Answer:
1) If 3 is an odd number, then 3 times 3 is an even number.
False because multiplying odd number by an odd number also gives an odd number.
2) If 6 is less than 7, then 4 is greater than 7.
False because 4 is smaller than 6. As 6 is smaller than 7 then 4 must also be smaller.
3) Six is divisible by 3, and 10 is a multiple of 2.
True. 6/3 = 2 and 2 x 5 = 10. Both the conditions are true so it is also true.
4) The average of the data is greater than the largest value in the data, or it’s less than the largest value in the data.
True.
We have two conditions in this statement and an 'or' between them. One of the conditions is true that is "average is less than the largest value in the data". So the statement as a whole is true.
5) The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.
True.
6) If an equilateral triangle has equal angles, then all its angles will measure 45°.
False.
A triangle has 3 angles whose sum = 180 degrees.
For equilateral triangle each angle will measure 180/3= 60 degrees.
Answer: 2 following statements are true
The first true statement:
Six is divisible by 3, and 10 is a multiple of 2.
We know this because 6 is divisible by 3, and again proven by when we divide 10 by 5 we get 2, so 10 is a multiple of 2.
The second true statement:
The slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value.
Step-by-step explanation:
Which statement regarding the interior and exterior angles of a triangle
Answer:
An exterior angle is supplementary to the adjacent interior angle.
Step-by-step explanation:
An exterior angle of a triangle and its adjacent interior angle form a linear pair. This means they form a straight line, and a straight line has a measure of 180°. Since they combine for a total of 180°, this means they are supplementary.
In a u.s. Poll 8 out of 12 citizens said they were happy with the job Obama is doing.if 126 people were surveyed how many people were happy with Obama?
Answer:
84 people
Step-by-step explanation:
create a proportion
8 x
----- = ---------
12 126
solve.. cross multiply
128x8 =1008
1008/12 =84
The number of people happy with the Obama job from the survey of [tex]126[/tex] people is equal to [tex]84[/tex] people.
What is number?
" Number is defined as the count of any given quantity."
According to the question,
Total number of people surveyed [tex]= 126[/tex]
As per U.S. poll,
Out of [tex]12[/tex] citizen number of people happy [tex]= 8[/tex] people
Out of [tex]1[/tex] citizen number of people happy [tex]= \frac{8}{12}[/tex] people
Out of [tex]126[/tex] number of people happy [tex]= \frac{8\times 126}{12}[/tex]
[tex]= 84[/tex] people
Hence, the number of people happy with the Obama job from the survey of [tex]126[/tex] people is equal to [tex]84[/tex] people.
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The graph below shows the line of best fit for data collected on the number of cell phones and cell phone cases sold at a local electronics store on
twelve different days.
Number of Cell Phone Cases Sold
50
*
0 5 10 15 20 25 30 35 40 45
Number of Cell Phones Sold
Which of the following is the equation for the line of best fit?
A. y = 0.8x
B. y = 0.2x
C. y=0.5x
D. y = 0.25x
Answer:
C
Step-by-step explanation:
The equation of a line is given by
and
slope (m) is given by:
Where (x_1,y_1) are the first set of point in the line and (x_2,y_2) is the second set of point
Let's take 2 points arbitrarily. (0,0) & (25,20)
Let's plug it and find the equation:
Now
C is the correct answer.
The correct option is (A)0.8x.
What is a Straight Line? A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.The standard form for linear equations in two variables is Ax+By=C.The equation of a line two points are [tex]y - y_{1} = m(x - x_{1} )[/tex]slope m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
the two points are [tex](x_{1} ,y_{1} ) & (x_{2} ,y_{2} )[/tex].
so, lets take two points (0,0) & (25,20)
lets put the value in equation,
m = [tex]\frac{20 -0}{25-0} = 0.8\\now \\ y - y_{1} = m(x - x_{1}) \\\\[/tex]
y - 0 = 0.8 (x-0)
y = 0.8x
Therefore, the correct option is (A)0.8x.
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Factor this polynomial expression.
x^2+ 10x + 25
Answer:
(x + 5)^2
Step-by-step explanation:
Learn to recognize perfect squares. x^2+ 10x + 25 is a perfect square of a binomial: x^2+ 10x + 25 = (x + 5)^2.
