We have to find the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$.
The Taylor Polynomial is given by:
(x)=∑
k=0
n
k!
f
(k)
(a)
(x−a)
k
where $f^{(k)}(a)$ is the $k$th derivative of $f(x)$ evaluated at $a$.
Using this formula, we can find the Taylor Polynomial as follows:
\begin{align*}
f(x) &= e^x \
f'(x) &= e^x \
f''(x) &= e^x \
f'''(x) &= e^x \
\end{align*}
Evaluating each derivative at $x=0$, we get:
\begin{align*}
f(0) &= e^0 = 1 \
f'(0) &= e^0 = 1 \
f''(0) &= e^0 = 1 \
f'''(0) &= e^0 = 1 \
\end{align*}
Substituting these values into the formula for the Taylor Polynomial, we get:
\begin{align*}
P_3(x) &= \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3 \
&= 1 + x + \frac{x^2}{2} + \frac{x^3}{6}
\end{align*}
Therefore, the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$, is $P_3(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}$.
The circle graph below shows the number of animals in Mushu's farm. Sheep Donkeys Camels Goats Cows If there were 24 goats, how many cows are there in the farm?
By assuming that the farmer has goat and cows in the ratio 3:4, the number of cows in the farm will be 32 cows.
If there were 24 goats, how many cows are there in the farm?To find out how many cows are in the farm, we need to know the total number of animals in the farm. Assuming the ratio of goats to cows is 3:4, we can write this as: [tex]3x : 4x[/tex]
Where 3x represents the number of goats, and 4x represents the number of cows. If we know that there are 24 goats, we can set up an equation to solve for x:
3x = 24
Dividing both sides by 3, we get:
x = 8
Now that we know the value of x, we can find the number of cows:
= 4x
= 4(8)
= 32
Therefore, there are 32 cows in the farm.
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solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +
If you have a standard score of Z = 1, what percentage of the population has scores less than you?
Step-by-step explanation:
From a z-score table
z-score = 1 corresponds to .8413 or 84.13 percentile
meaning 84 .13 % have a lesser score than you
how am i supposed to prove that theyre collinear
Answer:
They are collinear if they are on the same line
solve for the unknown to find the unit rate
1/5 ?
----- = -----
1/20 1
Answer: 4
Step-by-step explanation:
To find the unit rate, we can cross-multiply the fractions.
Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5.
Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20.
Now we have the equation 1/5 = 1/20.
To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4.
Therefore, the unit rate is 4.
What is the equivalent to this
None of the given options A, B, C, or D is correct as they all provide different answers.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
The question asks for the equivalent of 6 × 2. This means that we need to find a number that is equal to the result of multiplying 6 and 2 together.
When we multiply 6 and 2, we get:
6 × 2 = 12
So, the equivalent of 6 × 2 is 12.
However, none of the answer options provided matches this answer.
Option A suggests that the equivalent of 6 × 2 is 2 × 1, which is equal to 2, not 12.
Option B suggests that the equivalent of 6 × 2 is 3 × 2, which is equal to 6, not 12.
Option C suggests that the equivalent of 6 × 2 is 9 × 3, which is equal to 27, not 12.
Option D suggests that the equivalent of 6 × 2 is 18 × 1/2, which is equal to 9, not 12.
Therefore, none of the options provided is correct.
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You can afford a $1000 per month mortgage payment. You've found a 30 year loan at 5.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)
$
b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)
$
c) How much of that money is interest? (Round to the nearest cent, as needed.)
Answer:
a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).
In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.
Substituting these values into the formula, we get:
$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]
Simplifying and solving for P, we get:
P = $183,928.72
Therefore, you can afford a loan of approximately $183,928.72.
b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:
Total money paid = $1,000 x 360 = $360,000
Therefore, the total amount of money paid to the loan company will be $360,000.
c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:
Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28
Therefore, the amount of money paid in interest will be $176,071.28.
if f(x)= -3, then f'(x)=?
Answer:
0
Step-by-step explanation:
0
See the photo below
This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:
[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]
This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.
The problem involves some algebraic manipulation and the use of the linearity of the integral.
It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.
See the attached for the full solution.
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Help me pleas whith this
PLEASE HELP
Find the Area
2cm
___cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
1. Find radius:
If diameter is 2, divide it by 2 to get radius = 1
2. Find formula:
A=πr^2
3. Plug in:
A = π(1)^2
4. Solve (multiply):
A = π(1)^2:
3.14159265359
Or
3.14 cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
r=2
2/2=1
A=[tex]\pi[/tex](1)^2
=[tex]\pi[/tex]1
≈3.14x1
≈3.14cm^2
Use the graph to answer the questions for the questions
The vertex is (50, 630). The vertex is the peak and correspond with the coordinates of he maximum height of the arch.
