use pumping lemma {w | w ∈ {0,1}* and w has 1 except as third character}
Answers
none of the possible cases for y satisfy the conditions of the pumping lemma. This means that L cannot be a regular language, and we have a contradiction. Therefore, the language L = {w | w ∈ {0,1}* and w has 1 except as third character} is not regular.
We can prove that the language L = {w | w ∈ {0,1}* and w has 1 except as third character} is not regular by using the pumping lemma for regular languages.
Suppose that L is a regular language, and let n be the pumping length given by the pumping lemma. Consider the string \(s = 0^n1(0+1)^n\). Since s is in L and |s| = 2n+1 > n, we can apply the pumping lemma to s.
By the pumping lemma, we can write s as s = xyz, where |y| > 0, |xy| ≤ n, and for all\(i ≥ 0, xy^iz ∈ L\). Let's consider the possible cases for the string y:
y consists only of 0's: in this case,\(xy^iz\) still has 1 as its third character, so it cannot be in L.
y consists of both 0's and 1's: in this case, \(xy^iz\)has 1 as its third character when i is odd, but not when i is even. Therefore, \(xy^iz\) cannot be in L for all i.
y consists only of 1's: in this case, we can write y = 1^k, where 1 ≤ k ≤ n. Then, \(xy^iz = 0^n1^(k+i)(0+1)^(n-k)\)for all i ≥ 0. If we choose i = 0, then \(xy^0z = 0^(n+k)(0+1)^(n-k) ∈ L\). However, this contradicts the definition of L, since the second character in\(xy^0z\) is a 0, not a 1.
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Related Questions
cos 0 = 12/13. Find sin 0.
A. 5/12
B. 12/5
C. 13/12
D. 5/13
Answers
From the question given above, the following data were obtained:
Cos θ = 12/13
Sine θ =?
Next, we shall determine the opposite. This can be obtained as follow:
\(Cos \theta = \frac{Adjacent}{Hypothenus}\\\\Cos \theta = \frac{12}{13}\)
Adjacent = 12
Hypothenus = 13
Opposite =?Hypothenus² = Opposite² + Adjacent²
13² = Opposite² + 12²
169 = Opposite² + 144
Collect like terms
169 – 144 = Opposite²
25 = Opposite²
Take the square root of both side
Opposite = √25
Opposite = 5Finally, we shall determine the Sine θ. This can be obtained as follow:
Opposite = 5
Hypothenus = 13
Sine θ =.?\(Sine\theta = \frac{Opposite}{Hypothenus}\\\\Sine\theta = \frac{5}{13}\)
Therefore, the value of Sine θ is 5/13
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Answer:
D. 5/13
Step-by-step explanation:
Cannon wants to put as much as he can into a retirement account as soon as he starts working. He deposits $25,000 at then end of each year for 5 years in an account paying 6% interest compounded annually. How much will he have in the account at the start of the 6th year? A) $140,927.34 B) $174,382.96 C) $395,240 D) $557,593.99
Answers
The compound interest formula is given by the formula
\(A\text{ = }p(1+\frac{r}{100})t\)Where A = Amount after t years
r = rate = 6
t = time = 5
p = $ 25000
For the first year
\(\begin{gathered} A=\text{ 25000(1+0.06)} \\ =25000\times1.06=26500 \end{gathered}\)For the second year
P=26500+25000=51500
\(\begin{gathered} A=51500(1+0.06) \\ =515000\times1.06=54590 \end{gathered}\)For the third year
P=54590 + 25000=79590
\(\begin{gathered} A=79590\text{ }\times1.06 \\ =84365.4 \end{gathered}\)For the fourth year
P=84365.4 + 25000=109365.4
\(\begin{gathered} A=\text{ 109365.4}\times1.06 \\ =115927.324 \end{gathered}\)For the fifth year
P= 115927.324 + 25000 =140927.324
\(\begin{gathered} A=\text{ 140927.324}\times1.06 \\ =149382.962 \end{gathered}\)At the start of the 6th year
P= 149382.962+25000= 174382.96
Answer = $174382.96
Option B is correct
at a certain high school, the prom committee is going to choose new members. there are students from the junior class and students from the senior class who are willing to be new members. in how many ways can new members be chosen if more than must be from the senior class?
Answers
Answer:
Step-by-step explanation:
7 students from the Junior class.
6 students from the Senior class.
4 new members are to be chosen.
