Answer:
c) 36, 48, 60
Step-by-step explanation:
A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:
[tex]\boxed{a^2+b^2=c^2}[/tex]
where a < c and b < c.
It always consists of:
all even numbers, ortwo odd numbers and an even number.When a and b are both even, c is even.
When one of a and b is odd and the other is even, c is odd.
(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.
(17, 20, 23) is not a Pythagorean Triple since:
[tex]\implies 17^2+20^2=23^2[/tex]
[tex]\implies 289+400=529[/tex]
[tex]\implies 689 \neq 529[/tex]
(36, 48, 60) is a Pythagorean Triple since:
[tex]\implies 36^2+48^2=60^2[/tex]
[tex]\implies 1296+2304=3600[/tex]
[tex]\implies 3600=3600[/tex]
(19, 22, 25) is not a Pythagorean Triple since:
[tex]\implies 19^2+22^2=25^2[/tex]
[tex]\implies 361+484=625[/tex]
[tex]\implies 845\neq 625[/tex]
A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long.
Answer: If you are looking for Area, use the formula A=length x width
If you are looking for Perimeter, use the formula P= 2(length x width)
Step-by-step explanation:
So, the Area would be A=12x9 = 108 meters squared (you're multiplying 12 meters and 9 meters, which squares the unit)
and the Perimeter would be P= 2(12x9) = 216 meters
PLS HELP Which has the greatest rate
After solving the equation the greatest rate is y=x. therefore, the correct option is D
What does rate in math mean?
In mathematics, the term 'rate' usually refers to a ratio or a comparison between two different values. It is defined as the amount of one quantity with respect to another, and is most commonly expressed as a fraction, with one value being the numerator and the other being the denominator. For example, "the rate of increase" is a comparison between the amount of increase in an item over time, such as the rate of inflation over a period of time. Additionally, the term 'rate' can also be used to describe a rate of change, such as the rate of growth of a population. In this case, the rate of change describes how quickly the population is changing over time.
Given that:
For rate we have to differentiate all the function first
A) y = 3/4x + 1
dy/dx = 3/4
B) y = -x
dy/dx = -1
C) y = 1/2x +2
dy/dx = 1/2
D) y = x
dy/dx = 1
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Need help with this
Answer:
11.8 m
Step-by-step explanation:
this makes up a right triangle so we can use the Pythagorean theorem
a^2+b^2=c^2
a- height/leg a
b- length/ leg b
c- hypotheneus
since we are tying to find b we can isolate b^2 on one side of the equation
a^2+b^2=c^2
-a^2. -a^2
b^2=c^2-a^2
And now we can plug in values
b^2=36^2-34^2
b^2=1296-1156
b^2=140
Square root both sides
b=11.8
Hopes this helps please mark brainliest
suppose there are 10 research teams working independently from different data gathered in separate and independent random samples. each team performs an identical hypothesis test with 80% power to detect an alternative of interest with a certain effect size. in the case that this certain alternative of interest is true, what is the probability that at most 1 of the teams will make a type ii error?
The probability of at most one team making a Type II error is 0.3651.
1. The probability of a Type II error for a single team is 0.2 (since the power of the test is 0.8).
2. The probability of all 10 teams making a Type II error is 0.2^10. This is because the probability of each individual team making a Type II error is 0.2 and the probability of all 10 teams making a Type II error is the product of the individual probabilities (0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 = 0.2^10).
3. The probability of at least one team making a Type II error is 1 - 0.2^10. This is because the probability of at least one team making a Type II error is the complement of the probability of all 10 teams making a Type II error (1 - 0.2^10).
4. The probability of at most one team making a Type II error is 1 - (1 - 0.2^10). This is because the probability of at most one team making a Type II error is the complement of the probability of at least one team making a Type II error (1 - (1 - 0.2^10)).
5. The probability of at most one team making a Type II error is 0.3651.
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Which of the following has a graph that is parallel to the graph of 2x-y=6 and passes through the point at (3, -2) ?
