Question

1. in the figure, x:y = 2:3 and y:z = 3:5. if x = 10, find the value of z. 52. gridded response a race - car driver records the finishing times for recent practice trials. what is the mean time, in seconds, for the trials? table: trial 1 - 5.09, trial 2 - 5.10, trial 3 - 4.95, trial 4 - 4.91, trial 5 - 5.05 53. geometry if △lmn is similar to △lpo, what is z? figure with angles and triangles 54. which equation below illustrates the commutative property? a (3x + 4y)+2z = 3x+(4y + 2z) b 7(x + y)=7x + 7y c xyz = yxz d x + 0 = x 55. |x + 5|=-8 56. |b + 9|=2 57. |2p - 3|=17 58. |5c - 8|=12

Explanation:

Step1: Solve 51

Given $x = 10$, $x:y=2:3$ so $y=\frac{3}{2}x = 15$. And $y:z = 3:5$, then $z=\frac{5}{3}y = 25$.

Step2: Solve 52

Mean formula: $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 5$, $\sum_{i=1}^{5}x_{i}=5.09 + 5.10+4.95 + 4.91+5.05=25.1$. Mean is $\frac{25.1}{5}=5.02$.

Step3: Solve 54

The commutative property for addition is $a + b=b + a$. For $(3x + 4y)+2z=3x+(4y + 2z)$ it's the associative - property of addition, $7(x + y)=7x+7y$ is the distributive property, $xyz = yxz$ shows the commutative property of multiplication.

Step4: Solve 55

$|x + 5|=-8$. Since absolute - value is non - negative, there is no solution.

Step5: Solve 56

$|b + 9|=2$, then $b+9 = 2$ or $b + 9=-2$. So $b=-7$ or $b=-11$.

Step6: Solve 57

$|2p-3| = 17$, then $2p-3=17$ or $2p - 3=-17$. For $2p-3 = 17$, $2p=20$, $p = 10$; for $2p-3=-17$, $2p=-14$, $p=-7$.

Step7: Solve 58

$|5c-8| = 12$, then $5c-8 = 12$ or $5c-8=-12$. For $5c-8 = 12$, $5c=20$, $c = 4$; for $5c-8=-12$, $5c=-4$, $c=-\frac{4}{5}$.

Answer:

1. $z = 25$
2. $5.02$
3. B. $xyz = yxz$
4. No solution
5. $b=-7$ or $b=-11$
6. $p = 10$ or $p=-7$
7. $c = 4$ or $c=-\frac{4}{5}$