {6})$

According to the unit circle, $\frac {7 \pi} {6}$ is in the third quadrant and equals 210 degrees.

Then, we must find an expression equivalent to:

$Sin (210) = - \frac {1} {2} = - 0.5$

We have to:

$\frac{11 \pi} {6}$

It is in the fourth quadrant and is equivalent to 330 degrees, according to the unit circle.

$Sin (330) = - \frac {1} {2} = - 0.5$

Answer:

Option D

3 0

2 years ago

Read 2 more answers

Can someone help please??

Nady [450]

Answer:

The scores in order from least likely to most likely is 8, 3, 4, and 5.

Step-by-step explanation:

1. Calculate the probability of the spinner adding up to 1, 2, 3, 4, .... 8

You will get:

2 (1/16)

3 (2/16)

4 (3/16)

5 (4/16)

6 (3/16)

7 (2/16)

8 (1/16)

2. Given the scores from the problem, the probability of each number is 3 (2/16), 4 (3/16), 5 (4/16), and 8 (1/16).

3. With this, we can determine the scores in order from least likely to most likely is 8, 3, 4, and 5.

8 0

2 years ago

In the diagram, DC is 10 units and BC is 6 units. Line l is a perpendicular bisector of line segment A C. It intersects line seg

Orlov [11]

Answer:

12 units

Step-by-step explanation:

Point B is the midpoint of AC, and it is 6 units from C. Therefore A must be 12 units from C.

AC = 12 units

7 0

2 years ago

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If 3x-y=123x−y=123, x, minus, y, equals, 12, what is the value of \dfrac{8^x}{2^y} 2 y 8 x start fraction, 8, start superscrip

julia-pushkina [17]

Answer:

$2^{12}=4,096$

Step-by-step explanation:

You know that $3x-y=12$ and have to find

$\dfrac{8^x}{2^y}$

Use the main properties of exponents:

1. $(a^m)^n=a^{m\cdot n}$

2. $\dfrac{a^m}{a^n}=a^{m-n}$

Note that

$8=2^3,$

then

$7^x=(2^3)^x=2^{3\cdot x}=2^{3x}$

Now

$\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}$

Since $3x-y=12,$ then $2^{3x-y}=2^{12}=4,096$

3 0

2 years ago

Read 2 more answers