Required: Find the number of ways 4 new members can be chosen if 2 or fewer must be from the senior class. So, Therefore, the correct answer is 560 ways.
review the simple interest rate based on FICO scores to answer the question:
Callie plans to borrow $4,100.00 with a simple interest rate loan. determine the amount of Interest Callie will save if she is able to raise your credit score from 700 to 800.
$49.91
$70.27
$176.10
$157.32
Answers
Using simple interest, it is found that Callie will save $157.32 if she is able to raise your credit score from 700 to 800.
Simple InterestThe amount of interest after t years in simple interest is modeled by:
\(I = Prt\)
In which:
P is the initial amount. r is the interest rate, as a decimal.t is the time, in years.In this problem:
She plans to borrow $4,100.00 with a simple interest rate loan, hence \(P = 4100\).One year, hence \(t = 1\).With a credit score of 700, the rate is of \(r = 0.08132\), hence:
\(I = 4100(0.08132) = 333.41\)
With a credit score of 800, the rate is of \(r = 0.04295\), hence:
\(I = 4100(0.04295) = 176.09\)
Then, the amount saved is:
\(333.41 - 176.09 = 157.32\)
Callie will save $157.32 if she is able to raise your credit score from 700 to 800.
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what is 40x^2-48
40x
2
−48
Answers
. The length and width of a rectangular garden are 8 12 and respectively X-1 x+2 What is the perimeter of the garden?
Answers
Answer:
27
Step-by-step explanation:
thatssss enoughhhhhhhh!
Find two values of 8 with 0 ≤ θ<2π that satisfy the trigonometric equation. Round your answers to 4 decimal places.
7 sin θ-2 = 0.
The first value of 8 is (Enter the smaller value here).
The second value of 8 is (Enter the larger value here)
Answers
The two values of θ that satisfy the equation 7sinθ - 2 = 0 are The smaller value: 0.2915 (rounded to 4 decimal places)The larger value: 6.5731 (rounded to 4 decimal places)
To find the values of θ that satisfy the equation 7sinθ - 2 = 0, we can rearrange the equation and solve for sinθ:
7sinθ - 2 = 0
7sinθ = 2
sinθ = 2/7
To find the values of θ, we can take the inverse sine (sin^(-1)) of both sides:
θ = sin^(-1)(2/7)
Using a calculator, we can find the value of sin^(-1)(2/7) to be approximately 0.2915 radians.
Since we are looking for two values of θ between 0 and 2π, we can add or subtract the period of the sine function, which is 2π.
First value of θ:
θ = 0.2915 radians
Second value of θ:
θ = 0.2915 + 2π = 6.5731 radians
Therefore, the two values of θ that satisfy the equation 7sinθ - 2 = 0 are approximately:
The smaller value: 0.2915 (rounded to 4 decimal places)
The larger value: 6.5731 (rounded to 4 decimal places)
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find the probability of picking 5 vowels and 1 constant when 6 letters are picked with replacement from a set of alphabet tiles
Answers
The probability of picking 5 vowels and 1 constant when 6 letters are picked with replacement from a set of alphabet tiles is 2.12.
To find the probability of picking 5 vowels and 1 constant when 6 letters are picked with replacement from a set of alphabet tiles:
Given:
5 vowels1 consonantTo find:
The probability of picking 5 vowels and 1 consonant letter from the English Alphabet with a replacement.There is 26 English Alphabet.There are 5 vowels in the alphabet.There are 21 consonants in the alphabet.The probability of picking 5 vowels:
5 vowels = 5/26 × 5/26 × 5/26 × 5/26 × 5/26 = 3125/11,881376The probability of picking 1 consonant:
1 constant = 21/26 = 21/26The probability of picking 5 vowels and 1 consonants:
5 vowels 1 constant = 3125/11,881,376 × 21/26 = 65625/308915776 = 2.12436.Therefore, the probability of picking 5 vowels and 1 constant when 6 letters are picked with replacement from a set of alphabet tiles is 2.12.
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5) |-16 |- |-2|
Evaluate
Answers
Answer:
16-2=14
Explination:
Since they were both in the absolute value markers, they remain positive, but since there was a subtraction symbol between them then you subtract the 2 from the 16
Please help answer!!!!
Answers
The total number of students who attended Lacey's high school is represented with the expression \(4\times10^4\).
\(4\times10^4=40,000\)
The total number of students who attended Lacey's high school is 40,000.
