Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true?
A. a^2 + c^2 < b^2
B. a^2 + c^2 > b^2
C. b^2 + c^2 < a^2
D. a^2 + b^2 < c^2
Answers
For a triangle with an obtuse angle B and the longest side opposite it (side c), the correct statement is a^2 + c^2 > b^2.
The correct answer is option B.
In a triangle with sides a, b, and c, where angle B (opposite side b) is obtuse, and side c is the longest side (opposite the largest angle), we can apply the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles:
c^2 = a^2 + b^2 - 2ab * cos(B)
Given that angle B is obtuse, cos(B) will be negative. Therefore, the term -2ab * cos(B) will subtract from the sum of a^2 + b^2. The Law of Cosines now becomes:
c^2 = a^2 + b^2 + 2ab * cos(B)
Considering the given options:
A. a^2 + c^2 < b^2 - This is not necessarily true in this context.
B. a^2 + c^2 > b^2 - This is true based on the Law of Cosines.
C. b^2 + c^2 < a^2 - This is not necessarily true in this context.
D. a^2 + b^2 < c^2 - This is not necessarily true in this context.
Therefore, from the given options the correct one is option B.
Related Questions
Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay for the shirt?
$42
$36.60
$34
$33.60
Answers
Answer:
$33.60 is the correct answer.
Step-by-step explanation:
Price of the shirt = $40.00
discount rate = 20% or 20/100
so price of the shirt = 40 × 0.20 = 8
Shirt's price after 20% discount = 40 - 8 = $32.00
Now she paid 5% tax on the price after discount.
5% tax of 32.00
0.05 × 32 = $1.60
This amount will be added to his discounted price of a shirt.
= 32.00 + 1.60 = $33.60
Lydia pay $33.60 for the shirt.
Given the vector "v" and its inital point, find the terminal point:
"v"=<-1,3>;Initial Point:(4,2) ...?
Answers
The final point can be done by simple vector addition. Just add the corresponding components.
Final point: (4 + -1, 2 + 3) = (3, 5).
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
help with 8th grade math! will upvote!! <33
Which of these is a simplified form of the equation 8p + 4 = − p + 7 + 2p + 3p?
A. 14p = 11
B. 8 = 4
C. 4p = 3
D. 12 = 13
Answers
Starting with:
8p + 4 = -p + 7 + 2p + 3p
We can add all terms of "p" on the right side, leaving our equation to be
8p + 4 = 4p + 7
Now, we can subtract 4p from both sides:
4p + 4 = 7
Finally, subtract 4 from both sides
4p = 3
Find the difference. (-ab+8a-5)-(-8ab-4)
Answers
So first
Distribute the Negative Sign:
=(−a)(b)+8a−5+−1((−8a)(b)−4)
=(−a)(b)+8a+−5+−1((−8a)(b))+(−1)(−4)
=(−a)(b)+8a+−5+8ab+4=−ab+8a+−5+8ab+4
Then after all of that
Combine Like Terms:=−ab+8a+−5+8ab+4
=(−ab+8ab)+(8a)+(−5+4)
So now your answer is =7ab+8a+−1
-ab + 8a - 5 + 8ab + 4 =
8a + 7ab - 1 <===
Three fractions that are equivalent to:
12/36
4/5 and
3/12 ...?
Answers
Equivalent fractions for the following would be:
A. 12/36 = 2/6, 1/3 and 3/9
B. 4/5 = 8/10, 12/15 and 16/20.
C. 3/12 = 1/4, 6/24 and 9/36.
Hope these are the answers that you are looking for.
Let me know if you need more help next time. Thanks for posting!
Which of the statements about the following quadratic equation is true?
6x2 - 8 = 4x2 + 7x
The discriminant is greater than zero, so there are two real roots.
The discriminant is greater than zero, so there are two complex roots.
The discriminant is less than zero, so there are two real roots.
The discriminant is less than zero, so there are two complex roots.
Answers
If the discriminant of a quadratic equation is positive then, there are two real roots. Here, the discriminant obtained is 113 which is greater than zero. Hence, option a is correct.
What is quadratic equation ?A quadratic equation are polynomial equation with one variable having the degree of 2. This general form a quadratic equation is written as follows:
ax² - b x + c = 0
The discriminant for a quadratic equation is the term b² - 4ac.
