The limit to be calculated is:
[tex]\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}[/tex]Notice that:
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+5x+4}=\frac{(x-2)(x+4)}{(x+1)(x+4)} \\ =\frac{(x-2)}{(x+1)},x\ne-4 \end{gathered}[/tex]Remember that, in the limit when x->-4, the value of x approaches to -4, but it never is -4. Thus, we can use the last line of the identity above,
[tex]\begin{gathered} \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=\lim _{x\to-4}\frac{(x-2)(x+4)}{(x+1)(x+4)}=\lim _{x\to-4}\frac{(x-2)}{(x+1)}=\frac{(-4-2)}{(-4+1)}=-\frac{6}{-3}=2 \\ \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=2 \end{gathered}[/tex]The answer is 2.
textFor this fraction 12/13 the numerator is
It is given that the fraction is:
[tex]\frac{12}{13}[/tex]If a fraction is given by:
[tex]\frac{p}{q}[/tex]Then p is called numerator and q is called denominator.
Hence the numerator is 12 and denominator is 13.
Each gallon of gas cost $2.50. Nathan spent $30 on gas. Which value of x represents the number of gallons of gas Nathan purchased?
we have the following:
[tex]\begin{gathered} x=\frac{30}{2.5} \\ x=12 \end{gathered}[/tex]therefore the number of galllons is 12
The table below shows the number of months and the amount spent on internet service. Which equation represents the total cost (t) based on the number of months (m) of service?1. t=45m 2. t=2m 3. t=90m4. t=4me
Given:
Number of months and the amount spent on internet service is tabulated.
Let the total cost (t) and the number of months (m)
Therefore equation is
[tex]t=45m[/tex]Three girls play three rounds of a game. On each round there are two winners and one loser. The girl who loses on a round has to double the number of chips that each of the other girls has by giving up some of her own chips. Each girl loses one round. At the end of three rounds, each girl has 24 chips. How many chips did each girl have at the beginning of the game?
The Solution:
Let the 3 girls be represented with A, B, and C.
At round 1:
Let C be the loser while A and B are winners.
A has 12 chips
B has 21 chips
C has 39 chips
At round 2:
Let B be the loser while A and C are winners.
A has 24 chips
B has 42 chips
C has 6 chips
At round 3:
Let A be the loser while A and C are winners.
A has 24 chips.
B has 24 chips.
C has 24 chips.
Therefore, the girl A has 12 chips, girl B has 21 chips and girl C has 39 chips at the beginning of the game.
Sam paid $4.50 to have two shirts cleaned. If the dry cleaning service charges the same amount for any shirt, which equation can be used to represent the total cost, c, of having n shirts cleaned? A c = 4.5n B. c = 2.25n C. c = 4.5 +n D. c = 2.25 + n
Sam paid $4.50 to have two shirts cleaned.
If the dry cleaning service charges the same amount for any shirt then it means that for each shirt the rate is
[tex]\frac{\$4.50}{2}=\$2.25[/tex]If there are n shirts then the total cost (c) of the shirts can be represented by the following equation.
[tex]c=2.25n[/tex]If you substitute n = 2 shirts into the above equation then the total cost will be $4.50 which satisfies the given information.
Therefore, the correct answer is option B
a bank loaned out 2000, part of it at the rate of 8% per year and the rest at 16% per year. If the interest received in one year totaled $2000, how much was loaned at 8%?
The amount loaned at 8% interest is $15000
How to find how much was loaned at 8%?Using the simple interest formula, we find the interest obtained at each rate.
Simple interest, I = PRT where
P = initial amount, R = rate and T = timeNow, the interest obtained at 8%,I₁ = P₁R₁T where
P₁ = amount loaned at 8%, R₁ = rate = 8% per year = 0.08 and T = time = 1 year
Also, the interest obtained at 16%,I₂ = P₂R₂T where
P₂ = amount loaned at 16%, R₂ = rate = 16% per year = 0.16 and T = time = 1 yearSo, the total interest received is I = I₁ + I₂
= P₁R₁T + P₂R₂T
= P₁ × 0.08 × 1 + P₂ × 0.16 × 1
= 0.08P₁ + 0.16P₂
Since the total interest received is $2000,we have that
I = $2000.
