Pq=6x+25 and qr=16-3x; find pr

Mathematics

2 answers:

Svet_ta [12.7K]2 months ago

8 0

Answer:

PR equals 3x plus 41

Detailed solution:

We start with

PQ = 6x + 25

QR = 16 - 3x

Since Q lies between P and R, the segment PR is composed of PQ plus QR.

Therefore, we write

PR = PQ + QR

PR = (6x + 25) + (16 - 3x)

PR = 6x minus 3x plus 25 plus 16

PR = 3x + 41

Thus, PR equals 3x plus 41

Zina [12.3K]2 months ago

3 0

$Given:\\\overline{PQ}=6x+25\\\overline{QR}=16-3x\\\\Finding:\overline{PR}$

$If \; Q \; is \; a \; point \; in \; between \; the \; line \; segment \; \overline{PR}, \; \\ then \; the \; distance \; of \; line \; segment \; \overline{PR} \; \\ can \; be \; found \; by \; adding \; line \; segment \; \overline{PQ} \; and \; \overline{QR}.$

$Using \; the \; concept \; \overline{PQ}+\overline{QR}=\overline{PR} \;,\\ we \; need \; to \; set \; up \; an \; equation \; given \; below:$

$\overline{PR} =6x+25 +16-3x\\\\Step \; 1: Grouping \; Like \; Terms\\\overline{PR} =6x-3x+25 +16\\\\Step \; 2: Combining \; Like \; Terms\\\overline{PR} =3x+41$

Заключение:

$\overline{PR} \; is \; represented \; the \; expression \; 3x +41$

24

Step-by-step explanation:

Based on the logarithmic expressions given $log_ax = 3, log_ay = 7, log_az = -2$ , we need to identify the value of $log_a(\frac{x^3y}{z^4} )$

$from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}$ By substituting x = a³, y = a⁷, and z = a⁻² into the logarithmic function $log_a(\frac{x^3y}{z^4} )$ , we will derive;

$= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24$