Q: 1. Forty-one students each took an exam in math, biology and chemistry. • 12 students failed the ma...
A: Let, total number of students = n = 41 Number of students failed in Math is, n(A) = 12 Number of stu...
Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal...
A: Given that a is orthogonal to b So a·b=0also we have c·b=2
Q: 3. Find the product in simplest form. State any restrictions on the variable. 2 2 x`– 49 х — 2 x* – ...
A:
Q: In an election with four candidates, Leo wins 35 first-choice votes, Mike wins 25 first-choice votes...
A:
Q: Plz solve it within 30-40 mins I'll give you multiple upvote
A:
Q: Find the reduced row echelon form of the matrix (RREF). Please include: - The original augmented m...
A:
Q: equivalence
A:
Q: Algebraically factor the polynomial P(x)=x* +3x' – 3x² – 7x+6. |
A: Given polynomialp(x)=x4+3x3-3x2-7x+6solution:-put x=1p(1)=14+313-312-71+6p(1)=0here x=1 is a factor ...
Q: Sketch the graph of each line. 1 1) y=-x-1 4 Ay
A:
Q: a dietitian in a certain hospital ordered 4 ounces, about 115 grams, of chicken per patient for a di...
A: Given that: Per patient chicken meal=4 ounces Total weight of chicken served=496 ...
Q: For what values of k will the set of ordered pairs ((1,10),(2,9),(3,8),(4,7),(k+2,6)} represent a fu...
A:
Q: For both the X- and y-intercept(s), make sure to do the following. • If there is more than one, sepa...
A:
Q: Here is a graph of the function r. Use the graph to find the following. If there is more than one an...
A:
Q: A preschool field trip required 7 buses. Thirteen children rode in cars with their parents and the r...
A: Given the query is to find the number of students on each bus.
Q: The shortest ladder that will reach from the ground level to a high vertical wall is 5m. If it clear...
A:
Q: In a parallelogram MATH, if the angle M measures 82 degrees, find the measure of angle T. Choose the...
A: We use the property that the opposite angles of a parallelogram are equal.
Q: write in decimal One Millionths
A: write in decimal One Millionths
Q: Perforan the wnchceted cogerations 1 14-x-8x*, x% 13x²+a6_ x-sx-24 x 13x2+a6 x-sx-24 ウォメ3をメ 2. CY.2c...
A: Given that: 3. x3+y3x2+4x+4.4a2x-4a23x2-5x+2.3x2+4x-42ax2-2axy+2ay2
Q: Aaron was offered a job that paid a salary of $47,000 in its first year. The salary was set to incre...
A: NOTE: Refresh your page if you can't see any equations. . the first-year salary is $47000 so take a=...
Q: Evalute the following Zx Pnessionfon n=3 n-2 sutb
A: We have to find the value
Q: This exercise uses Newton's Law of Cooling. A roasted turkey is taken from an oven when its temperat...
A:
Q: What is the domain of the function below? 10 5- -10 -5 10 -5 -10
A: Given: We know that; The domain of the function is the subset from the set of real x for which th...
Q: Question 8 Let Events A and B be described as follows: P(A) = ordering room service • P(B) = watchin...
A: Given that: P(A)=Ordering room serviceP(B)=Watching television
Q: Solve for A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right co...
A:
Q: find the domain and range in set builder notation. 6)
A: topic - Domain and range of a function domain: input values of a function range : output values of a...
Q: Solve the system by substitution. y = -4x y = x – 5 Submit Answer
A:
Q: 62 – (8 · 3) + 2° (7 · 3) -
A: Given: - The equation is, 62-(8.3)+22(7.3) To solve: - The solution of the given equation.
Q: L022 B Continue x -intercept: | 6. y -intercept: 9 =d7 -x 4. 3. Find the y-intercept and x-intercept...
A: Given query is to find x and y intercept of the line.
Q: Ex 8 Let B = ((1,0), (0, 1)) and B' = (v, V2) Find B' so that %3D %3D =x + 2ry + y? + 10x-4y +5 can ...
A:
Q: Graph the quadratic function f(x) = (x+5) - 3. Give the (a) vertex, (b) axis, (c) domain, and (d) ra...
A: Given, fx=x+52-3To find : a vertex, b axis, c domain, drange
Q: Avani is starting a running plan to train for a race. In the first week of her running plan, Avani w...
A: Given that: Number of miles run by Avani in first week=7 miles.Number of miles run by Avani in subse...