Given the quadratic equation is 6x² - 8 = 4x² + 7 x
it can be rearranged as: 2x² - 7x - 8 =0
If the discriminant of the equation is greater than zero, then there will be two real roots.
solving the discriminant here:
b² - 4ac = (-7)² - 4× 2×(-8) = 113
Here, the discriminant is greater than zero. Therefore, there are two real roots.
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The momentum of a system before a collision is 2.4 × 103 kilogram meters/second in the x-direction and 3.5 × 103 kilogram meters/second in the y-direction. What is the magnitude of the resultant momentum after the collision if the collision is inelastic?
A. 1.7 × 103 kilogram meters/second
B. 2.1 × 103 kilogram meters/second
C. 3.4 × 103 kilogram meters/second
D. 4.2 × 103 kilogram meters/second
E. 5.7 × 103 kilogram meters/second ...?
Answers
Answer:
Option D - [tex]4.2\times 10^3[/tex] kilogram meters/second.
Step-by-step explanation:
Given : The momentum of a system before a collision is [tex]2.4 \times 10^3[/tex] kilogram meters/second in the x-direction and [tex]3.5 \times 10^3[/tex] kilogram meters/second in the y-direction.
To find : What is the magnitude of the resultant momentum after the collision if the collision is inelastic?
Solution :
In inelastic,
The magnitude of the resultant momentum after the collision (and before) can be determined by using the Pythagorean theorem.
[tex]c^2 = a^2 + b^2[/tex]
Where, a is the momentum before collision [tex]a=2.4 \times 10^3[/tex]
b is the momentum after collision [tex]b=3.5 \times 10^3[/tex]
c is the total amount of momentum before and after collision.
Substitute the value,
[tex]c^2 = (2.4\times10^3)^2 + (3.5\times10^3)^2[/tex]
[tex]c^2 =5760000+ 12250000[/tex]
[tex]c=\sqrt{18010000}[/tex]
[tex]c=4243.819[/tex]
[tex]c=4.2\times 10^3[/tex] kg m/s
Therefore, Option D is correct.
The magnitude of the resultant momentum after the collision if the collision is inelastic is [tex]4.2\times 10^3[/tex] kilogram meters/second.
Evaluate the expression –0.4(3x – 2) + for x = 4
Answers
Answer:
Step-by-step explanation:
=0
According to Edge. the answer is 0 :)
What is the principle for f)? The math is Simple Interest
Answers
Answer:
E
Step-by-step explanation:
Which expression is equivalent to 3x(-4x^2+5x-8)-6(x^2-5x+7)?
A. 12x^3-9x^2+6x-42
B.-12x^3-54x^2+6x-42
C.-12x^3+9x^2+6x-42
D.-27x^3-6x^2+6x-42
Answers
A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
A. True
B. False
Answers
Answer:
statement is true .
Step-by-step explanation:
Given : Statement A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
To find : Statement is true or false.
Solution : By polynomial theorem if x-a divide the polynomial P(x) and we get reminder zero then a would be the factor.
Therefore, statement is true .
Answer:
true
Step-by-step explanation:
A country's population in 1991 was 136 million. In 2000 it was 141 million. Estimate the population in 2016 using the exponential growth formula. Round your answer to the nearest million. ...?
Answers
Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.
We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time
Step 1:
A = 141 million = 141 000 000
P = 136 million = 136 000 000
n = ?
x = 2000 - 1991 = 9
Therefore:
[tex]141 000 000 = 136000 000 * e ^{n*9} \\ e ^{n*9} =141000 000 /136000000 \\ e ^{n*9} =1.04 [/tex]
Logarithm both sides of the equation:
[tex]ln(e ^{n*9})=ln(1.04) \\ n*9*ln(e) = ln(1.04) \\ 6n=ln(1.04) \\ n = \frac{ln(1.04)}{9} \\ n = \frac{0.04}{9} \\ n = 0.004[/tex]
Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2016
A = ?
P = 141 000 000
n = 0.004
t = 2016 - 2000 = 16
[tex]A = 141 000 000 * e ^{0.004*16} \\ A = 141000 000 * e^{0.0640} \\ A = 141000 000 * 1.066\\ A = 150306 000[/tex]
Thus, the population will be nearly 150 million in 2016
a system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions. is this statement true?
Always
Sometimes
Never
I think the answer is Sometimes . X=Y and X^2-Y^2=0 Has infinitely Solutions
Answers
Answer:
The statement that says that a system constructed by a linear and a quadratic equation, has infinitely solutions is never true.
Step-by-step explanation:
This situations can be explained more easy by the graphic solution of the system of equations. As we know, a cuadratic equation represents a parabola and the linear equation a line, so the solution of the system can be understood as the interseption od the parabola and the line.
In the attached figure above we expouse the three different cases could hapend. In the first case, we have two interceptions, so 2 solutions. For the second case, we have 1 interseption, which represents one solution. In the third case the line doesnt touch the parabola in any point thus we get no solution.
Therefore in none of the cases explained we found infinite solutions, this situacion can never happens.
In the example the second equation doesnot represents a quadratic equation. A quadratic equation has the form of:
Y = aX^2 + BX + C
Thus the given system cannot be understood as a the example of the kind.
"A 23kg kg child goes down a straight slide inclined 38∘ above horizontal. The child is acted on by his weight, the normal force from the slide, kinetic friction, and a horizontal rope exerting a 30N force as shown in the figure.(Figure 1)
How large is the normal force of the slide on the child?"
Answers
Force is simply the pull or push that acts on an object.
The normal force acting on the child is 159.12 N
The forces acting on the child are
The 30 N force at 38 degreesThe weight of the childThe weight of the child along the vertical component is:
[tex]\mathbf{Weight = mg \times cos(theta)}[/tex]
So, we have:
[tex]\mathbf{Weight = 23 \times 9.8 \times cos(38)}[/tex]
[tex]\mathbf{Weight = 177.62}[/tex]
The horizontal component of the 30 N force is:
[tex]\mathbf{F_2 = 30 \times sin (38)}[/tex]
So, we have:
[tex]\mathbf{F_2 = 18.50}[/tex]
The normal force (F) on the child is:
[tex]\mathbf{F = Weight - F_2}[/tex]
[tex]\mathbf{F = 177.62N - 18.50N}[/tex]
[tex]\mathbf{F = 159.12N}[/tex]
Hence, the normal force is 159.12 N
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Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at a speed of 4 ft/s. His distance d from you after t seconds is given by d = |120 − 4t|. After how many seconds is your neighbor 30 ft from you?
Answers
To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.
Explanation:To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.
Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.
For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.
For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.
So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.
How is each function related to y=x? Graph the function by translating the parent function
1) y=x+2 2) y=x-1.2
I need help with this. I don't know what to do. I was sick and stayed home but I had homework and I wasn't taught how to do it could. Someone help me with this by explaining it step by step? Thank you.
Answers
1 ) y = x + 2
It is translated vertically 2 units up.
2 ) y = x - 1.2
It is translated vertically 1.2 units down.
The graph is in the attachment.
Which equation does the graph of the systems of equations solve? It's a quadratic graph opening down and quadratic graph opening up. They intersect at (0,3) and (2,-5).
(a)x2 - 2x + 3 = 2x2 - 8x - 3
(b)x2 - 2x + 3 = 2x2 - 8x + 3
(c)-x2 - 2x + 3 = 2x2 - 8x - 3
(d)-x2 - 2x + 3 = 2x2 - 8x + 3
Answers
Answer:
D. [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex]
Step-by-step explanation:
We are given that,
The graph of the system of equations is a 'quadratic graph opening down and a quadratic graph opening up'.
This means that one quadratic equation will have leading co-efficient positive and other will have leading co-efficient negative.
So, we get that options A and B are discarded.
Further it is provided that the graph intersect at ( 0,3 ) and ( 2,-5 ).
This means that the pair of points must satisfy the given system of equations.
So, according to the options:
C. [tex]-x^{2} -2x+3=2x^{2} -8x-3[/tex]
Putting x = 0, gives 3 = -3, which is not possible.
So, option C is dicarded.
D. [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex]
Putting x = 0 gives 3 = 3 and x = 2 gives -5 = -5.
Hence, the graph of the given system solves the equation [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex].
Answer:
(d)-x2 - 2x + 3 = 2x2 - 8x + 3
Step-by-step explanation:
Which graph best represents the solution to the following system?
5x - 2y < (less than or equal to) 10
x + y < 5
Answers
The graph that best represents the solution to the given system is:
Graph A.
