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
Convert 53 yards per hour into inches per day
marin [14]

1 yard = 36 inches.

53 yards per hour x 36 inches per yard = 1908 inches per hour.

1 day = 24 hours.

1908 inches per hour x 24 hours = 45,792 inches per day.

4 0
3 years ago
Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic
lidiya [134]

Answer: A

Step-by-step explanation:

The first thing we need to do is to make sure our equation is in standard form. The given equation is not in standard form.

3x²-2x=0

Now that the equation is in standard form, we can find our A, B, C to see which quadratic equation is correct.

A=3

B=-2

C=0

We can automatically eliminate D because the first value is -3 when it is supposed to be -(-2). Also, the denominator is supposed to be 2a. We know that A=3. The denominator should be 2(3), not 2(-2).

Next, we can eliminate B and C. For the 4ac, we know it has to be 4(3)(0) because A=3 and C=0. B and C have given 4(3)(2) and 4(3)(1), respectively. This does not match A=3 and C=0.

Therefore, A is the correct answer.

4 0
3 years ago
Which size can of green beans shown in the table has the lowest unit price?
posledela
The can of green beans that has the lowest unit price is the 8 oz. size.

To find the unit price of each size, divide the cost by the size. (A number below that's in parentheses means it goes on forever)

0.89 ÷ 6 = 0.148(3)
1.04 ÷ 8 = 0.13
1.69 ÷ 10 = 0.169
4.79 ÷ 32 = 1496875
Among all of these answers, the can with 8 oz. has the least unit price/rate. Thus, this is the answer. 

3 0
3 years ago
Emmanuel bought 28 lb of potting soil this week. This amount is 4 lb more than twice the amount of potting soil he bought last w
hammer [34]
He bought 60 pounds last week and p stands for 60
5 0
3 years ago
How to subtract percentages that are fractions
natali 33 [55]
"you can convert the percent to a fraction or decimal. While you might need to subtract a percent from a percent when working in finance, if you are working on homework you more likely will come across problems where you need to subtract a percent from a whole number."
8 0
3 years ago
Other questions:
  • X=-3y-5 3x+9y=7 how can u solve this?
    10·2 answers
  • Please help 30 points Really hard mulitiquestions
    7·1 answer
  • Solve 5/8-17/8 and show work
    15·1 answer
  • $100 is deposited at the end of every week for five years in an account that pays 14%/an, compounded weekly. (8) What type of an
    15·1 answer
  • If the Volume of a Cone is 37.68inº and height is 9in, what is the diameter?
    13·1 answer
  • A baby’s weight increases by 8% over a month from birth to 4.05kg, what is the weight at birth?
    12·2 answers
  • Beverly bought a roll of 10 yards of ribbon.
    9·1 answer
  • Could i have some super super quick help? :(( (part iv is not necessary)
    9·2 answers
  • For one binomial experiment, n1 = 75 binomial trials produced r1 = 30 successes. For a second independent binomial experiment, n
    8·1 answer
  • A house on the market was valued at $245,000. After several years, the value increased by 9%. By how much did the house's value
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!