The function that has a graph that is parallel to the graph of 2x-y=6 is y = 2x - 8
How to determine the parallel line equation?From the question, we have the following parameters that can be used in our computation:
2x - y = 6
Subtract 2x from both sides of the equation
So, we have the following representation
-y = -2x + 6
Multiply both sides of the equation by -1
y = 2x - 6
Also, from the question;
We have the following points
The point is given as
Point = (3, -2) i.e. (x, y) = (3, -2)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
The slopes of parallel lines have the same values
This means that the slope of the other line is 2
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 2
(x₁, y₁) = (3, -2)
So, we have
y = 2(x - 3) - 2
Open the brackets
y = 2x - 6 - 2
Evaluate the like terms
y = 2x - 8
Hence, the line has an equation of y = 2x - 8
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Step-by-step explanation:
function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____
function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose
Which equation represents a linear function?
Answer: the first one
Step-by-step explanation:
...
STEM AND LEAF PLOT
what is the range in row A
Due tomorrow
Dec 4/2022
Answer:
C) 21
Explanation:
The middle column represents the tens place, while the column on the left is the ones place. Range is the difference between the highest number and the lowest number.
The lowest number for road A is 29, the 2 from the middle column and 9 from the left. The largest number is 50, the 5 from the middle column and 0 from the left column.
50 - 29 = 21
Please help, I don't really understand.
Answer:
Step-by-step explanation:
The standard form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept. Let's rewirite the given equation to match this format:
y = 6 - 6x
y = -6x + 6
The slope is -6 and the y-intercept is 6. The slope tells us the angle the line is taking. A negative slope such as this means that the line is angled down as it goes from left to right. The size of the number tells us just how steep the line is.
All parallel lines have the same slope. Any line with the format of y = -6 + b will be parallel. See the attached graph for proof. The graph shows several parallel lines to y=-6+b, including the three top lines, all with the same slope, but with three different values for b: +6, 0, and +10.
Perpendicular lines have a slope that is the negative inverse of the reference line, in this case y = -6x + 6. A perpendicular line will have a slope of -(1/-6) or 1/6 [the negative inverse of -6]. Perpendicular lines will have the form y = (1/6)x + b. See the attached graph. The three bottom equations are all perpendicular to y=-6x+6. All have the same slope (1/6), but differnt y-intercepts (b = 0, 6, and 10). The y-intercept numbers for both the parallel and perpendicular lines were randomly chosen, simply to illustrate the possibilities.
In summary,
"Slope of a parallel line" is -6, and
"Slope of perpendicular line" is (1/6)
i need help with this asap!!! its due tonight!!!! HELPP!!!!
Answer: a
Step-by-step explanation:
A special machine is used at a construction site to dig holes. A hole is dug to a depth of 4.75 feet when the machine hits rock. The progress slows to 3/5 feet per hour of digging. The depth of the hole must be at least 12 1/2 feet by the end of the day to stay on schedule.
What is the minimum amount of time the machine must continue at its present rate to complete the hole on schedule?
Select from the drop-down menus to correctly complete the statement.
The machine requires at least Choose... hours and Choose... minutes to complete the hole on schedule.
Chose #1: 18 28
Chose#2 9, 15, 45, 55
Answer:
The machine requires at least 9 hours and 45 minutes to complete the hole on schedule.
Step-by-step explanation:
To find this, you can use the formula provided in the previous response:
(required depth - current depth) / digging rate = hours of digging
Plugging in the values from the problem, you get:
(12.5 feet - 4.75 feet) / (3/5 feet per hour) = (7.75 feet) / (3/5 feet per hour)
This simplifies to:
(7.75 feet) / (3/5 feet per hour) = 15.5 hours
Then, to convert this number of hours to hours and minutes, you can divide by the number of minutes in an hour (60 minutes) and round up to the nearest whole number for the number of hours. The remainder will be the number of minutes:
15.5 hours / 60 minutes/hour = 0.258333... hours
Rounding up to the nearest whole number, you get:
0.258333... hours = 1 hour
The remainder is:
15.5 hours - 1 hour = 14.5 hours
14.5 hours / 60 minutes/hour = 0.241666... hours
Rounding up to the nearest whole number, you get:
0.241666... hours = 0 hours
The remainder is:
14.5 hours - 0 hours = 14.5 hours
14.5 hours / 60 minutes/hour = 0.241666... hours
Rounding up to the nearest whole number, you get:
0.241666... hours = 0 hours
The remainder is:
14.5 hours - 0 hours = 14.5 hours
14.5 hours * 60 minutes/hour = 870 minutes
Therefore, the machine requires at least 9 hours and 45 minutes to complete the hole on schedule.
