8. a dilation with scale factor ( k = 3 ) is applied to point ( (2, 1) ). the new coordinates are:
a. ( (6, 3) )
b. ( (5, 2) )
c. ( (4, 2) )
d. ( (3, 2) )
9. simplify ( sqrt{98} )
a. ( 7sqrt{2} )
b. ( 2sqrt{49} )
c. ( sqrt{49} cdot sqrt{2} )
d. ( 7sqrt{3} )
10. in a two - way table, if 30 students play basketball and 20 play football, with 10 playing both, whats the probability of randomly selecting a student who plays only basketball?
a. ( \frac{1}{2} )
b. ( \frac{1}{3} )
c. ( \frac{1}{4} )
d. ( \frac{2}{5} )
11. a ( 90^{circ} ) counterclockwise rotation around the origin transforms ( (3, 4) ) to:
a. ( (-4, 3) )
b. ( (4, -3) )
c. ( (-3, -4) )
d. ( (4, 3) )
12. if ( sin heta=\frac{5}{13} ), what is ( cos heta )?
a. ( \frac{12}{13} )
b. ( \frac{13}{12} )
c. ( \frac{5}{12} )
d. ( \frac{12}{5} )
13. factor: ( 4x^{2}-36 )
a. ( 4(x + 3)(x - 3) )
b. ( 2(2x + 6)(x - 3) )
c. ( (2x + 6)(2x - 6) )
d. ( 4(x^{2}-9) )
14. the exterior angle of a triangle measures ( 140^{circ} ). if one interior angle is ( 55^{circ} ), what is another interior angle?
a. ( 75^{circ} )
b. ( 85^{circ} )
c. ( 65^{circ} )
d. ( 95^{circ} )

Question

8. a dilation with scale factor ( k = 3 ) is applied to point ( (2, 1) ). the new coordinates are:
 a. ( (6, 3) )
 b. ( (5, 2) )
 c. ( (4, 2) )
 d. ( (3, 2) )
9. simplify ( sqrt{98} )
 a. ( 7sqrt{2} )
 b. ( 2sqrt{49} )
 c. ( sqrt{49} cdot sqrt{2} )
 d. ( 7sqrt{3} )
10. in a two - way table, if 30 students play basketball and 20 play football, with 10 playing both, whats the probability of randomly selecting a student who plays only basketball?
 a. ( \frac{1}{2} )
 b. ( \frac{1}{3} )
 c. ( \frac{1}{4} )
 d. ( \frac{2}{5} )
11. a ( 90^{circ} ) counterclockwise rotation around the origin transforms ( (3, 4) ) to:
 a. ( (-4, 3) )
 b. ( (4, -3) )
 c. ( (-3, -4) )
 d. ( (4, 3) )
12. if ( sin	heta=\frac{5}{13} ), what is ( cos	heta )?
 a. ( \frac{12}{13} )
 b. ( \frac{13}{12} )
 c. ( \frac{5}{12} )
 d. ( \frac{12}{5} )
13. factor: ( 4x^{2}-36 )
 a. ( 4(x + 3)(x - 3) )
 b. ( 2(2x + 6)(x - 3) )
 c. ( (2x + 6)(2x - 6) )
 d. ( 4(x^{2}-9) )
14. the exterior angle of a triangle measures ( 140^{circ} ). if one interior angle is ( 55^{circ} ), what is another interior angle?
 a. ( 75^{circ} )
 b. ( 85^{circ} )
 c. ( 65^{circ} )
 d. ( 95^{circ} )

Accepted Answer

### Question 8
# Explanation:
## Step1: Recall dilation formula
For a dilation with scale factor $ k $, the new coordinates $(x', y')$ of a point $(x, y)$ are given by $ x' = kx $ and $ y' = ky $.
## Step2: Apply scale factor $ k = 3 $ to $(2, 1)$
$ x' = 3\times2 = 6 $, $ y' = 3\times1 = 3 $. So the new coordinates are $(6, 3)$.
# Answer:
a. $(6, 3)$

### Question 9
# Explanation:
## Step1: Factor 98
We know that $ 98 = 49\times2 $, where 49 is a perfect square.
## Step2: Simplify the square root
Using the property $ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b} $ ($ a\geq0, b\geq0 $), we have $ \sqrt{98}=\sqrt{49\times2}=\sqrt{49}\cdot\sqrt{2} = 7\sqrt{2} $.
# Answer:
a. $ 7\sqrt{2} $

