Please include answer and steps to solve problem and explain if needed.

1) What is 10^-1 + 10^0 + 10^1?

2) 16 is 20% of....

3) If f(x) = x^2 + 1, then 2f(x) = ?

4) If f(x) = x^2 + 1, then f(2x) = ?

5) If f(x) = x^2 + 1, then f(y) = ?

6) If 2x + y = 3, and x - y =3, what is x?

7) If 2x + y = 3, and x - y = 3, what is y?

8) If you walk 3 miles in one hour and then 4 miles in two hours, what is your average speed for the entire trip? (in mph)

a 2.33, b 2.5, c 3.5, d 3.67, e 1.5

9) Jack and Joe leave their homes at the same time and drive toward each other. Jack drives at 60mph while Joe drives at 30mph. They pass each other in 10 minutes. How far apart were Jack and Joe when they started (in miles)?

a 5, b 15, c 30, d 90, e 300

Solution Preview

Please see the attached file.

1
A negative power is the inverse of the base taken by the same power only positive:

So here we have:

2
16 is 20% of what?

Here we use the triangle relations. We want to know what quantity is 100% if 16 is only 20%
If we denote this quantity as x we can write:

Hide the x with your finger. Now x will be equal to the multiplication of the diagonal pair (16 and 100) divided by the unmatched number (20% in this case)

And calculate:

Another ...

Solution Summary

The solution is has a detailed explanations how to solve 9 different problems in algebra.

Let u,v <- C^n and set A := I + uv^H <- C^nxn.
(a) Suppose A is invertible. Prove that Inverse(A) = I_n + auv^H , for some a <- C. Give an expression for a.
(b) For what u and v is A singular?
(c) Suppose A is singular. What is the null space of A, N(A) in this case?

What type of Algebraproblems covered in an Algebra 1 course do you find to be the most challenging? Why? What did you learn from the experience of an Algebra 1 course and how did you overcome this challenge? If you could provide some tips or advice to new Algebra 1 students, what would you share with them?

Section 4.1 Question #62 - Simplify. Assume that no denominator is 0 and that 00 is not considered
(x25)6
Section 4.2 Question number 12 - Express using positive exponents. Then, if possible, simplify
a −3 b

1. Simplify the following algebraic expressions:
2. Perform the indicated operations (Multiply/Divide) on the given algebraic expressions:
3. Factor the algebraic expressions completely:
4. Simplify the rational expressions:
5. Classify the given numbers as real and rational, real and irrational, or complex:
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With referrence to the last solutions u posted to me,may you please check no 1 I have a different solution from my workings.I not sure which one is correct,but I think mine might be.If so may u please edit the document because I failed to do so.I will use this over and over.

Elementary Algebra: Basic Operations with Polynomials)
2. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. -6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 - 5x + 6
D. 6x2 - 5x - 6
E. 6x2 - 13x - 6
(Elementary Algebra: Substituting Values into Algeb

The quotient when 3 more than a number is divided by 3 less than that same number
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-¥Ü-20____-10___0___10___)20_______30______?
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3. Write in interval notation the set of real numbers between -2 and 2, inclusive.