I am part of a hole I am twice the value of 1/8 I am percentage what am I
Answer: 25
Step-by-step explanation:
part of a low is anything lower than 1oo
twice of 1/8 = 2/8 = 1/4
Answer:
25%
Step-by-step explanation:
"twice" means two times.
"twice the value of 1/8" is
2 × 1/8
(to multiply a whole number times a fraction, multiply the big number × the top number)
2 × 1/ 8 is 2/8
2/8 is 1/4.
1/4 = .25 = 25%
Since the answer is a percent, change 1/4 to a decimal, .25, change the decimal to a percent.
Or you could change 1/4 to 25/100. Percent means "per hundred" 25/100 is 25%.
Let f(x)=7x and g(x)=7x+2−4. Which transformations are needed to transform the graph of f(x) to the graph of g(x)? Select each correct answer.
Responses
horizontal translation 2 units left
vertical translation 2 units up
vertical translation 4 units down
horizontal translation 2 units right
horizontal translation 4 units left
vertical translation 4 units up
The required answer choice is vertical translation 2 units up and vertical translation 4 units down.
What is translation?
In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the same size as the original shape, and thus the shapes are congruent. They were simply shifted in one or more directions. There is no change in the shape because it is simply moved from one location to another.
The -2 indicates that you need to translate 2 units up, and the -4 indicates that you need to translate 4 units down.
As a result, the answer is vertical translation 2 units up and vertical translation 4 units down.
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
C. x² -8x +16 = 20
Step-by-step explanation:
You want the next step in completing the square after you get x² -8x = 4.
Completing the squareThe constant in a perfect square monic trinomial is the square of half the coefficient of the linear term.
The coefficient of x is -8. Half that is -4, and its square is (-4)² = 16. This will be the value added to the equation in the second step.
x² -8x +16 = 4 +16
x² -8x +16 = 20
__
Additional comment
A monic polynomial has a leading coefficient of 1. We generally work with monic quadratics when completing the square. We do this by factoring the leading coefficient out of the variable terms.
help me quick please
Answer:
the percentage of change is 300%
Step-by-step explanation:
30 times 300% equals 90 more dollars which equals $120
Write the equation of the line passing through the points (-3,3) and (3,1).
The equation of the line is?
Answer:
Step-by-step explanation:
Step 1 Find the slope
1-3/3-(-3)
-2/6=1/3
m=-1/3
Use the point slope formula
y-1=-1/3(x-3)
y=-1/3x+2
HELP PLEASE.
Explore sums of complex numbers by moving points A and B and noticing how the sum of those points written in the expression below corresponds to the sum shown geometrically. Drag the points, A and B, to produce a result of -3 + 4i
This is also written on the attached image
The two points A and B that will be added to produce the complex number -3 + 4i are; -1 + 2i and -2 + 2i.
How to solve Complex Numbers?A complex number is defined as one that has both a real and an imaginary component, whereby both of them are preceded by the letter i which denotes the square root of -1.
Complex numbers are written in the general form; x + iy
Where;
x is the real part.
iy is the imaginary part.
From the graph attached, we can deduce that the two points that were added to obtain the result of -3 + 4i are;
A = -1 + 2i
B = -2 + 2i
Now, let us confirm the sum of the two points A & B;
A + B
= -1 + 2i + -2 + 2i
⇒ -3 + 4i
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Write whether each is an expression, equation, or an inequality.