The polynomial expression of the equation [tex]x^2+ 10x + 25[/tex] is [tex]&(x+5)^{2}[/tex].
What is a polynomial expression?A polynomial exists defined as an expression that exists composed of variables, constants, and exponents, that are connected utilizing mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).
Given expression [tex]x^2+ 10x + 25[/tex]
Rewrite in the form of [tex]$a^{2}+2 a b+b^{2}$[/tex] :
[tex]$25=5^{2}$[/tex]
[tex]$10 x=2 x \cdot 5$[/tex]
[tex]$$=x^{2}+2 x \cdot 5+5^{2}$$[/tex]
Apply Perfect Square Formula:
The perfect square formula exists described in the formation of two terms such as [tex](a + b)^{2}[/tex]. The expansion of the perfect square formula exists represented as[tex](a + b)^{2} = a^{2} + 2ab + b^{2}[/tex]
[tex]$\quad a^{2}+2 a b+b^{2}=(a+b)^{2}[/tex]
[tex]&x^{2}+2 x \cdot 5+5^{2}=(x+5)^{2} \\[/tex]
[tex]&=(x+5)^{2}[/tex]
The polynomial expression of the equation [tex]x^2+ 10x + 25[/tex] is [tex]&(x+5)^{2}[/tex].
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The slope of a line is -, and the y-intercept is 5. What is the equation of the line written in general form?
Answer:
y = mx + 5; m < 0
Step-by-step explanation:
The question mentions that the slope of the line is negative and the y-intercept is 5. The general form of the straight line is given by y = mx + c. Since "c" in the equation is the y-intercept, therefore, c = 5. This means that all the straight lines passing from the point (0,5) can be expressed in a general form y = mx + 5. However, the question mentions that the slope is negative and demands the general equation of all the negatively-sloped straight lines passing from (0,5). Therefore, for the condition to be met, m has to be negative. So the correct answer is y = mx + 5, where m is negative.
Write the expression 5x(x + 9) - 7(x + 9) in complete factored form.
A. (x + 9)(x + 9)
B. (5x - 7)(x+9)
C. (5x – 7)(x + 9)(x + 9)
D. (5x2 + 45x)(-7x - 63)
Answer:
B. (5x - 7)(x+9)
Step-by-step explanation:
5x(x + 9) - 7(x + 9
Factor out the quantity (x+9)
(x+9) (5x-7)
Rearrange the order
(5x - 7)(x+9)
Final answer:
The expression 5x(x + 9) - 7(x + 9) is factored by finding the common term (x + 9) and factoring it out, resulting in the complete factored form (5x - 7)(x + 9), which is Option B.
Explanation:
The expression given is 5x(x + 9) - 7(x + 9). To factor this expression, we look for a common factor in both terms. Here, the common factor is (x + 9). We can use the distributive property, also known as factoring by grouping, to factor out the common factor. Applying this, we get:
(x + 9) is the common factor, so we pull it out in front: (x + 9)(5x - 7).
Thus, the expression in complete factored form is Option B: (5x - 7)(x + 9).
The Empire State Building in New York City is 1250 feet tall. It took 30,000 workers only 1 year and 45 days to build, which is a record for a skyscraper. On a scale model of the building, the height is 25 inches.
What is the scale of the Empire State Building model?
Answer:
Step-by-step explanation:
1250 feet *12 inches per foot : 25 inches
15000 inches : 25 inches
Scale = 600:1 in other words 600 inches of the building represents 1 inch of the model.
If you want the scale to be feet of building per inch of the model, then don't multiply by 12
1250 feet : 25 inches
25 feet of building: 1 inch of the model.
Answer:
The scale is 1:600
Step-by-step explanation:
To calculate the scale you have to divide the two values of height for this case, but in the same units. So 1250 feet is equal to 15000 inches. Dividing 15000 by 25 is equal to 600, that is the scale. 1:600.