### Question 10
# Explanation:
## Step1: Find number of only basketball players
Total basketball players = 30, both basketball and football = 10. So only basketball players = $ 30 - 10 = 20 $.
## Step2: Find total number of players
Using the principle of inclusion - exclusion, total players = basketball + football - both = $ 30 + 20 - 10 = 40 $.
## Step3: Calculate probability
Probability of only basketball = $ \frac{\text{only basketball}}{\text{total}}=\frac{20}{40}=\frac{1}{2} $? Wait, no, wait: Wait, 30 play basketball, 10 play both, so only basketball is $ 30 - 10 = 20 $. Total students: basketball (30) + football (20) - both (10) = 40. Wait, but the options: Wait, maybe I made a mistake. Wait, 30 play basketball, 10 play both, so only basketball is $ 30 - 10 = 20 $. Football only is $ 20 - 10 = 10 $. Total students: $ 20 + 10 + 10 = 40 $? Wait, no, the two - way table: the formula for total is $ n(B\cup F)=n(B)+n(F)-n(B\cap F)=30 + 20 - 10 = 40 $. The number of only basketball is $ n(B)-n(B\cap F)=30 - 10 = 20 $. So probability is $ \frac{20}{40}=\frac{1}{2} $? But let's check the options. Option a is $ \frac{1}{2} $. Wait, but let's re - check. Wait, 30 play basketball, 10 play both, so only basketball is 20. Total students: 30 (basketball) + 20 (football) - 10 (both) = 40. So probability is $ \frac{20}{40}=\frac{1}{2} $.
# Answer:
a. $ \frac{1}{2} $

### Question 11
# Explanation:
## Step1: Recall 90 - degree counterclockwise rotation rule
The rule for a $ 90^{\circ} $ counterclockwise rotation about the origin is $(x,y)\to(-y,x)$.
## Step2: Apply the rule to $(3,4)$
For the point $(3,4)$, $ x = 3 $, $ y = 4 $. After rotation, the new point is $(-4,3)$.
# Answer:
a. $(-4, 3)$

### Question 12
# Explanation:
## Step1: Use the Pythagorean identity
We know that $ \sin^{2}\theta+\cos^{2}\theta = 1 $. Given $ \sin\theta=\frac{5}{13} $, we substitute into the identity: $ (\frac{5}{13})^{2}+\cos^{2}\theta = 1 $.
## Step2: Solve for $ \cos\theta $
$ \cos^{2}\theta=1 - (\frac{5}{13})^{2}=1-\frac{25}{169}=\frac{169 - 25}{169}=\frac{144}{169} $. Taking the square root (assuming $ \theta $ is in the first quadrant where cosine is positive), $ \cos\theta=\frac{12}{13} $.
# Answer:
a. $ \frac{12}{13} $

### Question 13
# Explanation:
## Step1: Factor out the greatest common factor (GCF)
The GCF of $ 4x^{2} $ and $ 36 $ is 4. So we factor out 4: $ 4x^{2}-36 = 4(x^{2}-9) $.
## Step2: Factor the difference of squares
We know that $ a^{2}-b^{2}=(a + b)(a - b) $. Here $ x^{2}-9=x^{2}-3^{2}=(x + 3)(x - 3) $. So $ 4(x^{2}-9)=4(x + 3)(x - 3) $.
# Answer:
a. $ 4(x + 3)(x - 3) $

### Question 14
# Explanation:
## Step1: Recall the exterior - interior angle relationship
An exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Also, an exterior angle and its adjacent interior angle are supplementary (sum to $ 180^{\circ} $).
## Step2: Find the adjacent interior angle
The exterior angle is $ 140^{\circ} $, so the adjacent interior angle is $ 180 - 140 = 40^{\circ} $.
## Step3: Find the other interior angle
We know that the sum of interior angles of a triangle is $ 180^{\circ} $. Let the other interior angle be $ x $. We know one interior angle is $ 55^{\circ} $, the adjacent interior angle is $ 40^{\circ} $. So $ 55 + 40+x=180 $? Wait, no, wait: The exterior angle is equal to the sum of the two remote interior angles. So if the exterior angle is $ 140^{\circ} $, and one remote interior angle is $ 55^{\circ} $, then the other remote interior angle is $ 140 - 55 = 85^{\circ} $.
# Answer:
b. $ 85^{\circ} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 8

Step1: Recall dilation formula

Step2: Apply scale factor \( k = 3 \) to \((2, 1)\)

Step1: Factor 98

Step2: Simplify the square root

Step1: Find number of only basketball players

Step2: Find total number of players

Step3: Calculate probability

Answer:

Question 9