So, I = 0.08P₁ + 0.16P₂
0.08P₁ + 0.16P₂ = 2000 (1)
Since the amount loaned by the bank is P = P₁ + P₂ and P = $20000, we have that
P₁ + P₂ = 20000
P₂ = 20000 - P₁ (2)
Substituting equation (2) into (1), we have that
0.08P₁ + 0.16P₂ = 2000 (1)
0.08P₁ + 0.16(20000 - P₁) = 2000
Expanding the brackets, we have
0.08P₁ + 0.16 × 20000 - 0.16P₁ = 2000
0.08P₁ + 3200 - 0.16P₁ = 2000
0.08P₁ - 0.16P₁ = 2000 - 3200
- 0.08P₁ = -1200
P₁ = -1200/-0.08
P₁ = 15000
So, the amount loaned at 8% is $15000
The question seems incomplete, here is the complete question
A bank loaned out $20,000, part of it at the rate of 8 % per year and the rest at 16 % per year. If the interest received in one year totaled $2000, how much was loaned at 8 %
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a 180 ounce bag weighs more than an 11 lb bag true or false
Let's make a conversion:
[tex]180oz\times\frac{1lb}{16oz}=11.25lb[/tex]Since:
[tex]11.25lb>11lb[/tex]It's true
The product of two consecutive odd numbers is 323. Find the numbers.
Let the two consecutive numbers be x and (x+2).
According to the given condition,
-0.15 decimal as a fraction or mixed number in simplified
Answer:
-3/20
Explanation:
Given the decimal number: -0.15
There are 2 digits after the decimal point, therefore in fraction form, we have:
[tex]-0.15=-\frac{15}{100}[/tex]Next, the fraction is reduced to its simplest form.
[tex]-\frac{15}{100}=-\frac{5\times3}{5\times20}=-\frac{3}{20}[/tex]The simplified form is -3/20.
Solve the system of equations by transforming a matrix representing the system of equation into reduced row echelon form. 2x+y-3z=-19 x+2y+z=-4 x-y+5z=21 what is the solution to the system of equations? Drag a choice into each box to correctly complete the table.
We want to write the following system
[tex]\begin{gathered} 2x+y-3z=-19 \\ x+2y+z=-4 \\ x-y+5z=21 \end{gathered}[/tex]As a matrix. To do that, we just take the coefficients and plug them in the same order in a matrix. Our system can be rewritten as:
[tex]\begin{bmatrix}{2} & 1 & {}-3 \\ {1} & {2} & 1{} \\ {1} & {-1} & {5}\end{bmatrix}=\begin{bmatrix}{-19} \\ {-4} \\ {21}\end{bmatrix}[/tex]Now, to solve this, we can use the gaussian elimination. It consists of adding, multiplying, and changing the order of the rows, until we have an identity matrix on the left side.
Let's start by subtracting the second row from the third row, and subtracting 2 times the second row from the first row.