Use guess-and-check to find two numbers that have the sum of 8 and a difference of 2. A. 6 and 2 B. 6 and 4 C. 4 and 4 D. 5 and 3
Answer:
D
Step-by-step explanation:
Option A, does 6 and 2 added makes 8? Yes
does 6 and 2 subtracted makes 2? No
Option B, does 6 and 4 added makes 8? No
does 6 and 4 subtracted gives 2? Yes
Option C, does 4 and 4 added gives 8? Yes
does 4 and 4 subtracted gives 2? No
Option D
Does 5 and 3 added give 8? Yes
Does 5 and 3 subtracted give 2? Yes
So we can see, Option D is the correct answer because it satisfies both conditions.
F(x)=3.7-2x g(x)=0.25x-5 what is f(x) +g(x)
Answer:
f(x) +g(x) = -1.3 - 1.75x
Step-by-step explanation:
f(x) +g(x) is simply obtained by adding the two given functions, f(x) and g(x). We are given that;
F(x)= 3.7-2x and g(x)= 0.25x-5
f(x) +g(x) = 3.7-2x + (0.25x-5)
f(x) +g(x) = 3.7 -5 + 0.25x - 2x
f(x) +g(x) = -1.3 - 1.75x
Answer:
f(x) +g(x) = -1.3 - 1.75x
Step-by-step explanation:
Find the range of the function. f(x)=(x-1)^2/x^3-2x^2+x
Answer:
Range = (-∞,0) U (0,∞)
Step-by-step explanation:
The given function is:
f(x) = (x-1)²/x³-2x²+x
We can reduce the denominator:
= (x-1)²/x(x²-2x+1)
we know that a²-2ab+b² = (a-b)²
= (x-1)²/x(x-1)²
= 1/x
The function 1/x is undefined for x = 0.
Hence, its domain lies in (-∞,0) U (0,∞).
Hence x can either be less than or greater than zero.
The function f(x) is greater than zero when x<0.
The function f(x) is less than zero when x>0.
There is no way the function can be zero because the numerator is constant.
Hence the domain of the function lies in the interval:
(-∞,0) U (0,∞)
Twice a certain number is tripled. The resulting number is
Answer:
6x the number.
Step-by-step explanation:
"Twice a certain number" means that you are multiplying that number (x) by 2.
"Tripled" means that the number (x) would be further multiplied by 3.
Simplify: 3 x 2 = 6
The resulting number would be 6x greater than the original number.
~
In 2006, Chris bought a new boat for $34,500. The boat was worth $24 500 in the year 2009. If Chris knows that the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary
Answer:
depreciation is $3,333.33 per year
Step-by-step explanation:
Initially : date = 2006, worth = $34,500
Finally : date = 2009, worth = $24,500
if we let x = date and y = worth, we end up with two points (coordinates) on the x-y graph
i.e
Initial = Point 1 (2006, 34500)
Final = Point 2 (2009, 24500)
The rate of change is simply the slope, m of the line joining these two points
given by:
m = (34500 - 24500) / (2006-2009)
= 10000 / -3
= -3,333.33
hence the annual rate of depreciation is $3,333.33 per year
Final answer:
The boat's value depreciated by $10,000 over 3 years, resulting in an annual depreciation rate of $3,333.33.
Explanation:
The student's question involves calculating the annual rate of change of the value of a boat from the year it was bought (2006) to the year 2009. To find the rate of change, we need to determine how much the value of the boat depreciated over the given time period and then divide it by the number of years.
The boat depreciated from $34,500 in 2006 to $24,500 in 2009, which is a decrease of $34,500 - $24,500 = $10,000 over the course of 3 years. To find the annual depreciation rate, we divide the total depreciation amount by the number of years: $10,000 ÷ 3 years = $3,333.33 per year. Therefore, the annual rate of depreciation is $3,333.33 per year, rounded to the nearest hundredth if necessary.