__________________________________________________________
The total number of students who attended Monique's high school is represented with the expression \(3\times10^5\).
\(3\times10^5=300,000\)
The total number of students who attended Monique's high school is 300,000.
__________________________________________________________
Monique's high school has a greater number of students than Lacey's high school does.
is the line through (-4, 26, 1) and (-2, 0, -3) parallel to the line through (10, 18, 4) and (5, 3, 14)?
Answers
No, the line passing through (-4, 26) and (-2, 0) is not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.
Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.
We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.
Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)
So, for first line we have (x₁, y₁)=(-4,26)
and (x₂, y₂)=(-2,0)
So, slope(m₁) of first line is =(0-26)/(-2 - (-4))
=>m₁ = -26/2
=>m₁ = -13 ----(eq1)
Similarly, for second line, we have (x₁, y₁)=(10,18)
and (x₂, y₂)=(5,3)
So, slope(m₂) of second line is =(3-18) / (5-10)
=>m₂ = -15/-5
=>m₂= 3 -------(eq2)
On comparing eq1 and eq2,we get
=>m₁≠m₂.
Hence, the given lines are not parallel.
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(Complete question) is:
Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?
Which of the following is equal to the fraction below?
Answers
Answer:
Choice B
Step-by-step explanation:
(7/4)^11 = 471.431...
(7^11)/(4^11) = 471.431...
what’s the answer to
2(s-10)=12
Answers
Answer: s = 16
2(s - 10) = 12
distribute the 2
2s - 20 = 12
add 20 to both sides
2s = 32
divide both sides by 2
s = 16
you can then check your work by putting in the 16
2 (16-10) = 12
2 (6) = 12
12 = 12
T/F: it is best to plan future activities for the group during the middle of the group
Answers
Answer:
False.
Step-by-step explanation:
It's ok to plan future activities for the group, but it's best to plan in the beginning of the group.
Find the volume of the given solid. Bounded by the coordinate planes and the plane 9x + 5y + z = 45.
Answers
The volume of the given solid that is bounded by the coordinate planes and the plane 9x + 5y + z = 45 is 45 units³.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.So, we have: 9x + 5y + z = 45
Let us consider z = 0.
Then we have:
9x + 5y = 45
Now, we obtain:
x = 45/9 - y
OR
y = 45/5 - x
Hence,
45/9 × 45/5
2,025/45
45 units³
Therefore, the volume of the given solid that is bounded by the coordinate planes and the plane 9x + 5y + z = 45 is 45 units³.
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Remember, we always want to draw our image first. Figure 26. Line TV with midpoint U. Segment lengths has been appropriately labeled. Since we know is the midpoint, we can say Answer substituting in our values for each we get: Answer Solve for We now want to solve for . Answer Answer Solve for , , and This is just the first part of our question. Now we need to find , , and . Lets start with and . We know that so let’s substitute that in. Answer Answer We will do the same for . From our knowledge of midpoint, we know that should equal , however let’s do the math just to confirm. We know that so let’s substitute that in. Answer Answer Using the segment addition postulate we know: Answer
Answers
The blanks in each statement about the line segment should be completed as shown below.
How to fill in the blanks about the line segment?Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:
8x + 11 = 12x - 1
Solve for x
We now want to solve for x.
−4x+11=−1
−4x = -12
x= 3
Solve for TU, UV, and TV
This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.
TU=8x+11 We know that x=3 so let’s substitute that in.
TU=8(3)+11
TU= 35
We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.
UV=12x−1 We know that x=3 so let’s substitute that in.
UV=12(3)−1
UV= 35
Based on the segment addition postulate, we have:
TU+UV=TV
35+35=TV
TV= 70
Find the detailed calculations below;
TU = UV
8x + 11 = 12x - 1
8x + 11 - 11 = 12x - 1 - 11
8x = 12x - 12
8x - 12x = 12x - 12 - 12x
-4x = -12
x = 3
By using the substitution method to substitute the value of x into the expression for TU, we have:
TU = 8x + 11
TU = 8(3) + 11
TU = 24 + 11
TU = 35
By applying the transitive property of equality, we have:
UV = TU and TU = 15, then UV = 35
By applying the segment addition postulate, we have:
TV = TU + UV
TV = 35 + 35
TV = 70
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& Calculate the standard deviation of the following data. 3456231275 694.2 616.9 248 26.3
Answers
The standard deviation of the data is 24.8
What is the standard deviationThe standard deviation is a measure of the spread or variability of a set of data from the mean. It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean.