Q: Factor f(x) into linear factors given that k is a zero of f(x). 2 f(x) = 4x + 23x- 34x+7: k= 1 f(x) ...
A:
Q: Grade & Sect Learning Competency: A. Finds the domain and rang B. Graphs and illustrates a line rang...
A:
Q: 30 The partial graph of P(x) is shown to the right. If the polynomial function 20- is written in the...
A: The given graph of the polynomial function is
Q: Aréă Find the radius, diameter, circumference and area for each of the following circles. SHOW ALL W...
A:
Q: D- Where do these lines intersect? Y= -3/2x 3x + 2y = -4 2 Where do these lines intersect? y= 2x - 4...
A:
Q: Determine if the following sequences are arithmetic or geometric, if they have a common difference o...
A: Q2)Given,-6,-2,2,6,10,14,...we can see that:-6 + 4 = -2-2 + 4= 22+4=66+4=1010+4=14So, it is in forma...
Q: Iscuss the continulty of the following function at the Indicated polnt(s): ) f(x) = x²-7x+12 %3D at ...
A: Given the query is to find the behaviour of the function at x = 3.
Q: 1. Suppose $1000 is invested at an annual rate of 5%. Compute the amount accumulated after 10 years ...
A:
Q: Write an equation, in point-slope form, of the line that passes through the given point, and that ha...
A:
Q: Calculate the probability of tossing a coin 15 times and getting the given number of heads. 3. 4 4. ...
A: We have to find the probability.
Q: Two square lots was sold for P2500 per square meter. If the smaller area is 3 less than half the ...
A:
Q: Suppose that the monthly demand function of a particular commodity is given by P= 200 -0.4x and the ...
A:
Q: EXAMPLE: Find the interval where the function is decreasing or increasing (1) f(x) = x3-12x +5
A: Given function is f(x) = (x^3)-12x+6 Find f'(x) f'(x) = 3(x^2)-12 Do f'(x)= 0 , solving for critical...
Q: What is the solution to the following system of equations?
A: We can find the solution of the graph as below.
Q: Derivative (d)is the instantaneous rate of change or the rate at a particular instant of a function ...
A:
Q: The system of linear equations a-b+2c=x a+2b-c=y 2b-2c=z is inconsistent when (x,y,z) equals
A: Given equations are a - b + 2c = x .......................1 a + 2b - c = y ...
Q: Homogeneous Equations solve dy/dx=x/y
A:
Q: -33/(x2 - 3x) = -3/(x - 3) + 6/x
A:
Q: x2 - x if x<0 Given the function f(x) = if Osxs3 what should be the value of k so that F(k) = f(0)- ...
A:
![In R[x], prove ideals (x3 – 1, x7 – 1) = (x – 1, x – 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33b016e2-bc51-40df-9e36-e74043ee4626%2F0feed94e-987c-45d1-bb18-fdd5b92dbea5%2F3dchhf6_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
- 31. Prove statement of Theorem : for all integers and .Let be a field. Prove that if is a zero of then is a zero ofSuppose that f(x),g(x), and h(x) are polynomials over the field F, each of which has positive degree, and that f(x)=g(x)h(x). Prove that the zeros of f(x) in F consist of the zeros of g(x) in F together with the zeros of h(x) in F.
- 14. Let be an ideal in a ring with unity . Prove that if then .34. If is an ideal of prove that the set is an ideal of . The set is called the annihilator of the ideal . Note the difference between and (of Exercise 24), where is the annihilator of an ideal and is the annihilator of an element of.Exercises If and are two ideals of the ring , prove that is an ideal of .
- 18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is isomorphic to .Let F be a field and f(x)=a0+a1x+...+anxnF[x]. Prove that x1 is a factor of f(x) if and only if a0+a1+...+an=0. Prove that x+1 is a factor of f(x) if and only if a0+a1+...+(1)nan=0.Prove that a polynomial f(x) of positive degree n over the field F has at most n (not necessarily distinct) zeros in F.
- If R=Z[x] and f(x) = x2 + 1, remain true, but g(x) =x. How do you prove that in R/I, [g(x)] x [g(x)] = -1R/I I is still the principal ideal generated by f(x)If you let R=Z[x] and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=(2x + I) exists in R/I, How do you prove that r^2=8 + I?If you let R=Z[x]and I = (x^2 -2) be the principal ideal generated by f(x) = (x^2 -2). If r=2x + I exists in R/I, How do you prove that r^2=8 + I?