Square root of 8649 with long division
Answer:
93 Is the square root
This figure is a regular 12-sided polygon. The diameter of the circle that circumscribes it
is 16 cm. Find the radius of the polygon.
cm
Type the correct answer then
press Enter
12 sides
Answer:
Answer:
The radius of the polygon is 8.28 cm
Step-by-step explanation:
See the attached document
A driver can stop his car from the red signal at a distance of of 20 m when he drives at 36 kmph
and 41.25 m when he drives at 54 kmph find his reaction time
Answer: 2.0 seconds & 2.75 seconds
Step-by-step explanation:
[tex]d=\dfrac{s\times r}{3.6}\quad where;\\\\\bullet d=\text{reaction distance (in meters)}\\\bullet s=\text{speed (in km/hr)}\\\bullet r=\text{reaction time (in seconds)}\\\bullet 3.6=\text{needed to convert km/hr into meters/second}\\\\\\\large{\text{When d=20m and s=36}}\\\\20=\dfrac{36}{3.6}\times r\\\\20=10r\\\\\large{\boxed{2=r}}\\\\\\\text{When d=41.25m and s=54}\\\\41.25=\dfrac{54}{3.6}\times r\\\\41.25=15r\\\\\large\boxed{2.75=r}[/tex]
What are the solutions to the equation (2x - 5)(3x - 1) = 0?
Answer:
The solution of the given equation is (5/2, 1/3)
Step-by-step explanation:
It is given an equation,
(2x - 5)(3x - 1) = 0
To find the solution of given equation
(2x - 5)(3x - 1) = 0 means that,
either (2x - 5) = 0 or (3x - 1) = 0
If 2x - 5 = 0
2x = 5
x = 5/2
or 3x - 1 = 0
3x = 3
x = 1/3
Therefore the solution of the given equation is (5/2, 1/3)
ANSWER
[tex]\: x =2 \frac{1}{2} \: or \: x = \frac{1}{3} [/tex]
EXPLANATION
The equation is given in the factored form as:
[tex](2x - 5)(3x - 1) = 0[/tex]
According to zero product principle
[tex]either \: \: (2x - 5) = 0 \: or \: (3x - 1) = 0[/tex]
This implies that,
[tex]either \: \: 2x = 5 \: or \: 3x = 1[/tex]
We divide the first equation by 2 and the second by 3
[tex]either \: \: x = \frac{5}{2} \: or \: x = \frac{1}{3} [/tex]
The solutions are
[tex]\: x =2 \frac{1}{2} \: or \: x = \frac{1}{3} [/tex]
Solve the equation below.
[tex]\frac{x+4}{6x} =\frac{1}{x}[/tex]
A. x= -2
B. x=0,2
C. x= 2
D. x=0,-2
Answer:
B. x=0,2
Step-by-step explanation:
(x+4) 1
-------- = -----
6x x
Using cross products
x * (x+4) = 1*6x
Distribute
x^2 +4x = 6x
Subtract 6x from each side
x^2 +4x-6x = 6x-6x
x^2 -2x = 0
Factor out an x
x (x-2) = 0
Using the zero product property
x=0 x-2 =0
x=0 x-2+2 =0+2
x =0 x=2
Answer:
Option C is correct.
Step-by-step explanation:
We need to solve the equation below and find value of x
[tex]\frac{x+4}{6x} =\frac{1}{x}[/tex]
Cross multiply
x(x+4)=6x
x^2+4x=6x
x^2+4x-6x=0
x^2-2x=0
Taking x common
x(x-2)=0
x=0 and x-2 =0
x=0 and x= 2
Verify solutions
putting x=0
x+4/6(0) = 1/0
the solution is undefined.
Putting x = -2
2+4/6(2) = 1/2
2+4/12 = 1/2
6/12=1/2
1/2=1/2
the solution is defined.
The solutions is x=2 as for x=0 the solution is undefined.
So, Option C is correct.
Which equation describes the same line as y-5=-2(x+4)
Option A (y=-2x-3) is the answer.
Step-by-step explanation:
First, you need to multiply the -2 by what is in the parentheses, in order to expand the equation. -2*x is -2x, and -2*4 is -8. This leaves you with -2x-8 on the right side of the equation.
Next, you need to isolate y on the left side of the equation. You can do this by subtracting -5 from both sides. Subtracting a negative causes it to become positive, so you are really just adding 5 to both sides.
This makes it so the y is now alone, and the right side has -2x-8+5. We add together the -8 and 5 to leave us with -3.
This makes the answer y=-2x-3.
Answer:The answer is A. You have to solve for Y .
Step-by-step explanation:
The point of concurrency of the altitudes of a triangle is called the _____
circumcenter.
centroid.
incenter.
orthocenter.
