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alukav5142 [94]
2 years ago
11

Translate this sentence into an equation. 39 is the product of Hector's height and 3. Use the variable h to represent Hector's h

eight.
Mathematics
1 answer:
gladu [14]2 years ago
7 0

Answer:

3h=39

Step-by-step explanation:

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What is the best description of a quadrilateral with four right angles?
lisov135 [29]

Square would be the best answer

7 0
3 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
A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than
alisha [4.7K]

The equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D

<h3>How to determine the equation</h3>

Let the number of rows be x

Number of cars in each row = x - 6 = 56

Number of rows for parking lot = 2x

Then,

Number of cars for new parking lot = 2x ( x - 6 = 56)

Expand the expression,

2 ( x - 6 = 56)

2x² - 12x = 112

Thus, the equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D

Learn more about word problems here:

brainly.com/question/1781657

#SPJ1

7 0
1 year ago
If the standard deviation of a data set was originally 8, and if each value in the data set was multiplied by 8.5, what would be
maxonik [38]

Answer:

D. 68 (APEX).........................................................................................

6 0
3 years ago
A jar contains $14.25 in quarters and dimes. There are 75 coins in the jar. Find the number of quarters in the jar.
Marianna [84]
Set up a system of equations.
d + q = 75
.1d + .25q = 14.25

Multiply the first equation by -.1 so that the "d's" will cancel.
-.1d -.1q = -7.5
.1d +.25q = 14.25
Now add the two equations together
      .15q = 6.75
divide both sides by .15
        q = 45
There are 45 quarters in the jar
8 0
3 years ago
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