Solving the modular arithmetic will result to
2 + n = 0 (mod 6): n = -22 + (3 + n) = 1 (mod 6): n = -4What is modular arithmetic?The term modular arithmetic is the arithmetic that works with whole numbers in a such that, following division by a modulus, all numbers are replaced by their remainders.
Solving the modular arithmetic: 2 + n = 0 (mod 6)
2 + n = 0 (mod 6)
n = -2
Solving the modular arithmetic: 2 + (3 + n) = 1 (mod 6):
2 + (3 + n) = 1 (mod 6)
5 + n = 1 (mod 6)
n = 1 - 5
n = -4
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What is a real solution example?
Solutions refers to the answer to the problem, The example of real solution can be the solution for the value of 'x' in a equation.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
x+2=0
x=-2
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A card is drawn from a standard deck of 52 cards. What is the theoretical probability, as a decimal, of drawing a number 8? Round the decimal to the nearest hundredth.
The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: A card is drawn from a standard deck of 52 cards. Let the probability be P then P= 1/52
=0.02
Hence, The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)
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How do you solve a 3 system of equations with 3 variables?
One way to solve a system of 3 equations with 3 variables is to use Gaussian elimination or Gauss-Jordan elimination method.
Gaussian elimination method:
Write the augmented matrix of the system of equations.Use row operations to transform the matrix into an upper triangular matrix.Use back substitution to find the values of the variables.The steps for Gaussian elimination are as follows:
Write the system of equations in matrix form, where the coefficients of the variables are in the matrix and the constants are in the column vector on the right side.Use row operations to transform the matrix into an upper triangular matrix. These operations include adding or subtracting multiples of one row to another, and multiplying or dividing a row by a non-zero scalar.Use back substitution to find the values of the variables. Starting with the last equation, substitute the known values of the variables into the other equations to find the value of the next variable. Repeat until all variables are known.Gauss-Jordan elimination method is similar to Gaussian elimination, however in the final step, it converts the matrix into a Reduced Row Echelon Form (RREF) which leads to more easily solving the system of equations.
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Joe the hiker decided to take a rest at the gas station before Kingston. While sitting at the picnic table, he noticed that there were many cars in the parking area. There were three times more silver colour cars than red cars. There were 2 more blue cars than red and silver cars together. There were twice more white cars than red. Joe counted 42 cars altogether in the parking lot.
How many white cars were there?
how many blue cars were ther?
how many red cars were there?
how many silvers were there
There are 7 white cars, 16 blue cars, 14 red cars and 5 silver cars.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let w represents white cars
b represent blue carr
r represents red cars
s represents silver cars
There were three times more silver colour cars than red cars
3s=r...(1)
There were 2 more blue cars than red and silver cars together
b+2=r+s..(2)
There were twice more white cars than red.
2w=r..(3)
42 cars altogether in the parking lot.
w+b+r+s=42
After solving the above equation we get
s=5, b=16, w=7 and r=14
Hence, there are 7 white cars, there are 16 blue cars, there are 14 red cars and 5 silver cars.
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The expression 8x +12y represents the sum of Harry and Mike's total monthly wages, where x represents the number of hours Harry worked and y represents the number of hours Mike worked. What is another way to write the expression, and what can you conclude from rewriting it in this way? 8(x +1. 5y); Harry's hourly wage is 1. 5 times Mike's. 8(x +1. 5y); Mike's hourly wage is 1. 5 times Harry's. 12(8x+y); Harry's hourly wage is 8 times Mike's. 8(x + 4y); Mike's hourly wage is 4 times Harry's.
this is a question of arithmetic and the solution is as follows,
The expression 8x + 12y represents the sum of harry and mike’s total monthly wages.
Generally the equation for the The Distributive property is mathematically given as,
a x (b +c) = a x b+ b x c.
Where
8x+12y
Therefore,
= 4 x 2x + 4 x 3x
= 4 x( 2x + 3x)
= 4( 2x + 3x)
Arithmetic
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division.
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Kate has $400. She wants to have $430 to buy a couch. How much interest would she have to earn in order to get the additional $30?
Select the best answer from the choices provided.
A. 3%
B. 4.5%
C. 6%
D. 7.5%
Answer:
D) 7.5%
Step-by-step explanation:
We can solve this through guessing and checking, or we can do this mathematically. We will try both approaches.
Mathematically:
We know that to get the extra $30 if we have $100, is a 30% interest. Now, since we have 4x 100, and these numbers are inversely proportional, we will need to divide 30 by 4. Doing this gives us 30/4 = 7.5, so the answer is 7.5%.