Step-by-step explanation:We are given a system of inequalities as:
[tex]5x-2y\leq 10[/tex]
and [tex]x+y<5[/tex]
i.e. the graph of first inequality is a solid straight line( since the inequality is not strict) that passes through (2,0) and (0,-5) and the shaded region is towards the origin( since it passes the zero point test)whereas the graph of second inequality is a dotted straight line(since the inequality is strict) that passes through (0,5) and (5,0) and the shaded region is towards the origin( since it passes the zero-point test)Hence, the graph is:
Graph A.
f(x)=2x- 1 what is odd number
Answers
f(x) = 2x-1
f(x)%2 = (2x-1)%2 = (2x-1+2)%2 = (2x+1)%2 = ((2*(x%2))%2 + 1)%2
now x%2 is either 1 or 0
for x%2 = 1
f(x)%2 = ((2*(1))%2 +1)%2 = (2%2+1)%2 = 1
for x%2 = 0
f(x)%2 = ((2*(0))%2 + 1)%2 = (0+1)%2 = 1
So in all cases f(x)%2 = 1 so f(x) must be odd for all positive integers
Here is another proof by mathematical induction :
let x = 1 be base condition then
f(1) = 1 so it is true for that
Lets assume f(x) is odd
then f(x+1) = 2(x+1)-1
f(x+1) = 2x+2-1
f(x+1) = 2x+1
f(x+1) = 2x-1 + 2
f(x+1) = f(x) + 2
f(x) = odd
so f(x) + 2 must be odd.
Average speed of Car 1 = 35 mph. Average speed of Car 2 = 55 mph. Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
How long before Car 2 overtakes Car 1? ___________ hour.
Answers
Answer:
.525
Step-by-step explanation:
35(t+18/60) = 55t
35t +10.5 = 55t
10.5 = 20t
0.525 = t
the slope of the line below is 0.8 write the equation of the line in point slope form using the coordinates of the coordinates of the labeled point do not use parenthesis on the y side
Answers
Final answer:
The equation of the line in point-slope form is y - y1 = 0.8(x - x1), where the point on the line and the slope are given.
Explanation:
To write the equation of a line in point-slope form, we need the slope of the line and the coordinates of a point on the line. In this case, the slope is given as 0.8. Let's assume the labeled point has coordinates (x, y). The equation in point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the labeled point. Substituting the given slope and the coordinates of the point, the equation becomes:
y - y1 = 0.8(x - x1)
Remember to not use any parentheses on the y side of the equation.
a number , x,rounded to 1 decimal place is 3.7 what is the error interval for x
Answers
The error interval will be [3.65,3.75).
What is an error interval?The error interval is the limit or range of accuracy where the number is truncated or rounded. This interval simply shows the range which it could be before rounding.
Given here the decimal number is 3.7 which is after rounded to 1 decimal place.
As the number is rounded to the nearest 0.1 unit, therefore, the error will be half of 0.1 which is 0.1/2= 0.05
Then the lower limit of the error interval will be 3.7-0.05= 3.65
the higher limit of the error interval will be 3.7+0.05= 3.75
the error interval will be 3.65≤x<3.75
As we are rounding 1st decimal unit, if the second decimal unit is greater than 5 then the first decimal unit will be 6. Similarly, if the second decimal unit is less than 5 then the first decimal unit will be 7.
There are the numbers below which on rounding give 3.7
3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74
Therefore the error interval will be [3.65,3.75).
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The error interval for a number x, which when rounded to one decimal place is 3.7, is [3.65, 3.75).
Explanation:When a number, x, rounded to one decimal place is 3.7, the error interval for x represents the range of actual values x could be to give that rounded figure. So, if x is rounded to 3.7, it means that the value must be at least 3.65 and less than 3.75 when considering rounding to one decimal place. Essentially, the number must be in the half-open interval [3.65, 3.75).
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Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply.
A. π/3+nπ/2
B. π/12+nπ
C. π/6+nπ/2
D. 5π/12+nπ ...?
Answers
proof
sinx cosx = 1/4 is equivalent to 2 sinx cosx = 1/2 or sin2x =1/2
so 2x = arcsin(1/2) = π/6 + 2nπ, so x = π/12+nπ
Answer:
Its B and D.
