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
Kyle wants to make $10,000 in gift cards. Each gift card is worth $100 and costs 1,200,000 in points. How many points does Kyle
OleMash [197]
Kyle needs 100 $100 gift cards to reach $10,000 in gift cards (100x100=10,000). Each gift card is 1,200,000 points so 100x1,200,000=120,000,000. Kyle needs 120,000,000 points to make $10,000 worth of gift cards.
6 0
3 years ago
The solution set of a linear system whose augmented matrix is [a b c d] is the same as the solution set of Ax = d, where A = [a
Charra [1.4K]

Answer:

True

Step-by-step explanation:

First statement

[a b c | d][x]

[a b c]x=d

ax+bx+cx=d

Second statement

Ax=d

Given that A = [a b c]

[a b c]x=d

ax+bx+cx=d

ax+bx+cx=d

Then, they are going to have the same solutions

6 0
3 years ago
If U = the set of odd natural numbers and B = {13, 15, 17, 19, 21, 23, . . .}, find B′.
Yuki888 [10]

Answer:

{1,3,5,7,9,11}

Step-by-step explanation:

B' stands for the complement of B.

B' means set elements in the universe that aren't in B.

Here is the universe:

U={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,...}

(The dots mean it continues with that pattern forever and ever.)

And the elements we taking out:

B={13,15,17,19,21,23,...}

So we taking out the odd numbers from U that are odd and greater than or equal to 13. (The dots mean it continues with that pattern forever and ever.)

So B' is the set of natural odd numbers that are less than 13:

{1,3,5,7,9,11}

8 0
3 years ago
Read 2 more answers
good morning :) The rental car holds 22 gallons of gas and gets 20 miles per gallon. The trip to Ellis City is 1760 miles. How m
Effectus [21]
1760/ 20 = 88
88/22 = 4
answer = 4
6 0
3 years ago
Find the slope of the line through the points (6,16) and (−6,4)
MakcuM [25]

m = \frac{y2-y1}{x2-x1}

m = \frac{4-16}{-6-6} \\m = \frac{-12}{-12} \\\\m = 1

Therefore, the slope of the line is 1. In case if you want to know the equation.

y=mx+b\\y=x+b\\4=-6+b\\4+6=b\\10=b\\

Therefore, the equation is y=x+10 by substituting the (-6,4) or we can substitute (6,16) too.

y=mx+b\\y=x+b\\16=6+b\\16-6=b\\10=b\\

It's the same, you can use any orders given.

Overall, the slope is 1 and the equation is y=x+10

3 0
3 years ago
Other questions:
  • Determine weather the algebraic expression is linear expression explain
    15·1 answer
  • Geoffrey is a lab technician and earns $9.65 per hour and works 40 hours a week. Estimate Geoffrey s annual wages, based on 50 w
    5·1 answer
  • How do I calculate this? Is there a formula?
    6·2 answers
  • The algebraic expression for​ "the quotient of 77 and​ x" is
    10·1 answer
  • The top speed of a coyote is 43 miles per hour. find approximate spee in kilometer per minute
    14·1 answer
  • What is the slope of the line that passes through the points (3, 8) and (8, 13) ?(
    11·1 answer
  • 6th grade math help me pozzzz
    8·1 answer
  • Write two different expressions to represent the sale price of a fishing pole, f, after a 20% discount.
    8·1 answer
  • Someone please help me, write a variable equation to represent the situation, and solve it by using inverse operations.
    8·1 answer
  • PLSS HELP IF YOU TURLY KNOW THISS :)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!