Guess and Check:
This way is a bit slower, but we will go through each answer and find how much money we would get from them. So, we would take our percent, change it to a number of that percent, considering we are taking it from 100, and multiply it by 4 since we have $400. We will get each of these respectively:
A) 3% = 3 * 4 = $12
B) 4.5% = 4.5 * 4 = $18
C) 6% = 6 * 4 = $24
D) 7.5% = 7.5 * 4 = $30
As you can see, D) gives us that extra $30, so the answer is D) 7.5%.
Hope this helped!
Solve |x| + 7 < 4.
{x | x < -11 or x > -3}
Ø
{x | -3 < x < 3}
The solution of equation is ∅.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols.
Given equation |x| + 7 < 4
subtract 7 from both sides
|x| + 7 - 7 < 4 - 7
|x| < -3
but |x| ≥ 0, for all real values,
so solution is ∅.
Hence the solution of equation is ∅.
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Mei needs to cut a 12-inch loaf of bread into slices that are inch thick.
a. How many 2-inch thick slices can Mei cut from the 12-inch loaf of bread?
b. How many inches of bread would be left over?
a. The number of 2-inch thick slices that Mei can cut from the 12-inch loaf of bread is 6.
b. The inches of bread that would be left over is zero.
How to illustrate the expression?The information given an be solved by Illustratingnut with an expression. This is simply used to show the relationship between the variables that are provided or the data given regarding an information.
Since Mei needs to cut a 12-inch loaf of bread into slices that are inch thick, the number of 2-inch thick slices that Mei can cut from the 12-inch loaf of bread is:
= 12 / 2
= 6
There'll be no left over
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Let Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).
(a) Using the distribution method, find the pdf of U = Z 2. (We proved this in class by using the MGF method. )
(b) Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution. Write down the corresponding parameters for each
On using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2
What is the Gamma Distribution ?
A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.
Given,
Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).
Using the distribution method, find the pdf of U = Z 2.
And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.
Suppose e Z ∼ N (0, 1), then
mZ (t) = 1√2πetxe−x2/2dx
= et2/21/√2π
[tex]e ^ {-(x-t)^{2} /2[/tex] dx
= [tex]e ^ {t^{2}[/tex]/ 2
hence, on using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2
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Please help:)
The table summarizes data about the median debt for graduating students from a sample of universities in California and New York.
median debt less than $9,000
median debt at least $9,000
total
California universities
130
445
575
New York universities
72
271
343
total
202
716
918
Is there an association between the state and the amount of median debt for graduates? Explain your reasoning
Yes, there is an association between the state and the amount of median debt for graduates.
What is median debt?Median debt is the midpoint of a range of debt levels for a specific group of people or organizations. This debt is usually reported as the sum of all loans and credit card balances owed by the group, divided by the total number of people or organizations in the group. Median debt is different from average debt, as it is not affected by extreme values. Median debt is a good measure of the financial health of a group because it provides an indication of the typical amount of debt held by an individual or organization.
In California, the median debt for graduates is significantly lower than in New York, with 130 graduates having median debt less than $9,000 and 445 graduates having median debt at least $9,000. In New York, 72 graduates have median debt less than $9,000 and 271 graduates have median debt at least $9,000. This indicates that graduates from California universities are more likely to have lower median debt than graduates from New York universities.
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The table above gives values of the function f at selected values of x. Which of the following statements must be true
On solving the provided question, we can say that the function's value
[tex]limx→4+f(x)=6limx→4+f(x)=6[/tex]
What is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
function's value will be -
limx→4+f(x)
=6limx→4+f(x)
=6
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Complete question is: The table above gives values of the function fat selected values of [tex]$\mathrm{x}$[/tex]. Which of the following statements must be true?
[tex]$$\text { A } \lim _{x \rightarrow 2} f(x)=3$$[/tex]
[tex]$$B \lim _{x \rightarrow 2} f(x)=8$$[/tex]
[tex]C\ $\lim _{x \rightarrow 2} f(x)$ does not exist.[/tex]
[tex]D\ $\lim _{x \rightarrow 2} f(x)$[/tex] cannot be definitively determined from the data in the table.
On a negatively skewed curve, which is true?
The mean of negatively skewed facts can be less than the median. If the information graphs symmetrically, the distribution has 0 skewness, no matter how lengthy or fat the tails are.
What is a curve ?
Curve can be defined as the path on which it is usually generated by the equation.
In statistics, a negatively skewed (also called left-skewed) distribution is a sort of distribution wherein more values are targeting the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
negatively skewed distribution refers to the distribution kind where greater values plot at the graph's proper facet, the tail of the distribution is longer on the left aspect, and the suggest is decrease than the median and mode. It is probably 0 or poor due to the data being distributed negatively.
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gong rented a truck for one day. There was a base fee of $19.95, and there was an additional charge of 71 cents for each mile driven. Hong had to pay $125.74 when he returned the truck. For how many miles did he drive the truck?