[tex]\begin{gathered} \begin{bmatrix}{2-2\times1} & 1-2\times2 & {}-3-2\times1 \\ {1} & {2} & 1{} \\ {1-1} & {-1-2} & {5-1}\end{bmatrix}=\begin{bmatrix}{-19-2\times(-4)} \\ {-4} \\ {21-(-4)}\end{bmatrix} \\ \begin{bmatrix}{0} & -3 & {}-5 \\ {1} & {2} & 1{} \\ {0} & {-3} & {4}\end{bmatrix}=\begin{bmatrix}{-11} \\ {-4} \\ {25}\end{bmatrix} \end{gathered}[/tex]Multiplying the first row by (- 1), we have:
[tex]\begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {-3} & {4}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {25}\end{bmatrix}[/tex]Adding the first row to the third row, we have:
[tex]\begin{gathered} \begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {-3+3} & {4+5}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {25+11}\end{bmatrix} \\ \begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {0} & {9}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {36}\end{bmatrix} \end{gathered}[/tex]Multiplying the last row by 1/9:
[tex]\begin{bmatrix}{0} & 3 & {}5 \\ {1} & {2} & 1{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{11} \\ {-4} \\ {4}\end{bmatrix}[/tex]Now, subtracting the third row from the second row, and subtracting 5 times the third row from the first row, we have:
[tex]\begin{gathered} \begin{bmatrix}{0} & 3 & {}5-5\times1 \\ {1} & {2} & 1-1{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{11-5\times4} \\ {-4-4} \\ {4}\end{bmatrix} \\ \begin{bmatrix}{0} & 3 & {0} \\ {1} & {2} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-9} \\ {-8} \\ {4}\end{bmatrix} \end{gathered}[/tex]Dividing the first row by 3:
[tex]\begin{bmatrix}{0} & 1 & {0} \\ {1} & {2} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-3} \\ {-8} \\ {4}\end{bmatrix}[/tex]Subtracting the twice the first row from the second row:
[tex]\begin{gathered} \begin{bmatrix}{0} & 1 & {0} \\ {1} & {2-2\times1} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-3} \\ {-8-2\times(-3)} \\ {4}\end{bmatrix} \\ \begin{bmatrix}{0} & 1 & {0} \\ {1} & {0} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-3} \\ {-2} \\ {4}\end{bmatrix} \end{gathered}[/tex]And finally, permuting the first and the second row
[tex]\begin{bmatrix}{1} & 0 & {0} \\ {0} & {1} & 0{} \\ {0} & {0} & {1}\end{bmatrix}=\begin{bmatrix}{-2} \\ {-3} \\ {4}\end{bmatrix}[/tex]And this is our answer.
[tex]\begin{bmatrix}{1} & 0 & {0} \\ {0} & {1} & 0{} \\ {0} & {0} & {1}\end{bmatrix}\begin{bmatrix}{x} \\ {y} \\ {z}\end{bmatrix}=\begin{bmatrix}{-2} \\ {-3} \\ {4}\end{bmatrix}[/tex]what is the acceleration of a car that goes from 10 mph to the speed of 50 mph in four seconds
The acceleration is given by the variation of the speed divided by the time.
So:
[tex]\begin{gathered} a=\frac{v-v0}{t} \\ a=\frac{50-10}{4} \\ a=40/4 \\ a=10m/s^{2} \end{gathered}[/tex]Answer: 10m/s²
The amount of detergent dispensed into bottles of liquid laundry detergent bottles for a particular brand is normally distributed with a mean of 87.9 ounces with a standard deviation of 1.3 ounces. If twenty-four bottles are randomly chosen from the factory, what is the probability that the mean fill is more than 88.2 ounces?
The probability that the mean fill is more than 84.8 ounces is 0.39358
From the question, the given parameters about the normal distribution are
Mean value of the set of data = 88.2
Standard deviation value of the set of data = 1.3
The actual data value = 88.2
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (88.2 - 87.9)/1.3
Evaluate the difference of 88.2 and 87.9
z = 0.3/1.3
Evaluate the quotient of 0.3 and 1.1
z = 0.23
The probability that the mean fill is more than 88.2 ounces is then calculated as:
P(x > 88.2) = P(z > 0.23)
From the z table of probabilities, we have;
P(x > 88.2) = 0.5910
Hence, the probability that the mean fill is more than 84.8 ounces is 0.5910
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An uber charges a flat fee of $1.50, plus an additional $0.75 per mile. If Max only
has up to $12 to spend?
