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3 years ago

How do you work out 5/6y-2=8

2 answers:

6 0

$\frac{5}{6} y - 2 = 8 \\ \\ \frac{5y}{6} - 2 = 8 \ / \ simplify \\ \\ \frac{5y}{6} = 8 + 2 \ / \ add \ 2 \ to \ each \ side \\ \\ \frac{5y}{6} = 10 \ / \ simplify \\ \\ 5y = 10 \times 6 \ / \ multiply \ each \ side \ by \ 6 \\ \\ 5y = 60 \ / \ simplify \\ \\ y = \frac{60}{5} \ / \ divide \ each \ side \ by \ 5 \\ \\ y = 12 \ / \ simplify \\ \\$

The final answer is y = 12.

aliya0001 [1]3 years ago

3 0

5/6y-2=8
+2 +2
Add the reciprocal to cancel out the twos andd 8+2=10
so you have left 5/6y=10 and you'll take the reciprocal of 5 divided by 6 times five and cancels the 5/ out and also multiply 10*5 and you're left with 6y=50 then you just divide by six and there you go you have y=12

hope this helped

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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

Jerry’s loan had a principal of $22,000. He made quarterly payments of $640 for nine years until the loan was paid in full. How

Leto [7]

Answer: $1040

A = P + I

A = Total

P = Principal

I = Interest

First find the total amount

A = 640(4)(9)

A = 23040

Plug In the Numbers

23040 = 22000 + I

Substract 22000 on both sides

I = $1040

8 0

3 years ago

A family goes out to eat. The meal costs $44. The sales tax rate is 9%. They leave a 20% tip. How much did they spend?

REY [17]

Answer:

$56.76

Step-by-step explanation:

$56.76 because 20% of 44 is 8.80 which is the tip and 9% of 44 is 3.96 which is the tax rate giving you an answer of $56.76. Hope this helps!

6 0

3 years ago

Bakery has bought 250 pounds of muffin dough. They want to make waffles or muffins in half-dozen packs out of it. Half a dozen o

Alexus [3.1K]

Answer:

250 batches of muffins and 0 waffles.

Step-by-step explanation:

-1

If we denote the number of batches of muffins as "a" and the number of batches of waffles as "b," we are then supposed to maximize the profit function

P = 2a + 1.5b

subject to the following constraints: a>=0, b>=0, a + (3/4)b <= 250, and 3a + 6b <= 1200. The third constraint can be rewritten as 4a + 3b <= 1000.

Use the simplex method on these coefficients, and you should find the maximum profit to be $500 when a = 250 and b = 0. So, make 250 batches of muffins, no waffles.

You use up all the dough, have 450 minutes left, and have $500 profit, the maximum amount.

6 0

3 years ago

1 - 2/4=?????<br>I forgot how too do these T-T

Tema [17]

Answer:

1/2

Step-by-step explanation:

you can simply the fraction making it 1/2 and 1 - 1/2 = 1/2

3 0

2 years ago

Read 2 more answers