5. 3+5-7 = 1
6.3x-5t+4
7.9r+ 10_>14
8. 10+s≠4
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 28 feet up. The ladder makes an angle of 60° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.
A 31.2 foot ladder is required to access an electrical box that is 28 feet up.
Which ratios in trigonometry are there?
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.
A right-angled triangle is formed by the ladder, the distance from the wall to the ladder's base, and the distance from the ground to the electrical box.
The link between the sides and angles of a right-angled triangle is demonstrated through trigonometric ratios.
If x stands for the ladder's length, then:
28 feet/x for sin(64).
28 feet/sin x = (64)
x = 31.2 ft
Therefore, a 31.2-foot ladder is required to reach an electrical box that is 28 feet up.
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23.4 is what percent of 288? Round to the nearest tenth..?
It should be noted that 23.4 is 8.1 percent of 288.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
23.4 is what percent of 288 will be calculated thus:
= 23.4 / 288 × 100
= 8.1%
The percentage is 8.1%.
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what are two square roots of 121
Answer:
11
Step-by-step explanation:
11*11 = 121
Please help!! Find the measure of numbered angles 1 and 2
Answer:
Step-by-step explanation:
the adjacent angles are congruent
angle 1 = 51°
the sum of the angles is 360°
51 · 2 + 2 · angle (2) = 360
102 + 2angle(2) = 360
2angle (2) = 360 - 102
2 angle (2) = 258
angle (2) = 258/2
angle (2) = 129°
angle (3) = 129°
the area of a square is 264cm². Find length & perimeter of square.
Answer:
Here,
Given:
Area of a square- 264 sq. cm
To find:
1. The length ( side)
2.Perimeter.
Solution :
Now,
Let the side of the square be x cm.
according to the formula for finding the area of a square:
Area= side× side
264= x× x
264= x^2
√264= x
16.2481= x
16.25= x
hence,
Length= side= 16.25 cm.
Now,
Perimeter of a square:
= 4× side
= 4× 16.25
= 65
Hence,
perimeter of the square= 65 cm
Step-by-step explanation:
I hope I helped you
I'm having trouble understanding, please help.
Answer:
2x+y=-4
Step-by-step explanation:
y-2=-2(x+3) is in point-slope form.
Ax+By=C is standard form.
We have to bring x and y to the same side of the equation.
First, let's distribute.
y-2=-2(x)-2(3)
y-2=-2x-6
Next, we will add 2 to both sides to get rid of the -2 on the left side of the equation.
y=-2x-6+2
Then, we will add 2x to both sides to get rid of the -2x on the right side of the equation.
2x+y=-6+2
Now x and y are on the same side of the equation. We just need to simplify the right side.
2x+y=-4
This is the answer in standard form.
Answer:
2x + y = -4
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]
Given equation:
[tex]y-2=-2(x+3)[/tex]
To write the given equation in standard form, collect the terms with variables on the one side of the equation (ensuring the term in x is positive), and collect the constants on the other side of the equation.
Distribute the right side of the equation:
[tex]\implies y-2=-2 \cdot x+(-2) \cdot 3[/tex]
[tex]\implies y-2=-2x-6[/tex]
Add 2x to both sides of the equation:
[tex]\implies y-2+2x=-2x-6+2x[/tex]
[tex]\implies y-2+2x=-6[/tex]
Add 2 to both sides of the equation:
[tex]\implies y-2+2x+2=-6+2[/tex]
[tex]\implies y+2x=-4[/tex]
Rearrange the left side to standard form:
[tex]\implies 2x+y=-4[/tex]
Given the ytem of equation: 3x − 3y = 6 2x 6y = 12 Solve for (x, y) uing elimination
The values of x and y after solving the equations by using elimination method are :- 3 and 1
What is a system of equations?A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.