Answer:
The correct answer option is 'orthocenter'.
Step-by-step explanation:
The point of concurrency of the altitudes of a triangle is called the 'orthocenter'.
Orthocenter is the point in a triangle where all of the three altitudes of the triangle intersect each other.
Explaining further, a line which is perpendicular to the opposite side and passes from a vertex of a triangle is called the altitude of the triangle.
Therefore, the correct option is D. orthocenter.
Write an equation of the line that passes through (-5,0) and is parallel to the line y=-4/5x-1
Answer:
y = -⅘x - 4
Step-by-step explanation:
. So your point is an x-intercept. It happens at times. Alright. Now, we have to know that parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so we keep the -⅘. Moving forward, we simply plug the coordinate into the Slope-Intercept Formula, y = mx + b --> 0 = -⅘[-5] + b. From this, we can see that our y-intercept is [0, -4], so our parallel line is y = -⅘x - 4. Do you understand?
What is the slope-intercept form of the equation of a line that passes through (1, –6) with a slope of 5?
Question 7 options:
a)
y = 5x + 1
b)
y = 5x – 11
c)
y = 5x + 11
d)
y = 5x – 6
Answer:
b) y = 5x - 11Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the slope m = 5 and the point (1, -6). Put them to te equation:
-6 = 5(1) + b
-6 = 5 + b subtract 5 from both sides
-11 = b
Finally we have the equation of a line:
y = 5x - 11
Determine the equation of the inverse of y= ex+3.4
The inverse function is: [tex]\[ y = \ln(x + 4) - 3 \][/tex]
To find the inverse of the function [tex]\( y = e^{x+3} - 4 \)[/tex], we'll first swap the roles of x and y and then solve for y.
1. Start with the original function:
[tex]\[ y = e^{x+3} - 4 \][/tex]
2. Swap x and y:
[tex]\[ x = e^{y+3} - 4 \][/tex]
3. Solve for y:
[tex]\[ x + 4 = e^{y+3} \] \[ e^{y+3} = x + 4 \][/tex]
4. Take the natural logarithm (ln) of both sides to isolate y:
[tex]\[ \ln(e^{y+3}) = \ln(x + 4) \][/tex]
[tex]\[ y + 3 = \ln(x + 4) \][/tex]
5. Subtract 3 from both sides:
[tex]\[ y = \ln(x + 4) - 3 \][/tex]
Complete question: Find the Inverse y=e^(x+3)-4
Which ordered pair represents the y-intercept of the graph of the equation
y = -5x + 6?
O A. (-5,0)
O B. (6.0)
O C. (0,6)
O D. (0,-5)
Your question asks which pair represents the y-intercept in the equation.
Answer: C). (0,6)To find the answer in your question, we are going to need to find the key terms in the question.
Key terms:
y-intercept
y = -5x + 6
With the information above, we can find the answer.
We know that the equation is similar to the equation: y= mx + b
We need to find what the y-intercept is in the equation.
When you look at the equation, y = -5x + 6, you would know that the y intercept would be the last number (6). Therefore, 6 would be our y intercept.
But, we need to get the number 6 in the right ordered pair.
An ordered pair is represented as (x,y).
So, we would plug in the 6 in the y spot, since it's the y-intercept. We would plug in 0 to x, since we're only focusing on the y-axis, any number on this would not allow the ordered pair to be on the y-axis.
This means that your ordered pair should be (0,6).
C). (0,6) should be your FINAL answer
I hope this helps!Best regards, MasterInvestorThe y-intercept of the equation y = -5x + 6, is represented by the ordered pair (0,6). This is established by substituting x=0 in the equation, which results in y = 6. Hence, the line intersects the y-axis at this point on a graph.
Explanation:In the equation y = -5x + 6, the y-intercept is the value of y when x equals zero. This can be determined by substituting x=0 into the equation. So, let's do this:
Substitute x = 0 into the equation, we get: y = -5*(0) + 6, which simplifies to y = 6. Therefore, the y-intercept is 6, and in an ordered pair it is represented as (0,6).
So, the correct answer is option C: (0,6). This is the point where the line crosses the y-axis on a graph.
