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3 years ago

What is the solution to this equation 3(80 - 9x) = x - 96

Mathematics

2 answers:

NISA [10]3 years ago

5 0

X=12

Multiply the parentheses into 3 so it becomes

240-27x=x-96

And continue the problem like normal collecting the like terms making it

-27x-x=-96-240

Then calculate the terms and divide both sides by -28

andreev551 [17]3 years ago

3 0

240-27x = x-96

240 - 28x = -96

28x = 336

x = 12

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Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

creativ13 [48]

So hmm check the picture below

we know the vertex is at the origin, and the focus point is below it, that means two things, the parabola is vertical and it's opening downwards

notice the distance "p", from the vertex to the focus point, is just 7 units, however, since the parabola is opening downwards, the "p" value will be negative, so p = -7

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{4{{ p}}(y-{{ k}})=(x-{{ h}})^2 }\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
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h=0\\
k=0\\
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3 years ago

A hardware store clerk mixed nuts worth $1.32 per kilogram with bolts worth $1.20 per kilogram. If he made 108 kilograms of a mi

AlladinOne [14]

Answer:

the way to work these types of problems is to create a table. The table will have three rows and three columns.

The table:

Let x represent the kilograms of nuts, then 138 - x will represent the kilograms of bolts.

Product Amount Cost Total

--------------------------------------------------------

Nuts x .60 .60 * x

Bolts 138 - x .66 .66 * (138 - x)

Mix 138 .65 .65 * (138)

Step-by-step explanation:

The equation:

The nuts plus the bolts must equal the mix or:

.60 * x + .66 * (138 - x) = .65 * 138

I do not like to work with decimals, so multiply each term by 100:

60 * x + 66 * (138 - x) = 65 * 138

Remove the parenthesis and combine like terms:

-6x = -66 * 138 + 65 * 138

-6x = -138

Divide both sides by -6:

x = 23

Solution:

The mixture contains 23 kilograms of nuts.

The mixture contains 138 - 23, or 115 kilograms of bolts.

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