42. using midpoints in the diagram below, b is the mid - point of $overline{ac}$, $ab = 9$, and $ad = 25$. find $cd$.
43. challenge the mid - point of $overline{ab}$ is $m(7,5)$. the coordinates of point a are $(4,1)$. find the coordinates of point b. explain.
44. multiple choice t is the mid - point of $overline{qr}$. what is the value of x? a 17 b 22 c 29.5 d 88
45. multiple choice what is the mid - point of the segment joining $(2,7)$ and $(-6,2)$? f $(-2,\frac{9}{2})$ g $(-4,9)$ h $(-2,4)$ j $(\frac{9}{2},-2)$
mixed review evaluating statements use the diagram at the right to determine whether the statement is true or false. (lessons 1.3, 1.5)
46. point a lies on line m.
47. point e lies on line l.
48. points b, e, and c are collinear.
49. lines l and m intersect at point e.
50. point e is between points b and c.
51. point f is between points a and b.
classifying angles name the vertex and sides of the angle. then state whether it appears to be acute, right, obtuse, or straight. (lesson 1.6)
52.
53.
54.
algebra skills evaluating expressions evaluate the expression. (skills review, p. 670)
55. $2cdot15 + 40$
56. $120-35cdot3$
57. $\frac{1}{2}cdot50 + 145$
58. $\frac{5}{4}cdot16 - 20$
59. $6 + 3cdot5-2$
60. $11cdot4 + 7-20$
61. $12cdot2-3cdot4$
62. $5-10cdot6 + 1$
63. $2-(3 + 4)cdot5$

Question

Accepted Answer

### 42.
# Explanation:
## Step1: Use mid - point property
Since $B$ is the mid - point of $\overline{AC}$, then $AB = BC$. Given $AB = 9$, so $BC=9$.
## Step2: Calculate $CD$
We know that $AD = 25$, and $AD=AB + BC+CD$. Substituting the known values: $25=9 + 9+CD$. Then $CD=25-(9 + 9)=7$.
# Answer:
$7$

### 43.
Let the coordinates of point $B$ be $(x,y)$. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
We have $x_1 = 4,y_1 = 1$ and $M(7,5)$.
For the $x$ - coordinate of the mid - point: $\frac{4 + x}{2}=7$, then $4+x = 14$, and $x = 10$.
For the $y$ - coordinate of the mid - point: $\frac{1 + y}{2}=5$, then $1 + y=10$, and $y = 9$.
So the coordinates of point $B$ are $(10,9)$.

### 44.
# Explanation:
## Step1: Use mid - point property
Since $T$ is the mid - point of $\overline{QR}$, then $QT=TR$. So $4x-10 = 78$.
## Step2: Solve for $x$
Add $10$ to both sides of the equation: $4x=78 + 10=88$. Then divide both sides by $4$: $x = 22$.
# Answer:
B. $22$

### 45.
# Explanation:
## Step1: Recall mid - point formula
The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1+x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1 = 2,y_1 = 7,x_2=-6,y_2 = 2$.
## Step2: Calculate the mid - point
For the $x$ - coordinate: $\frac{2+( - 6)}{2}=\frac{2 - 6}{2}=-2$. For the $y$ - coordinate: $\frac{7 + 2}{2}=\frac{9}{2}$.
# Answer:
F. $(-2,\frac{9}{2})$

### 46 - 51
# Explanation:
## 46
By observing the diagram, point $A$ lies on line $l$ not line $m$, so the statement "Point $A$ lies on line $m$" is false.
## 47
By observing the diagram, point $E$ lies on line $l$, so the statement "Point $E$ lies on line $l$" is true.
## 48
Points $B$, $E$, and $C$ are not on the same straight line, so the statement "Points $B$, $E$, and $C$ are collinear" is false.
## 49
Lines $l$ and $m$ intersect at point $E$, so the statement "Lines $l$ and $m$ intersect at point $E$" is true.
## 50
Point $E$ is not between points $B$ and $C$, so the statement "Point $E$ is between points $B$ and $C$" is false.
## 51
Point $F$ is between points $A$ and $B$, so the statement "Point $F$ is between points $A$ and $B$" is true.
# Answer:
46. False
47. True
48. False
49. True
50. False
51. True

### 52
The vertex of $\angle ABC$ is $B$, and the sides are $\overrightarrow{BA}$ and $\overrightarrow{BC}$. It appears to be an acute angle (less than $90^{\circ}$).

### 53
The vertex of $\angle JKL$ is $K$, and the sides are $\overrightarrow{KJ}$ and $\overrightarrow{KL}$. It appears to be an obtuse angle (greater than $90^{\circ}$ and less than $180^{\circ}$).

### 54
The vertex of $\angle QPR$ is $P$, and the sides are $\overrightarrow{PQ}$ and $\overrightarrow{PR}$. It appears to be an acute angle (less than $90^{\circ}$).

### 55 - 63
## 55
# Explanation:
## Step1: Multiply first
$2\times15 = 30$.
## Step2: Add
$30 + 40=70$.
# Answer:
$70$

## 56
# Explanation:
## Step1: Multiply first
$35\times3 = 105$.
## Step2: Subtract
$120-105 = 15$.
# Answer:
$15$

## 57
# Explanation:
## Step1: Multiply first
$\frac{1}{2}\times50 = 25$.
## Step2: Add
$25+145 = 170$.
# Answer:
$170$

## 58
# Explanation:
## Step1: Multiply first
$\frac{5}{4}\times16=20$.
## Step2: Subtract
$20 - 20=0$.
# Answer:
$0$

## 59
# Explanation:
## Step1: Multiply first
$3\times5 = 15$.
## Step2: Add and subtract in order
$6+15 - 2=19$.
# Answer:
$19$

## 60
# Explanation:
## Step1: Multiply first
$11\times4 = 44$.
## Step2: Add and subtract in order
$44+7 - 20=31$.
# Answer:
$31$

## 61
# Explanation:
## Step1: Multiply first
$12\times2 = 24$ and $3\times4 = 12$.
## Step2: Subtract
$24-12 = 12$.
# Answer:
$12$

## 62
# Explanation:
## Step1: Multiply first
$10\times6 = 60$.
## Step2: Add and subtract in order
$5-60 + 1=-54$.
# Answer:
$-54$

## 63
# Explanation:
## Step1: Calculate the sum in parentheses
$3 + 4=7$.
## Step2: Multiply
$7\times5 = 35$.
## Step3: Subtract
$2-35=-33$.
# Answer:
$-33$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

42.

Step1: Use mid - point property

Step2: Calculate \(CD\)

Step1: Use mid - point property

Step2: Solve for \(x\)

Step1: Recall mid - point formula

Step2: Calculate the mid - point

Answer:

43.

44.