What are the 3 ways to solve system of equations?There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method
In the above equations
Multiplying equation 1 with 2 and adding it to equation 2 we get
X= 3
Y=1
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2y = x - 4 please help
Answer:
y=1/2x-2
Step-by-step explanation:
What is the slope of line p?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Slope can be determined by using two points (x1, y1) and (x2, y2) and putting them in rise-over-run format (rise-over-run is equal to slope)
in this case we can use (3, 2) as (x1, y1) and (0, 0) as (x2, y2)
Rise-over-run format is: [tex]\frac{y2 - y1}{x2 - x1}[/tex]
so substitute our number in and you get: [tex]\frac{2-0}{3-0}[/tex]
solve to get: [tex]\frac{2}{3}[/tex]
this is your slope
a rectangle is drawn so that the width is 2 feet shorter than the length. the area of the rectangle is 3 square feet. find the length of the rectangle.
The length of the rectangle is found as 7 feet.
Explain the properties of rectangle?It consists of four vertices and four sides. Every vertex has a 90 degree angle.A quadrilateral is a rectangle.The opposing sides are level and parallel to one another.90 degrees is the angle of each interior.360 degrees is the total of all interior angles.For the stated question;
Let the length and the width of the rectangle be 'L' and 'B'.
Then, width is given as;
W = L-2
Area = 35 square feet
A = LW = 35
Put the value of W
L(L-2) = 35
L² -2L - 35 = 0
L² -2L - 35 =0
(L-7)(L+5) = 0
L > 0 so, L=7 is solution
Thus, the length of the rectangle is found as 7 feet.
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The correct question is-
A rectangle is drawn so that the width is 2 feet shorter than the length. the area of the rectangle is 35 square feet. find the length of the rectangle.
Find the missing length indicated.
Triangle 1's x value is 8 and LN's length is 14 units. Triangle 2's x value is 8 and IH's length is 11 units. Triangle 3's x value is 9 and CB's length is 23 units. Triangle 4's x value is 11 and its IH length is 11 units.
What is similar triangle?If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.
Here,
Since these are similar triangle,
ME=EN
MN=ME+EN
MN=2ME
this will be same for all the triangles,
1. 2x-9/2x-2=1/2
2(2x-9)=2x-2
4x-18=2x-2
2x=16
x=8
LN=2x-2
LN=14 units
2. 2x-5/x+14=1/2
2(2x-5)=x+14
4x-10=x+14
3x=24
x=8
IH=2x-5
=11 units
3. (x+14)/(x+19)=1/2
2(x+14)=x+19
2x+28=x+19
x=9
CB=x+14
CB=23 units
4. 2x-11/x+11=1/2
2(2x-11)=x+11
4x-22=x+11
3x=33
x=11
IH=2x-11
IH=11 units
In triangle 1, The value of x is 8 and length of LN is 14 units. In triangle 2, The value of x is 8 and length of IH is 11 units. In triangle 3, The value of x is 9 and length of CB is 23 units. In triangle 4, The value of x is 11 and length of IH is 11 units.
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PLEASE HELP ME WITH THIS QUESTION!!!
QUESTION ATTACHED BELLOW
THANKS IN ADVANCE!
Answer:
y ≥ 2x + 4
hope this may help!
Please help it about calculus
The limit of the function [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)] when x tends to 1 is - 3 / 2.
How to find the limit of a function
In this problem we must determine the limit of a function, that is, the value to which the function goes when x tends to 1. This can be done by means of limit properties for polynomial and trigonometric limits.
First, write the limit:
[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)]
Second, use limit properties and algebra properties:
[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3 + 3 - 3 · x] / (2 · x - 2)]
[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3] / (2 · x - 2)] + [tex]\lim_{x \to 1}[/tex] [(3 - 3 · x) / (2 · x - 2)]
(3 / 2) · [tex]\lim_{x \to 1}[/tex] [[1 - cos (1 - x)] / (1 - x)] + (3 / 2) · [tex]\lim_{x \to 1}[/tex] [(1 - x) / (x - 1)]
Third, use polynomial and trigonometric limits:
(3 / 2) · 0 + (3 / 2) · (- 1)
Fourth, simplify the result:
- 3 / 2
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