Step-by-step explanation:
On a certain map 3/4 inch represents one mile, what distance, in miles is represented by 1 3/4 inches
Answers
1/4 of an inch is 1/3 of a mile
Solve for x: 3 − (2x − 5) < −4(x + 2)
x < −8
x > −8
x < −3
x > −3
I just need help because i don't know how i would do it with x on both sides
Answers
3 − (2x − 5) < −4(x + 2)
3 - 2x + 5 < -4x - 8
8 - 2x < -4x - 8
4x - 2x < -8 - 8
2x < -16
x < -8
Answer: [tex]x<-8[/tex]
Step-by-step explanation:
The given inequality : [tex]3-(2x-5)<-4(x+2)[/tex]
To solve the inequality for x , first we open the parenthesis , we get
[tex]3-2x+5<-4x+(-4)2[/tex]
[tex]\Rightarrow\ 3-2x+5<-4x-8[/tex] [Note : (-)(+)=(-)]
[tex]\Rightarrow\ 3+5-2x<-4x-8[/tex]
[tex]\Rightarrow\ 8-2x<-4x-8[/tex]
Add 4x on both sides , we get
[tex]8-2x+4x<-4x-8+4x[/tex]
[tex]8+2x<-8[/tex]
Subtract 8 from both sides , we get
[tex]2x<-16[/tex]
Divide both sides by 2 , we get
[tex]x<-8[/tex]
Hence, the correct answer is : [tex]x<-8[/tex]
Explain why a point in the polar plane cannot be named by a unique ordered
pair (r, theta).
Answers
example; the rectangular coordinate of (1,1)
in polar you can describe this point as (pi/4,1) or (5pi/4, -1) and so on
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
A point in the polar plane can have multiple representations due to the periodic nature of angles and the possibility of using negative radii to represent a point in the opposite direction from the pole.
Explanation:The question asks to explain why a point in the polar plane cannot be named by a unique ordered pair (r, θ). In the polar coordinate system, each point is determined by a radius (r) and an angle (θ).
However, a point can have multiple representations due to the periodic nature of angles. If you add or subtract multiples of 2π radians (or 360 degrees) from θ, you will land on the same point in the polar plane.
Additionally, if the radius (r) is negative, the direction is reversed, which also leads to the same point being represented by (-r, θ + π), where θ is the initial angle.
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In the function y=-2(x-1)^2+4, what effect does the number 4 have on the graph, as compared to the graph of the function y=x^2?
A. It shifts the graph 4 units to the right.
B. It shifts the graph down 4 units.
C. It shifts the graph up 4 units.
D. It shifts the graph 4 units to the left. In the function y=-2(x-1)^2+4, what effect does the number 4 have on the graph, as compared to the graph of the function y=x^2?
A. It shifts the graph 4 units to the right.
B. It shifts the graph down 4 units.
C. It shifts the graph up 4 units.
D. It shifts the graph 4 units to the left.
Answers
Answer:
it shifts the graph up four units
Step-by-step explanation:
it shifts the graph up four units because its outside of the phranthasies, in y=a(x+h)k k is the shift vertically
In the function y=-2(x-1)²+4, the number 4 represents a vertical translation, shifting the graph up by 4 units when compared to the function y=x². Option C) is the correct answer.
In the function y=-2(x-1)²+4, the number 4 acts as a vertical translation of the graph. Comparing this function to the standard parabola y=x², the addition of 4 to the equation represents shifting the entire graph of the parabola upwards by 4 units. Therefore, the correct answer to the effect of the number 4 on the graph, as compared to the graph of the function y=x² is: C. It shifts the graph up 4 units.
Understanding graph transformations is key in analyzing how different parts of the function equation affect the function's graphical representation.
A positive constant added to a function results in a vertical shift of the graph in the upward direction. This means that every point on the graph y=x² is moved 4 units higher on the y-axis to create the graph of y=-2(x-1)²+4.
name the property of real numbers illustrated by the equation step by step
-10+4=4+(-10)
Answers
a + b = b + a.
In this case, you are using -10 for a, and 4 for b.
The Commutative Property of Addition.
The pair of points (3,8) and (x, 6) are on the graph of am inverse variation. What is the missing value?
Answers
y varies inversely with x
y=k/x , where k is any constant
y=-16 when x=-64
-16 = k/ (-64)
-16 = k/-64
k=(-16)(-64) = 1024
2)
y =k/x , where k is any constant
y=8 when x=3
8 = k/3
k=24
y=24/x
when y=6
6 = 24/x
6x=24
x=4
Missing value is 4
3)
xy/4=-3
xy=-12
y=-12/x
y=kx
k=-12
4)
Which of these numbers has the least value?
a. 7.2 x 10
b. 8.1 x 10
c. 9,100,000
d. 9.5 x 10
Answers
As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
The digit 5 acts as a limit.
After solving we get.
a. 7.2 x 10 will gives 72.
b. 8.1 x 10 will gives 81.
c. 9,100,000
d. 9.5 x 10 will gives 95.
As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.
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