The solutions is the base of the arch and this (20, 0) and (80, 0)
vertex form, y = -0.7(x - 50)² + 630
Quadratic equation factored form, y = -0.7 (x - 80) (x - 20)
The equations are the same when plotted on a graph and examined mathematically. physically it looks different.
the domain is (-∞, ∞)
The height of the monument 15 feet from the left side is 472.5 feet
How to find the quadratic equationsince the zeroes of the quadratic equation is (20, 0) and (80, 0), hence we have that
y = a(x - 20)(x - 80) and the equation pass points (50, 630)
630 = a(50 - 20)(50 - 80)
630 = a * 30 * -30
630 = -900a
a = -0.7
Quadratic equation has a standard vertex form, y = a(x - h)² + k
y = a(x - h)² + k
vertex (h, k) = (50, 630) and a = -0.7
plugging the values
y = -0.7(x - 50)² + 630
Quadratic equation has a standard factored form, y = a(x - h)² + k
y = a(x - r2)(x - r1)
where r2 and r1 are the roots r1 = 20 r2 = 80 an a = -0.7
plugging the values
y = -0.7 (x - 80)(x - 20)
The height of the monument 15 feet from the left side is gotten from the graph
this is 15 feet from 20 hence x = 35 feet
from the graph it can traced to be 472.5 feet
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Which geometric term describes ∠ T A G ?
Answer:
angle
Step-by-step explanation:
since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!
Answer: i know it is acute
Camille opened a savings account and deposited $8,063.00 as principal. The account earns 14.69% interest, compounded quarterly. What is the balance after 10 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Save answer
Answer:$26,141.13.
Step-by-step explanation:
Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:
A = 8,063.00 * (1 + 0.1469/4)^(4*10)
A ≈ 26,141.13
Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.
Write an equation in point-slope form. Part I: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation. (3 points) Part II: Using the equation of the line you wrote in Part I, write an equation of a line that is perpendicular to this line. Show your work. (3 points)
The line's equation in point-slope form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.
How do you formulate an equation in point-slope form?A line's point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex]. Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.
We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,
[tex]y - y1 = m(x - x1)[/tex]
As an illustration, suppose we want to formulate the equation of the line passing through the coordinates (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:
y - 5 = 2(x - 2)Let's say the given line has the equation [tex]y - y1 = m(x - x1)[/tex], where (x1, y1) is a point on the line and m is the slope of the line.
we can use the given point (2, 5). Then we can plug in the values into the point-slope form:
[tex]y - 5 = (-1/2)(x - 2).[/tex]
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Lastly, let’s consider the alternative method of paying for college: paying with loans. You take out a loan in the amount of your tuition and fees cost for 5 years rounded up to the nearest thousand dollars (for example if the total cost is $55,787 the loan would be for $56,000). The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take 27.25 years to pay off the loan.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, the interest that is earned on both the principal amount and any previously accumulated interest. In other words, it is interest that is calculated not only on the original amount of money but also on any interest that has been earned previously. This can result in significant growth of an investment or loan balance over time, as the interest earned on the accumulated interest can compound exponentially. Compound interest can be calculated using a specific formula that takes into account the principal amount, the interest rate, and the compounding frequency.
Now,
First, we need to calculate the total amount of the loan. We round up the tuition and fees cost for 5 years to the nearest thousand dollars:
Total cost = $70,000
Rounded up to nearest thousand = $70,000
So, the amount of the loan is $70,000.
Next, we can use the formula N= (-log(1-i*A/P))/(log(1+i)) to calculate the number of monthly payments needed to pay off the loan.
N = (-log(1-0.0025*70000/250))/(log(1+0.0025))
N = (-log(1.75))/(log(1.0025))
N = 326.45
Rounding up to the nearest whole number, it will take 327 monthly payments to pay off the loan.
So, it will take 327/12 = 27.25 years to pay off the loan.
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Triangle PQR is drawn with coordinates P(0, 2), Q(0, 5), R(1, 4). Determine the translation direction and number of units if R′(−7, 4).
8 units down
8 units up
8 units to the right
8 units to the left
It follows that the translation direction is 8 units to the left and 0 units up or down.
Describe translation?A translation is a geometric change in Euclidean geometry where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the origin of the coordinate system or as adding a constant vector to each point
The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.
We can use the following procedures to get the translation direction and number of units for R′(7, 4):
1. Determine the difference between R and R′'s x-coordinates: −7 − 1 = 8
2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0
It follows that the translation direction is 8 units to the left and 0 units up or down.
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Find the surface area. Round to the nearest hundredth
Answer:
122.30 cm²
Step-by-step explanation:
Divide the polyhedron into shapes:
+) 2 triangles with the same area.