Answer:
14 miles
Step-by-step explanation:
If you have $12 to spend and there's a flat fee $1.50
You subtract your $1.50 from $12
12-1.50=10.50
Then you divide 10.50 by .75
10.50÷.75=14
So you get 14 miles with $12
ess BosseCoursesRead bar graprisBella counted the number of students who play various instruments in her school's marching band and graphedthe results.file48> 1 34032ASCNumber of students24As16MY8Со0TATUSFluteSaxophone DrumsTrombone TrumpetMYInstrumentProWhich instruments did the same number of students play?ProChoose 2 answers:TeaFluteTrombone
SOLUTION:
Step 1 :
In this question, we are told that Bella counted the number of students who play various instruments in her school's marching band and graphed
the results.
We are asked to find the instruments did the same number of students play.
Step 2:
From the graph, we can see clearly that the same number of students play
Saxophone and Drums.
CONCLUSION:
SAXOPHONE -- OPTION D
DRUMS -------------OPTIO
I mostly need to know if this are correct and if the answers would gave been affected.
Yes, your answers are correct.
And the answer would be different if the non-Normal because all the calculations are based on a normal ditributed production of the chocolate bars; if the production of the chocalte bars had a non normal distribution, for example a skewed distribution (to the left or to the right) all the values used in the calculation would be different.
The Panthers and the Vikings are competing for the state basketball championship. The data shows the height in inches of the starting lineup for
each team.
Panthers: 72, 74, 71, 73, 75
Vikings: 71, 77, 76, 74, 74
Which statement is true about the data?
The average height of the Viking's starting lineup is 1.4 inches greater than the average height of the Panther's starting lineup.
The Panthers and the Vikings are competing for the state basketball championship. The data shows the height in inches of the starting lineup for each team.
The heights of the players on the Panther's team are 72, 74, 71, 73, and 75. The heights of the players on the Viking's team are 71, 77, 76, 74, and 74.
Let the average height of the Panther's starting lineup be denoted by the variable "A1".
A1 = (72 + 74 + 71 + 73 + 75)/5
A1 = 365/5
A1 = 73
So, the average height of the Panther's starting lineup is 73 inches.
Let the average height of the Viking's starting lineup be denoted by the variable "A2".
A2 = (71 + 77 + 76 + 74 + 74)/5
A2 = 372/5
A2 = 74.4
So, the average height of the Viking's starting lineup is 74.4 inches.
The difference in the average height is calculated below.
d = A2 - A1
d = 74.4 - 73
d = 1.4
Hence, the average height of the Viking's starting lineup is 1.4 inches greater than the average height of the Panther's starting lineup.
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5y - 10 = -25A) y = 3 B) y = 7 C) y = -3 D) y = -7
We want to solve the equation;
[tex]5y-10=-25[/tex]We start by collecting like terms;
[tex]\begin{gathered} 5y=-25+10 \\ 5y=-15 \\ y=-\frac{15}{5} \\ y=-3 \end{gathered}[/tex]are these equivalent 12:8 and 18:12
To ascertain fi the ratio 12:8 is equivalent to 18:12 we have to reduce the ratios
[tex]12\colon8=\frac{12}{8}=\frac{3}{2}=3\colon2[/tex][tex]undefined[/tex]Please help me find the volume of x for number two
8.1
Remember cos = adjacent side (in this case X) / hypotenuse (10)
Solve this world problem
The function is
y=0,7x+80
and they ask you the point (6, )
this means x=6
so we need to replace x=6 on the function and find out the value of y
Y=0,7*6+80
Y=4.2+80=84.2
So the answer is: (6, 84.2)
and this means that 6 years before 1999, the number of households that have at least one microwave is 84.2 million
For C. 2014 is (2014-1999=15) 15 years after 1999
So we replace x=15
Y=15*0,7+80=90.5
So the answer is: 90.5 million households
the sum of three consecutive numbers is one hundred five.What is the smallest of the three numbers
For this problem we know that the sum of 3 consecutive numbers is one hundred five. Let's assume that the 3 numbers is: a, a+1, a+2
And we can set up the following equation:
[tex]a+(a+1)+(a+2)=105[/tex]And we can solve for a like this:
[tex]3a+3=105[/tex]We can subtract 3 in both sides and we got:
[tex]3a=102[/tex]And we can divide both sides by 3 and we got:
[tex]a=\frac{102}{3}=34[/tex]And we can conclude that the smallest number is 34
A doughnut shop sells 24 boxes of doughnuts in 2 hours. How many boxes do they sell in 4 hours?
shop sells 24 boxes in 2 hrs
so in 1 hrs shop sells 24/2 = 12 boxes,
so in 4 hrs shop sells 12 x 4 = 48 boxes.
The population of a certain species of owl at a wildlife preserve can beapproximated by the functionN(t) =20401+39e-0.51where N(t) represents the number of owls and t is the time (in years).a.) What was the initial population of the owls?b.) How many owls will there be in the wildlife preserve in the long run? Inother words, what is the limit as t approaches infinity?c.) how many years will it take until there are 950 owls in the wildlife preserve?
Question A.
The initial population ocurrs at t=0. Then, by substituting this value into the given model ,we get
[tex]N(0)=\frac{2040}{1+39e^0}[/tex]which gives
[tex]\begin{gathered} N(0)=\frac{2040}{1+30} \\ N(0)=\frac{2040}{40} \\ N(0)=51 \end{gathered}[/tex]then, the answer is 51 owls.
Question B.
The limits when t approaches to + infinity is
[tex]\begin{gathered} N(0)=\frac{2040}{1+39e^{-\infty}} \\ N(0)=\frac{2040}{1+0} \\ N(0)=\frac{2040}{1}=2040 \end{gathered}[/tex]then, the answer is 2040 owls.
Question 15.
In this case, we need to find t when N(t) is 950, that is,
[tex]950=\frac{2040}{1+39e^{-0.5t}}[/tex]By moving the denominator to the left hand side, we have
[tex](1+39e^{-0.5t})950=2040[/tex]then, by moving 950 to the right hand side, we obtain
[tex]\begin{gathered} (1+39e^{-0.5t})=\frac{2040}{950} \\ 39e^{-0.5t}=\frac{2040}{950}-1 \end{gathered}[/tex]which is
[tex]39e^{-0.5t}=1.147368[/tex]so, we get
[tex]\begin{gathered} e^{-0.5t}=\frac{1.147368}{39} \\ e^{-0.5t}=0.029419 \end{gathered}[/tex]By applying natural logarithms to both sides, we have
[tex]\begin{gathered} -0.5t=\ln (0.029419) \\ t=\frac{-\ln(0.029419)}{0.5} \end{gathered}[/tex]then, the answer is
[tex]t=7.05[/tex]By rounding o the neares interger, the answer is 7 years
Andrea, Ben, Christine, and Doug all live on the same street as their school. The street runs from east to west.Andrea lives 5 1/2 blocks to the west of school.Ben lives 4 blocks to the east of school.Christine lives 2 blocks to the west of school.Doug lives 6 1/2 blocks to the east of school.Use this information to complete the following.Part ARepresent the relative position of the houses on a number line with the school at zero, points to the west represented by negative numbers, and points to the east represented by positive numbers.Part BHow far does Ben live from Andrea? Show how you arrived at your answer using sums or differences.
From the statement of the problem, we know that.
• Andrea lives 5 1/2 blocks to the west of school → x = -5.5,
,• Ben lives 4 blocks to the east of school → x = +4,
,• Christine lives 2 blocks to the west of school → x = -2,
,• Doug lives 6 1/2 blocks to the east of school → x = +6.5.
A) Using the data above, we have:
B) The x coordinate of:
• Andrea is x_A = -5.5,
,• Ben is x_B = +4.