Answer:
19.95 + .71 × x = 125.74
x = 141.053
x is the answer
What is the inverse of negative 7?
The inverse of negative 7 when reciprocled is found to be as - 1/7.
The reciprocal of a number is known as the inverse of that number . The term reciprocal can be defined as, an expression or function which is related to another in such a manner that their product is unity, which means 1 , the quantity obtained by dividing the number one by a given quantity gives the original number back.
The term inverse means the reciprocal of an operation. Subtraction means to take away, and addition means to obtain the sum. Therefore , we can say that addition is the reverse of subtraction .As a result, addition and subtraction are diametrically opposed operations.
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Given that there are 4 quarts, 8 pints, or 16 cups in 1 gallon, which of the following amounts is greater than 2 gallons? Select all that apply.
A) 5 quarts, 2 pints
B) 1 gallon, 3 quarts
C) 9 quarts
D) 40 cups
E) 1 gallon, 9 pints
Answer:
C, D, E
Step-by-step explanation:
A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount spent on lunches. The variance of the cost of nine business dinners was and the variance on 12 lunches was . What test value should be used in an F test
Directions: Follow the instructions for the following inequalities.
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Please Write Your Answer Below:
Answer:
1. 4x3<7×3
12×2<21×2
24×4<42×4
96×9<168×9
864<1512
2. 11+3>-2+3
14+3>1+3
17_4>4-4
13>0
3. -2/leg-2
-18/leg-18
4. -4<8
0<2
Juanita changed $20 into euros when the exchange rate was €1=$1.2685.
How many euros did she receive?
Give your answer correct to 2 decimal places.
-15x+4x+2-x= x+ as a no solution
The equation -15x + 4x + 2 - x = x has solution and the solution is 2/13
How to determine if the equation has no solutionFrom the question, we have the following parameters that can be used in our computation:
-15x+4x+2-x= x+
Express the equation properly
So, we have the following representation
-15x + 4x + 2 - x = x
Collect the like terms in the equation
This gives
-x - 15x + 4x - x = -2
Evaluate the like terms
So, we have the following representation
-13x = -2
Divide both sides by -13
This gives
x = 2/13
Hence, the solution is 2/13
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You have $5$ red shirts, $5$ green shirts, $6$ pairs of pants, $8$ green hats and $8$ red hats, all of which are distinct. How many outfits can you make consisting of one shirt, one pair of pants, and one hat without having the same color of shirts and hats
Total = 240+240 = 480 potential combinations with a red shirt, green pants, and a green hat, or a green shirt, red pants, and a red hat, respectively.
How many outfit combinations can be put together from 6 shirts?The total number of possible outcomes for all four of these scenarios is 208, which is equivalent to 64 + 64 plus 16 plus 64. Consequently, we have a total of 120 different costumes to choose from (8 + 5 + 3). 8 × 5 × 3 = 120 . Given that you have 4 options for shirts, 3 options for shorts, and 2 options for shoes, the formula should be formatted as 4 × 3 ×2. You now have 24 wardrobe choices.
A "set" is made up of one top and one bottom. Since every bottom can be worn with every top, multiplying the tops by the bottoms gives us the total number of possible outfit combinations. Since dresses often aren't worn with tops or bottoms, they are introduced after the multiplication has occurred.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
1/2
3
1/3
If Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1) then the scale factor used is 1/3
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1).
A(−3, −3)---->A(−3/3, −3/3)---->A′(−1, −1)
B(3, 3)---->B(3/3, 3/3)---->B′(1, 1)
C(0, 1)---->C(0/3, 1/3)---->B′(0, 1/3)
Hence, the scale factor used is 1/3.
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hello!!!! please help me with this- i will you give brainlist :]
The completed blanks in the statement are underlined as follows
Standard form: x⁶ + 53x⁵ + 2x⁴ - 2The degree is 6 . The leading coefficient is 1This is called a polynomial because it has 4 termsHow to complete the blanks in the statementFrom the question, we have the following parameters that can be used in our computation:
A mathematical expression
The mathematical expression is given as
2x⁴ + 53x⁵ - 2 + x⁶
The standard form
To do this, we rearrange the expression from the highest power to the least
So, we have the following representation
x⁶ + 53x⁵ + 2x⁴ - 2
The degree
This is the highest power in the expression
So, the degree is 6
The leading coefficient
This is the coefficient of the term that has highest power of x
So, the leading coefficient is 1
The name of the expression
The expression has 4 terms
So, the name is a polynomial
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What is the area of the shaded region?
6 mm
21 mm2
24 mm
42 mm
48 mm2
4 mm
3 mm
2 mm
5 mm
Answer:
The area of the shaded region is, [tex]24mm^{2}[/tex]
Step-by-step explanation:
First we have to calculate the area of ΔABC and ΔXYZ.