The formula for the sample standard deviation is:
s = √([∑(xi - x)^2]/(n-1))
where s is the standard deviation, xi is each individual data point, x is the sample mean, n is the sample size, and is the sum of all the squared differences.
The standard deviation is s=24.8
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Evaluate expressions- if A=4 and B=9 what is the value of the following expression
20/a+7•b
A.28
B.33
C.68
D.108
Answers
Answer:
68
Step-by-step explanation:
just put the value of a and b in the expression and you will get the answer
20/a+7.b is
20/4+7×9
5+63
68
Answer:
C. 68
Step-by-step explanation:
Fill in your values.
20/ 4 + 7 x 9
Solve using PEMDAS.
5 + 7 x 9
5 + 63
68
in the accompanying figure, AB and CD are two chords of a circle with centre O. OE is perpendicular to CD and OF is perpendicular to AB #fOE = 4 cm, OF = 3 cm and AB= 8 cm, calculate, giving reasons, the length of CD. AB is a chord E
Answers
As a result, the CD is either 14 cm or 15 cm long.
What does "perpendicular" mean in practice?Perpendicular lines are those that cross at a straight angle to one another. Examples include the separate sides of a rectangle and the stairs of a straight staircase. The sign that indicates two perpendicular lines is ⊥ ⊥.
The product of a segments of one chord, when two chords cross in a circle, equals the product of a segments that make up the additional chord. The crossing chords theorem refers to this. This theorem allows us to determine CD's length in the manner shown below:
Let CE = x and ED = y. Then CD = x + y.
The intersecting chord theorem provides us with:
AE × BE = CE × DE
Inputting the values provided yields:
(8/2) × (8/2 - x) = x × y
By condensing and rearranging, we obtain:
y = 16/8 - 2x/8
y = 2 - x/4
Given that OE is parallel to CD, we have:
OE² + DE² = OD²
Using Pythagorean theorem and the provided values as a substitute, we arrive at:
4² + y² = (x + 3)²
By replacing y = 2 - x/4, we obtain:
16 + (2 - x/4)² = (x + 3)²
By enlarging and condensing, we obtain:
x² - 40x + 121 = 0
The quadratic formula yields:
x = (40 ± √(40² - 4×1×121))/2
x = (40 ± 12)/2x = 26 or x = 14
Since x + y = CD, we have:
CD = 26 + y or CD = 14 + y
Substituting y = 2 - x/4, we get:
CD = 26 + 2 - 26/4 or CD = 14 + 2 - 14/4
CD = 28/2 or CD = 30/2
CD = 14 or CD = 15
Therefore, the length of CD is either 14 cm or 15 cm.
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Problem 4 Find a basis for the nullspace of the matrix A. A=[1 2 3]
0 1 0
Answers
The nullspace of matrix A is given by the set of all vectors x that satisfy the equation Ax = 0, where A is the given matrix.
To find a basis for the nullspace, we need to solve the homogeneous system of equations represented by the equation Ax = 0.
The given matrix A is:
\(\[ A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 0 \end{bmatrix} \]\)
To find the nullspace of A, we need to solve the equation Ax = 0. This can be done by setting up the augmented matrix [A|0] and performing row operations to obtain the reduced row echelon form.
Performing row operations on the augmented matrix [A|0]:
\(\[ \begin{bmatrix} 1 & 2 & 3 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \rightarrow \begin{bmatrix} 1 & 0 & 3 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \]\)
The reduced row echelon form of the augmented matrix is obtained. From this, we can see that the third column is a free variable (denoted as x3). The corresponding solution can be written as \(x = \(\begin{bmatrix} -3x3 \\ 0 \\ x3 \end{bmatrix}\)\), where x3 can take any real value.
To find a basis for the nullspace, we can choose two linearly independent vectors that span the nullspace. One choice can be \(\(\begin{bmatrix} -3 \\ 0 \\ 1 \end{bmatrix}\)\), which corresponds to x3 = 1. Another choice can be \(\(\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}\)\), which corresponds to x3 = 0.
Therefore, a basis for the nullspace of matrix A is \(\(\left\{ \begin{bmatrix} -3 \\ 0 \\ 1 \end{bmatrix}, \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \right\}\)\).
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of 3400 babies in the hospital 1244 are boys and the rest are girls what percent are girls
Answers
Answer:
^
Step-by-step explanation:
Whitney calculated that the circular clock on her wall has a circumference of 18.84 inches. What is the clock's area?
Answers
Answer:
28.25in
Step-by-step explanation:
simplify the following expression
4(m) + 3(2) + 15
Explain
Answers
3(2)=6
Leaving you with:
4m+6+15
You can only combine like terms therefore 4m can not be added to 6 or 15 because of the variable m
4m+21
During the past school year, there were 640 students and 52 teachers. What is the ratio of students to each teacher rounded to the nearest tenth?
a.
12.3:1
c.
160:13
b.
1:12.3
d.
13:160
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
The ratio of student to teacher is 12.3 to 1
29 kg of apples cost $290. How much
would 31 kg cost?
Answers
Answer:
$310
Step-by-step explanation:
$290/29
=$10
31 multipled by 10
=$310
The lengths of the sides of triangle PQR are consecutive even integers. The perimeter of triangle PQR is 42 cm. What is the length of the longest side?
Answers
Answer:
16 cm
Step-by-step explanation:
Let the three consecutive even integers representing the sides of the triangle PQR be x, (x +2) and (x + 4).
Since, perimeter of triangle PQR = 42 cm
\( \therefore \: x + (x + 2) + (x + 4) = 42 \\ 3x + 6 = 42 \\ 3x = 42 - 6 \\ 3x = 36 \\ x = \frac{36}{3} \\ x = 12 \\ \\ \because \: longest \: side = x + 4 \\ \therefore \: longest \: side = 12 + 4 \\ \red{ \bold{ \therefore \: longest \: side = 16 \: cm}} \\ \)
By using only those factors given in interest tables, find the values of the factors that follow, which are not given in your tables. Show the relationship between the factors by using factor notation, and calculate the value of the factor. For example, (F/P,8%,38)=(F/P,8%,30)(F/P,8%,8)=18.6253. Click the icon to view the interest factors for discrete compounding when i=8% per year. (c) Find the value of the (P/A,8%,145) factor. Select the correct choice below and fill in the answer box to complete your choice. A. (P/A,8%,145)= 0.08
1−(P/F,8%,45)
= (Round to four decimal places. ) B. (P/A,8%,145)= 0.08
1−(P/F,8%,100)(P/F,8%,45)
= (Round to four decimal places.) C. (P/A,8%,145)=(P/A,8%,100)(P/A,8%,45)= (Round to four decimal places. ) D. (P/A,8%,145)= 1−(P/F,8%,100)(P/F,8%,45)
0.08
= (Round to four decimal places.) At what rate of interest compounded annually will an investment double in nine years? The investment will double in nine years at \% compounded annually. (Round to two decimal places.)
Answers
The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.
To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:
(P/A, i%, n) = (1 - (1 + i)^(-n)) / i
Substituting the values given:
i = 8%
n = 145
(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08
Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:
(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)
Therefore, the correct choice for the value of (P/A,8%,145) is:
C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)
Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:
(F/P, i%, n) = (1 + i)^n
We want the investment to double, so we have:
(1 + i)^9 = 2
Taking the ninth root of both sides:
1 + i = 2^(1/9)
Solving for i:
i ≈ 0.0809 or 8.09% (rounded to two decimal places)
Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.
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Can someone please how to do fractions in the lowest terms
Answers
Answer:
In order to out a fraction in lowest terms, you must divide by the Greatest Common Factor, or GCM, of the numerator and denominator in the fraction. Let's say we have the fraction 25/100. We know that the greastest common factor of 25 and 100 is 25, as 25 ÷ 25 = 1 and 100 ÷ 25 = 4 so 25/100 in lowest terms is 1/4:
25 25 1
___ ÷ ___ = ___
100 25 4
If the GCM of a fraction equals 1, the fraction is simplified. Because the only common factor of 1 and 4 is 1, we know this fraction is simplified.
1 1 1
__ ÷ ___ = ___
4 1 4
Hope this helps <3 Please contact me if your still confused
what is a congruent polygon
Answers
A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.
Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.
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Given the graphs of y = f(x) and y = g(x), what is the value of f(x)-g(x) where the two graphs intersect?
Answers
Answer:
0
Step-by-step explanation:
If they want the values of where the graphs intersect, that means the values are both = to each other, meaning subtracting the same value by the same value is 0