The area of the triangle is
(4.3×11)÷2 = 23.65 cm².
And with two triangles of the same area we take the sum of both areas
23.65 + 23.65 = 47.3 cm²
+) 3 rectangles with different areas.
(3×6) + (3×8) + (3×11) = 75 cm²
So the surface area is the sum of areas of the triangles and rectangles
47.3 + 75 = 122.3 = 122.30 cm²
1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
a. How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
A. There are 9 sample spaces.
B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9
What is meant by sample spaces?
In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is used to define the space of events and calculate probabilities.
What is meant by probability?
Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.
According to the given information
A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.
B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.
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A stack of books has a mass of 21 killagrams if each book in the stack has a mass of 3 kilograms how many books are in the stack
There are 7 books in the stack.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the number of books in the stack, we can divide the total mass of the stack by the mass of each book:
Number of books = Total mass of the stack / Mass of each book
In this case, the total mass of the stack is 21 kilograms, and the mass of each book is 3 kilograms.
Number of books = 21 kg / 3 kg/book
Simplifying the right side, we get:
Number of books = 7 books
Therefore,
There are 7 books in the stack.
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What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = [tex]\frac{168}{7}[/tex] = 24
A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 10 feet. The slant height is 12 feet. What is the height of the heater? Round to the nearest tenth of a foot.
The height of the heater is approximately 6.6 feet.
What is Pythagoras theorem?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:
h² + 10² = 12²
Simplifying and solving for h, we get:
h² + 100 = 144
h² = 44
h ≈ 6.6 feet
Therefore, the height of the heater is approximately 6.6 feet.
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please help me
To begin a bacteria study, a petri dish had 2300 bacteria cells. Each hour since, the number of cells has increased by 12%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
The exponential function showing the relationship is y = 2300(1 + 0.12)^t
The exponential function showing the relationshipThe exponential function showing the relationship between y and t can be written as:
y = 2300(1 + 0.12)^t
where 2300 is the initial number of bacteria cells, 0.12 is the growth rate (12% expressed as a decimal), and t is the time in hours since the start of the study.
This function is obtained by using the formula for exponential growth, which is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is the time.
In this case, a = 2300, r = 0.12, and y represents the amount of bacteria cells after t hours.
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Help me I don’t understand
Answer: C, 125
Step-by-step explanation: That is the slope of the line, which remains constant. The slope represents the distance over the time, and distance divided by time equals the speed. This means that the speed remains constant throughout.
13. What is the surface area of a dome (a half sphere) with a radius of 12 meters?
288 meters squared
48 meters squared
967 meters squared
576 meters squared
Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.
Plugging in the radius r = 12 meters, we get:
Surface area = 2π(12)^2
Surface area = 2π(144)
Surface area ≈ 904.78
Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.
So the answer is: 967 meters squared.
Step-by-step explanation:
Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.
1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.
Based on the results, which statements are true? (Pick all that apply)
A. Most students found a pine tree.
B. More students found a maple tree than a pine tree.
C. More students found a birch tree than an oak tree.
D. More students found a pine tree than a birch tree.
E. More students found a maple tree than an oak tree.
The statements that are correct concerning the outcome of events between Jasmine and her classmates include the following:
Most students found a pine tree.
More students found a pine tree than a birch tree. That is option A and D respectively.
How to calculate the number of students per tree?The quantity of students that found birch tree = 1/7 = 0.14
The quantity of students that found pine tree = 7/9 = 0.8
The quantity of students that found maple tree = 1/4 = 0.25
The quantity of students that found oak tree = 11/23 = 0.48
Therefore, the statement that are correct about the outcome of the event between Jasmine and her classmates is as follows:
Most students found a pine tree.
More students found a pine tree than a birch tree.
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Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)
Answer:
...............................
Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
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please answer in detail
Answer:
AB: y = 2x + 4
Step-by-step explanation:
Line AB is parallel to the line y = 2x + 3
When 2 lines are parallel they have the same coefficient of x.
=> AB: y = 2x + m (1)
Because line AB passes through the point (0, 4)
Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4
So AB: y = 2x + 4
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y are y(y + 5) = 750, y² – 5y = 750 and y(y – 5) + 750 = 0
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
The equations that can be used to solve for y, the length of the room are:
1. y(y + 5) = 750
2. y² – 5y = 750
3. y(y – 5) + 750 = 0
Option 1 and 2 are quadratic equations that can be solved by factoring, completing the square, or using the quadratic formula. Option 3 is also a quadratic equation but it requires rearranging to the standard form before applying the same methods. The last option, (y + 25)(y – 30) = 0, is not a quadratic equation but it can be easily solved using the zero product property.
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