Area of ΔABC = [tex]\frac{1}2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]
Area of ΔABC = [tex]\frac{1}{2}[/tex]×[tex]5mm[/tex]×[tex]12mm[/tex]
Area of ΔABC =[tex]30mm^{2}[/tex]
and,
Area of ΔXYZ = [tex]\frac{1}{2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]
Area of ΔXYZ = [tex]\frac{1}{2} X3mmX4mm[/tex]
Area of ΔXYZ = [tex]6mm^{2}[/tex]
Now we have to calculate the area of the shaded region.
Area of the shaded region = Area of ΔABC - Area of ΔXYZ
Area of the shaded region = [tex]30mm^{2} - 6mm^{2}[/tex]
Area of the shaded region = [tex]24mm^{2}[/tex]
Therefore, the area of the shaded region is, [tex]24mm^{2}[/tex]
determine whether each table represents a linear or non-linear function explain
Each of the tables is classified as linear or non-linear on the image presented at the end of the answer.
How to classify the functions as linear or non-linear?A function is classified as linear or non-linear depending on the rate of change of the function.
If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.
Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.
For example, the top-left function is non linear, as when x changes by one from x = 1 to x = 2, y changes by 3, from y = 1 to y = 4, while when x changes by one from x = 2 to x = 3, y changes by 5.
The bottom-right function is linear, as for each increase of x by 5, the value of y decays by 4.
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A plane flew 390 nautical miles in 45 min. Find its average speed in knots ( nautical miles per hour)
Answer:
Step-by-step explanation:
1.change minutes to hours,45 minutes is [tex]\frac{3}{4}[/tex] hours
2.then use 390÷ [tex]\frac{3}{4}[/tex]=390·[tex]\frac{4}{3}[/tex]=130·4=520 nautical per hour
Which ratio forms a probation with 18/30
=20/35
=50/90
=36/46
=60/100
Answer:
Which ratio forms a probation with 18/30
=20/35
=50/90
=36/46
=60/100
Step-by-step explanation:
Bella has a cell phone plan in which she pays of each call minute and text message she sends. The total number of minutes used and text messages sent last month was 561. If call minutes cost 8€ each and text messages cost 5€ each and her pill was $34. 26, how many minutes did she use?
If the total number of minutes used and text messages sent last month was 561 , then the number of minutes she use is 207 minutes .
The total number of minutes used and text messages is = 561 ;
the cost for per minute cost is = 8 cents ;
the cost for per text message is = 5 cents ;
Bella's total bill amount is = $34.26 = 3426 cents
let the number of minutes used be = x minutes ; and
let the number of text messages be = y ;
So ,According to the question ,
the equations representing the situations are ,
[tex]x+y=561[/tex] and [tex]8x+5y=3426[/tex]
Substituting the values of [tex]y=561-x[/tex] in the equation [tex]8x+5y=3426[/tex] ,
we get ;
[tex]8x + 5(561-x)= 3426[/tex]
On solving ,
we get ; x = 207 minutes ;
So , the number of text messages (y) = [tex]561-207[/tex]
= 354 text messages.
Therefore , the number of minutes is = 207 minutes .
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road to white house Math
The value of f(4) - g(-5) if function f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x) = 3 / 2x + 2 and g(x) = 2x² - 3
Calculate the value of f(4) and g(-5) as shown below,
f(4) = 3 / 2 × 4 + 2
f(4) = 12 / 2 + 2
f(4) = 6 + 2
f(4) = 8
g(-5) = 2 × (-5)² - 3
g(-5) = 2 × 25 - 3
g(-5) = 50 - 3
g(-5) = 47
Now, calculate the value of f(4) - g(-5) as shown below,
f(4) - g(-5) = 8 - 47
f(4) - g(-5) = -39
Thus, the value of f(4) - g(-5) is -39.
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For what value of k (- 2 is a zero of the polynomial 3x² 4x 2k?
The polynomial's zero is 2 since the value of k = -2 is [tex]3x^{2}[/tex] +4x+2k . A polynomial is an equation that combines variables, constants .
what is polynomial ?Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).
given
−2 is a zero of f(x)=[tex]3x^{2}[/tex]+4x+2k
f(−2)=0
∴[tex]3(-2)^{2}[/tex] +4(−2)+2k=0
=>12−8+2k=0
=>2k=−4
=>k=−2
The polynomial's zero is 2 since the value of k = -2 is [tex]3x^{2}[/tex] +4x+2k .
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HELP ASAP PLS 50!!!!
Identify or mark the missing side or angle that would make triangle ABC a congruent to triangle PDF by SAS
Answer:
AC = PF
Step-by-step explanation: