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2 years ago

Find the value x and write the property used here.

Mathematics

2 answers:

Serga [27]2 years ago

6 0

Step-by-step explanation:

Soln,

Here,

45°+65°+y(let)=180°[ being a triangle]

or,110°+y=180°

or,y=180°-110°

so,y=70°

Now,

x=?

so,

x+y=180°[being straight angle]

or,x+70°=180°

or,x=180°-70°

x=110°

THEREFORE,x=110°

solved!

Len [333]2 years ago

4 0

Answer:

x = 110°

Step-by-step explanation:

Exterior angle property states that the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is

x = 45° + 65° = 110°

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Jackie’s test scores for the first semester are listed below.

jek_recluse [69]

Answer:

The answer is 91

Step-by-step explanation:

90 x 6 = 540

The numbers need to equal 540 all together to make an average of 90.

97 + 86 + 83 + 95 + 88 = 449

540 - 449 = 91

To check:

97 + 86 + 83 + 95 + 88 + 91 = 540

Therefore, the answer is 91

8 0

2 years ago

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

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9 months ago

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Andrej [43]

Answer:

Step-by-step explanation:

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2 years ago

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alexdok [17]

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2 years ago

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Anna35 [415]

Answer:

Let 'a' be the first term, 'r' be the common ratio and 'n' be the number of terms

Series = 2+6+18.......= 2+2•3¹+ 2•3².......= 728

Now,

$Sum = \frac{a( {r}^{n} - 1) }{(r - 1)} \\$

So,

$\frac{a( {r}^{n} - 1)}{(r - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{(3 - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{2} = 728 \\ {3}^{n} - 1 = 728 \\ {3}^{n}=728+1\\ {3}^{n} = 729 \\ {3}^{n} = {3}^{6} \\ \boxed{ n = 6}$

Therefore, number of terms is 6

6 is the right answer.

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