The distance between Ben and Andrea is equal to the difference between its coordinates:
[tex]d=x_B-x_A=4-(-5.5)=4+5.5=9.5.[/tex]We find that Ben lives 9.5 blocks from Andrea.
without graphing, identify the equation of the axis of symmetry for f(x)=-3|x-2|-7
Solution:
Given:
[tex]f(x)=-3|x-2|-7[/tex]From the absolute function, the axis of symmetry is;
[tex]\begin{gathered} y=|x-a| \\ where: \\ a\text{ is the axis of symmetry} \end{gathered}[/tex]Hence, comparing it to the equation given;
[tex]\begin{gathered} f(x)=-3|x-2|-7 \\ y=|x-a| \\ \\ a=2 \\ Hence,\text{ the axis of symmetry is at x = 2} \end{gathered}[/tex]Therefore, OPTION C is correct.
Answer: other guy is wrong it’s x= -2
Step-by-step explanation:
Which is less: (-25) + 12 or 40 + (-63)? Show your work.
The first expression
(-25) + 12
open the parentheses
-25 +12
= - 13
for the second expression
40 + (-63)
in mathematics
- x + = -
40 - 63
= -23
from the two results
-13 and -23
-13 is greater than -23, therefore -23 is less or 40 + (-63)
answer: 40 + (-63) is less
15/9 equals 40 over n
Given the following equation:
[tex]\begin{gathered} \frac{15}{9}=\frac{40}{n} \\ \\ \end{gathered}[/tex]You need to solve for the variable "n" in order to find its value.
The steps are shown below:
1. You can multiply both sides of the equation by "n":
[tex]\begin{gathered} (n)(\frac{15}{9})=(\frac{40}{n})(n) \\ \\ \frac{15n}{9}=40 \end{gathered}[/tex]2. Now you need to multiply both sides of the equation by 9:
[tex]\begin{gathered} (9)(\frac{15n}{9})=(40)(9) \\ \\ 15n=360 \end{gathered}[/tex]3. Finally, you can divide both sides of the equation by 15:
[tex]\begin{gathered} \frac{15n}{15}=\frac{360}{15} \\ \\ n=24 \end{gathered}[/tex]The answer is:
[tex]n=24[/tex]An employee at a state park has 84 photos of animals found at the park. She wants to arrange the photos in rows so that every row except the bottom row has the same number of photos. She also wants there to be at least 8 rows. Complete the description of two different ways she can arrange the photos.
Reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.5 rows of 10 photos and last row with 3 photos,
6 rows of 8 photos and last row with 5 photos,
7 rows of 7 photos and last row with 4 photos,
Hence, reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
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In Exercises 1-3, the perpendicular blsectors of ABC Intersect at point G, or the anglebisectors of AXYZ intersect at point P. Find the Indicated measure. Tell which theoremyou used.
We have a line:
And we draw its perpendicular bisector:
Then, any point on the bisector is equidistant to the endpoints of the line:
This is called: the perpendicular bisector theorem.
1In this case we have that:
Since the line is the black one, the bisector is the purple one, then both red segments measure the same : 9.
Answer: BG = 9 (bisector theorem)
2In this case, as we can observe in the image, the red lines are equidistant then CG = 10
Answer: CG = 10 (bisector theorem)
name the vertex of anglea) name the vertex of the angleb)name the sides of the angle e)give three ways to name the anglec) classify the angle
(a) We can name the vertex as B.
(b) We can name the sides as A and C.
The image below shows the angles with their names.
(c) The angle on the left is an obtuse angle because it measures more than 90°. The angle on the right is a right angle because it's equal to 90°.
(e) At last, we name these angles in three ways, using a greek later, using the three letters on the points, or just given the letter of the vertex.
[tex]\begin{gathered} m\angle\alpha \\ m\angle\text{ABC} \\ m\angle B \end{gathered}[/tex]