Please help!

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/

SVEN [57.7K]

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.

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

3 0

4 years ago

At a storage company, items are stored in containers that have a base of 5 1/2 yds by 1 2/3 yds. If there is a 3 x 3 array of th

blondinia [14]

Answer:

68.70 yd.

Step-by-step explanation:

First we would convert these into decimals. 5 1/2 would turn into 5.50, and 1 2/3 is 1.66.

(1.66 yd.) * 5.50 yd. =

7.6338428 yd.

7.6338428 yd.*3*3=

= 68.7045852 yd.

shorten the decimal for a shorter, less accurate answer.

8 0

2 years ago

The field hockey coach is purchasing new uniforms for the team. Company A charges a one-time printing fee of $100 and $12 per un

CaHeK987 [17]

$100 - $61
$39 (how much you need for the price to become equal)
$15 - $12
$3 (how much cheaper it is per uniform)
$39/$3
13 uniforms is where it is equal
14 uniforms is where it is a better deal

8 0

3 years ago

FIRST ONE TO ANSWER WINS BRAINLIEST (ANSWER THE RED) PLS

Troyanec [42]

Answer:

Ok so Preston has 0.5 hags of mulch for each square yard on the first one and the second one is 1 yard per

Step-by-step explanation:

8 0

3 years ago

CAN SOMEONE PLEASE HELP ME!! MUCH APPRECIATED

salantis [7]

Answer:

9x² -15x +1

Step-by-step explanation:

The area can be figured as the difference of the enclosing rectangle area ((3x-2)×(4x-1)) and the area of the white space at the lower left (horizontal dimension x+1).

The vertical dimension of the white space at lower left is The difference of the given vertical dimensions:

(4x -1) -(x -2) = 3x +1

So, the area of the figure is ...

(3x -2)(4x -1) -(x +1)(3x +1)

= (12x² -3x -8x +2) -(3x² +x +3x +1) . . . . "FOIL" each product

= 12x² -3x -8x +2 -3x² -x -3x -1 . . . . . eliminate parentheses

= x²(12 -3) +x(-3-8-1-3) +(2-1)

= 9x² -15x +1

_____

<em>Comment on products of binomials</em>

The product of any polynomial with any other can be found using the distributive property repeatedly. When both polynomials are <em>binomials</em>, a mnemonic can help you make sure all product terms are included.

(a +b)(c +d) = a(c +d) + b(c +d) . . . . use the distributive property to eliminate the first set of parentheses

= ac +ad +bc +bd . . . . . . . . . . . . . . use the distributive property to eliminate remaining parentheses

You will notice that the final product is the sum of the terms ...

ac . . . product of First terms of the binomials

ad . . . product of Outer terms of the expression

bc . . . product of Inner terms of the expression

bd . . . product of Last terms of the binomials

The letters of these descriptive words form the mnemonic FOIL, which is sometimes used as a verb (as above: FOIL each product).

8 0

3 years ago