
Concept explainers
To find the four consecutive integers and choose the correct option.

Answer to Problem 24CR
Explanation of Solution
Given information:
There are four consecutive integers and the sum of the squares of second and third integers is 61.
Solution:
Let the second integer =
Let the third integer =
According to the question:
Sum of the squares of second and third integers is 61.
Therefore,
Expand the parenthesis using identity
Subtract 61 from both sides
Combine like terms
Divide each term by 2 to make above quadratic simpler to solve, we get
We need to compare above quadratic equation with standard quadratic equation
Now, we need to get the values of a, b and c and apply product sum rule to factor the quadratic.
On comparing quadratic
Product of value of a and c =
Value of
Now, we need to get two factors of -30 those add upto
We could see
So, split middle term
Now, making it into two groups and factor out Greatest Common Factor (GCF) of each group
Factor out
Factor out the common parenthesis
Applying zero product rule. Set each factor equal to 0 and solve for x .
If we take second integer -6, third integer would be
Therefore, the second integer is 5.
And third integer =
Fourth integer=
First integer =
Therefore, correct option is (a) {4, 5, 6, 7}.
Chapter 5 Solutions
Algebra: Structure And Method, Book 1
Additional Math Textbook Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Algebra and Trigonometry (6th Edition)
- Answer this questionarrow_forward1. vector projection. Assume, ER1001 and you know the following: ||||=4, 7=-0.5.7. For each of the following, explicitly compute the value. འབ (a) (b) (c) (d) answer. Explicitly compute ||y7||. Explain your answer. Explicitly compute the cosine similarity of and y. Explain your Explicitly compute (x, y). Explain your answer. Find the projection of onto y and the projection of onto .arrow_forward2. Answer the following questions using vectors u and v. --0-0-0 = find the the cosine similarity and the angle between u and v. འརྒྱ (a) (b) find the scalar projection of u onto v. (c) find the projection of u onto v. (d) (e) (f) find the scalar projection of onto u. find the projection of u onto u. find the projection of u onto and the projection of onto . (Hint: find the inner product and verify the orthogonality)arrow_forward
- Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning. Please type out answerarrow_forwardThe function f(x) = log x is transformed to produce g(x) = log (x) – 3. Identify the type of transformation and describe the change. Please type out answerarrow_forwardEach graph below is the graph of a system of three linear equations in three unknowns of the form Ax = b. Determine whether each system has a solution and, if it does, the number of free variables. A. O free variables ✓ B. no solution C. no solution D. no solution E. 1 free variable F. 1 free variablearrow_forward
- Solve the following systems of equations and show all work.y = x2 + 3y = x + 5 Please type out answerarrow_forwardSolve the following system of equations. Show all work and solutions.y = 2x2 + 6x + 1y = −4x2 + 1 Please type out answerarrow_forwardDalia buys 20 collectible gems per month. Grace sells 10 gems from her collection of 120 each month. When will Dalia have more gems than Grace? Show your work. Dear Student If You Face any issue let me know i will solve your all doubt. I will provide solution again in more detail systematic and organized way. I would also like my last 3 questions credited to mearrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education





