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Alina [70]
3 years ago
6

What is the value of x?

Mathematics
1 answer:
SashulF [63]3 years ago
4 0
3x - 25 =6x - 80
6x-3x = 80 - 25
3x = 55
x = 18.33
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Find the remaining trigonometric ratios of θ if csc(θ) = -6 and cos(θ) is positive
VikaD [51]
Now, the cosecant of θ is -6, or namely -6/1.

however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.

we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

\bf csc(\theta)=-6\implies csc(\theta)=\cfrac{\stackrel{hypotenuse}{6}}{\stackrel{opposite}{-1}}\impliedby \textit{let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
\pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a\implies \stackrel{IV~quadrant}{+\sqrt{35}=a}

recall that 

\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad\qquad 
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\\\\\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}
\qquad \qquad 
% cotangent
cot(\theta)=\cfrac{adjacent}{opposite}
\\\\\\
% cosecant
csc(\theta)=\cfrac{hypotenuse}{opposite}
\qquad \qquad 
% secant
sec(\theta)=\cfrac{hypotenuse}{adjacent}

therefore, let's just plug that on the remaining ones,

\bf sin(\theta)=\cfrac{-1}{6}
\qquad\qquad 
cos(\theta)=\cfrac{\sqrt{35}}{6}
\\\\\\
% tangent
tan(\theta)=\cfrac{-1}{\sqrt{35}}
\qquad \qquad 
% cotangent
cot(\theta)=\cfrac{\sqrt{35}}{1}
\\\\\\
sec(\theta)=\cfrac{6}{\sqrt{35}}

now, let's rationalize the denominator on tangent and secant,

\bf tan(\theta)=\cfrac{-1}{\sqrt{35}}\implies \cfrac{-1}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{-\sqrt{35}}{(\sqrt{35})^2}\implies -\cfrac{\sqrt{35}}{35}
\\\\\\
sec(\theta)=\cfrac{6}{\sqrt{35}}\implies \cfrac{6}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{6\sqrt{35}}{(\sqrt{35})^2}\implies \cfrac{6\sqrt{35}}{35}
3 0
3 years ago
HELP I WILL MARK BRAINLIEST
Ede4ka [16]

Answer:

the answer is A.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The front of an A-frame house is in the shape of a triangle.The height of the house is 20 feet.The area of the front of a A-fram
ipn [44]
600 divided by 20=30
30x2=60 which is the answer

equation= 600=2x area divied by height 
7 0
3 years ago
Help please! the question is in the picture below for reference when answering! thank you so much!
Reil [10]

Answer:

Neither perpendicular or parallel

Step-by-step explanation:

The y-intercept would not be the same, and the slope would be different. That means that line wont be parallel, or perpendicular.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

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3 0
2 years ago
HELP ASAP!! WILL MARK AS BRAINLIEST IF ANSWERED NOW!!!!
tiny-mole [99]

Answer: She should blend 98 lbs of high-quality beans.

She should blend 72 lbs of cheaper beans

Step-by-step explanation:

Let x represent the number of pounds of high quality beans that she should blend.

Let y represent the number of pounds of cheaper beans that she should blend.

She needs to prepare 170 lbs of blended coffee beans. This means that

x + y = 170

She plans to do this by blending together a high-quality bean costing $4.75 per pound and a cheaper bean at $2.00 per pound. The blend would sell for $3.59 per pound. This means that the total cost of the blend would be 3.59×170 = $610.3. This means that

4.75x + 2y = 610.3 - - - - - - - - - -1

Substituting x = 170 - y into equation 1, it becomes

4.75(170 - y) + 2y = 610.3

807.5 - 4.75y + 2y = 610.3

- 4.75y + 2y = 610.3 - 807.5

- 2.75y = - 197.2

y = - 197.2/-2.75 = 71.9

y = 72 pounds

x = 170 - y = 170 - 71.9

x = 98.1

x = 98 pounds

4 0
3 years ago
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