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Yuri [45]
3 years ago
15

Can 5 qt 1 pt of fruit punch and 3 qt 1pt of ginger ale be poured into a 2 gal container with out it over flowing

Mathematics
1 answer:
vlada-n [284]3 years ago
3 0

Answer:

No

Step-by-step explanation:

5qt+3qt=2 gallon already

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In the equation, y = 4k, identify the dependent and independent variables
ivolga24 [154]
Y is the independent variables
k is the dependent variable
5 0
2 years ago
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
Which of the following lists does not include all the factors of the number?
Sever21 [200]
The Answer is 21 because 7 and 3 can go in it as well
4 0
2 years ago
A piece of metal is cut in the shape of a triangle what is the area of the piece of metal
Kruka [31]
It depends on which triangle it actually is
3 0
3 years ago
Choose the point-slope form of the equation below that represents the line that passes through the point (−1, 6) and has a slope
IrinaVladis [17]

Answer:

The correct answer is option B.

Step-by-step explanation:

Two point form of the equation:

(y-y_1)=\frac{y_2-y_1}{x_2-x_1}\times (x-x_1)

\frac{y_2-y_1}{x_2-x_1}=Slope=m

(y-y_1)=m\times (x-x_1)

A line passing through the point (-1,6) with slope ,m = -3.

The equation of the line will be:

y-6=(-3)(x-(-1))=(-3)(x+1)

Hence, the correct answer is option B.

3 0
2 years ago
Read 2 more answers
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