Question

the box plots summarize the masses, in kilograms, of two groups of gazelles. based on the box plots, which of the following statements must be true? a. the mean mass of group 1 is greater than the mean mass of group 2. b. the mean mass of group 1 is less than the mean mass of group 2. c. the median mass of group 1 is greater than the median mass of group 2. d. the median mass of group 1 is less than the median mass of group 2. unit 4/8/12 advanced algebra (no quadratics since that was sum#2) #8 equivalent expressions if p = 3x + 4 and v = x + 5, which of the following is equivalent to pv - 2p + v? a. 3x²+12x + 7 b. 3x²+14x + 17 c. 3x²+19x + 20 d. 3x²+26x + 33 #9 equivalent expressions which expression is equivalent to (\frac{8x(x - 7)-3(x - 7)}{2x - 14}), where x > 7? a. (\frac{x - 7}{5}) b. (\frac{8x - 3}{2}) c. (\frac{8x^{2}-3x - 14}{2x - 14}) d. (\frac{8x^{2}-3x - 77}{2x - 14}) #10systems x = 49 y=(sqrt{x}+9) the graphs of the given equations intersect at the point (x, y) in the xy - plane. what is the value of y? a 10 b 40 c 81 d 130 #11 equivalent which of the following is equivalent to the expression (x^{4}-x^{2}-6)? a. ((x^{2}+1)(x^{2}-6)) b ((x^{2}+2)(x^{2}-3)) c ((x^{2}+3)(x^{2}-2)) d ((x^{2}+6)(x^{2}-1)) #12 equivalent 7m = 5(n + p) the given equation relates to the positive numbers m, n, p. which equation correctly gives n in terms of m and p? a. (n=\frac{5p}{7m}) b. (n=\frac{7m}{5}-p) c (n = 5(7m)+p) d (n = 7m - 5 - p)

Explanation:

Step1: Solve #8

Substitute \(p = 3x + 4\) and \(v=x + 5\) into \(pv-2p + v\).
\[

$$\begin{align*} pv-2p + v&=(3x + 4)(x + 5)-2(3x + 4)+(x + 5)\\ &=(3x^2+15x+4x + 20)-(6x + 8)+(x + 5)\\ &=3x^2+19x+20-6x - 8+x + 5\\ &=3x^2+(19x-6x+x)+(20 - 8+5)\\ &=3x^2+14x + 17 \end{align*}$$

\]

Step2: Solve #9

Factor out \((x - 7)\) from the numerator of \(\frac{8x(x - 7)-3(x - 7)}{2x-14}\).
\[

$$\begin{align*} \frac{8x(x - 7)-3(x - 7)}{2x-14}&=\frac{(x - 7)(8x - 3)}{2(x - 7)}\\ &=\frac{8x-3}{2} \end{align*}$$

\]

Step3: Solve #10

Given \(x = 49\) and \(y=\sqrt{x}+9\), substitute \(x = 49\) into the equation for \(y\).
\[y=\sqrt{49}+9=7 + 9=16\]

Step4: Solve #11

Let \(u=x^2\), then \(x^4-x^2 - 6=u^2-u - 6\).
Factor \(u^2-u - 6=(u - 3)(u + 2)\).
Substitute back \(u=x^2\), we get \((x^2+2)(x^2 - 3)\).

Step5: Solve #12

Starting with \(7m=5(n + p)\), first distribute the 5 on the right - hand side: \(7m=5n+5p\).
Then isolate \(n\): \(5n=7m - 5p\), so \(n=\frac{7m}{5}-p\).

Answer:

#8: B. \(3x^2+14x + 17\)
#9: B. \(\frac{8x-3}{2}\)
#10: 16
#11: B. \((x^2+2)(x^2 - 3)\)
#12: B. \(n=\frac{7m}{5}-p\)