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3 years ago

How would I solve 8 over 3 equals 24 over x

2 answers:

8 0

8 over 3 equals 24 over x can be written down as:

8/3 = 24/x

So now:

8/3 = 24/x / * 3 (both sides)
8 = 72/x / * x (both sides)
8x = 72 / ÷ 8 (both sides)
x = 9

Furkat [3]3 years ago

6 0

8 = 24
3 x

Its a proportion, so you cross multiply the 3 and the 24, then divide by 8.

3 × 24 = 72

72 ÷ 8 = 9

Your final answer is:

x = 9

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3 years ago

hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

1 year ago

A construction worker bought several bottles of juice for $3 at the comedian store she paid for them the $20 bills if J represen

irina [24]

Expression 20 – 3J represents the change in dollars, which construction worker will receive after buying J bottles of juice.

Solution:

Given that

A construction worker bought several bottles of juice for $3 at the comedian store

She paid for them the $20 bills

Number of bottles of juice is represented by variable J

Need to write an expression for the change she receives.

From given information

Price of 1 juice bottle = $3

$\text { So price of J juice bottles }=\mathrm{J} \times \text { Price of } 1 \text { juice bottle }$

$=\mathrm{J} \times 3=3 \mathrm{J}$

Change she receives = Amount she paid - price of J juice bottles

=> Change she receives = 20 – 3J

Hence expression 20 – 3J represents the change in dollars, which construction worker will receive after buying J bottles of juice.

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4 years ago