1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marshall27 [118]
3 years ago
14

Suppose that $p$ and $q$ are positive numbers for which \[\log_9 p = \log_{12} q = \log_{16} (p + q).\] what is the value of $q/

p$?
Mathematics
1 answer:
SVEN [57.7K]3 years ago
3 0

Given p,q>0 and \log_9p=\log_{12}q=\log_{16}(p+q)=x (say).

Then,

p=9^x\\ q=12^x\\ p+q=16^x

From the above 3 equations,

\frac{q}{p} =(\frac{12}{9} )^x\\ \frac{q}{p} =(\frac{4}{3} )^x\\ \frac{p+q}{p} =(\frac{16}{9} )^x\\ \frac{p+q}{p} =(\frac{4}{3} )^{2x}\\

From the equations, we get

\frac{p+q}{p}=(\frac{q}{p})^2\\ 1+\frac{q}{p}=(\frac{q}{p})^2\\ (\frac{q}{p})^2-\frac{q}{p}-1=0\\ \frac{q}{p}=\frac{1 \pm \sqrt{5}}{2}

Since p,q>0, the negative value is rejected.

\frac{q}{p}=\frac{1 + \sqrt{5}}{2}

You might be interested in
Please help!
olchik [2.2K]
The tax is $1.253 hope this helps!
3 0
3 years ago
Read 2 more answers
I need helpppppp asap
user100 [1]

Answer:

graph A

Step-by-step explanation:

When looking at a graph, there are two different axes. The vertical values--marked by the center up/down line--are "y-values"; and this is called the "y-axis"

The horizontal values--marked by the left/right line--are "x-values"; and this is called the "x-axis"

For the x-axis, values to the left side of the origin (the place where the y-axis and x-axis intercept) are smaller than 0--they are all negative values.

Values to the right side of the origin are positive--greater than 0.

For the y-axis, positive numbers are on the top half [once again, the midpoint / 0 is where the two lines are both = to 0; the origin] and negative numbers are on the bottom half.

Ordered pairs (points) are written as (x,y)

(x-value, y-value)

We are looking for a graph that decreases (along the y-axis), hits a point below the origin, and goes flat/stays constant.

When a graph is decreasing (note: we read graphs from left to right), the line of the graph is slanted downwards (it looks like a line going down).

So, if we look at the graphs, we can see Graph A descending, crossing the y-axis {crossing the middle line /vertical line / y-axis} at a value of -7, and then staying constant (it is no longer increasing or decreasing because the y-values stay the same)

hope this helps!!

4 0
1 year ago
In each figure below, find m<1 and m<2 if a is parallel to b. You don't have to show work.
Gekata [30.6K]

Answer:

m <5 = 71 degrees.

m <8 = 109 degrees.

5 0
3 years ago
if a person earns $2600 in 4 weeks, how much can the person earn in 20 weeks at the same rate of pay?
AlladinOne [14]

Howdy!

To do this we first have to find the unit rate of 2,600.

2,600/4=650 each week. Then, we just multiply 650x20, with 20 being the number of weeks.

650x20=13,000<---Answer

-Seth

4 0
2 years ago
PLEASE HELP!!! I NEED HELP ASAP!!! &lt;333
Olegator [25]

Answer:

Step-by-step explanation:

Divide: 3/13 = 3 ÷ 13

3/13 = 0.230769230769...

B) is your answer

~

6 0
2 years ago
Read 2 more answers
Other questions:
  • Round 55.983 to the nearest hundredth.
    15·2 answers
  • Find Sn for the arithmetic series 5+7+9 + … and determine the value of n for which the series has sum 165.
    6·1 answer
  • PleaseI really need help on this please
    10·2 answers
  • the company needs to know how many books will fit into one box.Each book's cover has an area of 25 1/8 square inches. Each books
    10·1 answer
  • Michael has $1,082.99 in his checking account. He is going to spend $507 43 on a new television, and he will spend the rest on
    6·1 answer
  • Expand the linear expression 4(10x-4 )
    12·2 answers
  • Question in the picture ​
    15·1 answer
  • Pls help will give brainilist
    9·2 answers
  • Find the amount A accumulated after investing $4800 for 17 years at an interest rate 6.2% compounded quarterly.​
    15·1 answer
  • Determine if true:<br> 2x6-3=10
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!