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factor 200t+8t^3-80t^2
Answer:
8t(t - 5)^2
Step-by-step explanation:
I would immediately rearrange these terms in descending order by powers of t:
8t^3 - 80t^2 + 200t
Then I'd factor out 8t:
8t(t^2 - 10 t + 25).
Finally, I'd factor the quadratic t^2 - 10 t + 25:
(t - 5)^2
and so 200t+8t^3-80t^2 in factored form is 8t(t - 5)^2.
Answer:
Step-by-step explanation:
It would be better to list the terms in descending order.
8t^3 - 80t^2 + 200t Take out a common factor of t
t(8t^2 - 80t + 200) Now take out 8
8t (t^2 - 10t + 25) Now factor the polynomial
8t(t - 5)(t - 5)
What is the equation of the line of best fit given by a regression calculator for the data in the table?
Step-by-step answer:
The answer is circled in red on the output of the calculator, attached. This is how we need to look for when we use a graphing calculator, which says
"linear regression, y=5.10x+9.12"
However, we need to check the answer by looking at least one point on the curve. Say we use the point (10,60) on the straight line, and compare with y(10) = 5.10*10+9.12 = 60.12, quite close to 60. The other answer options all give numbers far away from 60 when x=10.
Answer:
The correct option is 2.
Step-by-step explanation:
The given data is
x y
5 36
9 64
12 72
18 96
26 141
35 189
The general form of regression line is
[tex]y\approx ax+b[/tex]
From the given picture of graphing calculator, it is clear that the equation of regression line is
[tex]y\approx 5.098x+9.118[/tex]
Approx the value of a and b upto tenth.
[tex]y\approx 5.10x+9.12[/tex]
The equation of the line of best fit is y ≈ 5.10x+9.12. Therefore the correct option is 2.
I really need help with this one
Answer:
its y is less than -7
Step-by-step explanation:
Answer:
y > -7
Step-by-step explanation:
multiply both sides by -1, remember to reverse the inequality when multiplying (or dividing by -1 on both sides
Hence:
-y (-1) > 7(-1) -----> remember to reverse inequality
y > -7 (answer)
Evaluate the expression |2x – 5| for x = –3 and for x = 3.
A. 3, 13
B. 13, 3
C. 11, 1
D. 1, 11
Answer:
C. 11, 1
Step-by-step explanation:
Plug in your given x-values, then take the absolute values [ALWAYS POSITIVE] of each.
Solve for y
Y/m + y/n = p
Answer:
y = mnp/(m + n)
Step-by-step explanation:
I assume that both capital y and small case y are meant to be the same variable. If not, let me know, and I'll solve it again for small case y.
y/m + y/n = p
Factor y out on the left side.
y(1/m + 1/n) = p
y = p/(1/m + 1/n)
Multiply the right side by (mn)/(mn).
y = pmn/[(1/m + 1/n)mn]
y = pmn/(n + m)
y = mnp/(m + n)
Solve for y:
y/m + y/n = p
yn + ym = pmn
y = pmn / n + m
Hope this helps :)
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What is the greatest common factor of 6 and 8
Answer:
2
Step-by-step explanation:
Factors of |6| factors of 8
, , , , , , , , , 1×8
2×4
1×6
2×3
The greatest common factor is 2.
What is greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.
Given numbers:
6 and 8
Now to calculate the greatest common factor we have to
6=2*3
4=2*4
Hence, the only common factor is 2.
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Use properties of equality to solve these equations. Identify the properties used and describe how you used them. help pls
6. (–5 • 7)25 = x(7 • 25)
7. 5x = 0
8. 63 = 1x
9. 1/8x=1
10. 65 • 92 • 17 = 92 • 17 • x
Answer:
10. 65 = x
9. 8 = x
8. 63 = x [it gave you the answer]
7. 0 = x
6. -5 = x
Step-by-step explanation:
#6 uses the Associative Property of Multiplication. #7 uses the Zero Product Property of Multiplication. #8 gave you the answer because x = 1x. For #9, you have to multiply ⅛ by its multiplicative inverse [reciprocal (8)] to get 1. #10 uses the Commutative Property of Multiplication.
**Associative and Commutative are the same thing, EXCEPT Commutative does NOT use grouping symbols. Associative does.