math
PROFESSOR CALLEN
mth_219_final.docx|
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1. a. Evaluate 4(x+4y) when x equals x=3 and y=1.
4(x+4y) =
b. Is the number you obtained in part (a) a solution of 5z−76=64? no or yes?
2. Simplify the algebraic expression. 5(4x+4)−17
3. Evaluate the algebraic expression for the given value of the variable. 8y – 3y^2 y^2 -6
4. Solve the equation. Use words or set notation to identify that the equation has no solutions or the equation is true for all real numbers. 3+3(3x−6)=8−3(2x+1)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is .(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. All real numbers are solutions.
C. The equation has no solution
5. Solve the formula for the specified variable. A=P+PRT for R.
R=
6. Use both the addition and multiplication properties of inequality to solve the inequality and graph the solution on a number line. 4 (x plus 1) - 8 < 3 x + 5
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is (Type your answer in interval notation.)
B. The solution set is ∅, the empty set.
What is the graph of the solution set?.
7. For the equation given below, complete parts a through b.
4 x + y = 2
a. Put the equation in slope-intercept form by solving for y.
y = (Simplify your answer.)
b. Identify the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is
(Type an integer or a simplified fraction.)
B.The slope is undefined
Identify the y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept is (Type an integer or a simplified fraction.)
B. There is no y- intercept
8. Find the indicated function values for the function below.
f(x) = 6 x - 5
x−3
a. f(0)=(Simplify your answer.)
b. f(1)=(Simplify your answer.)
c. f(−1)=(Simplify your answer.)
d. f(a+h)=(Simplify your answer.)
e. Why must 33 be excluded from the domain of f? Choose the correct answer below.
A. This value of x would make the denominator zero.
B. This value of x would make the denominator undefined.
C. This value of x would make the denominator positive.
D. This value of x would make the denominator negative.
9. Add the polynomials. Add the polynomials.(6x2−4x+4)+(x2+2x+9)
The sum is (Simplify your answer. Do not factor.)
10. Subtract the polynomials. (7y3+2y2−y)−(5−y2−3y+7)
The difference is (Simplify your answer.)
11. Divide the polynomial by the monomial. Check the answer by showing that the product of the divisor and the quotient is the dividend.
2x7−30x5−6x4
6x3
12. Divide as indicated. 12x2+16x−7÷15x2+20x2−49
`13. A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 270 square yards. Find the length and the width.
The parking lot has a width of
The parking lot has a width of
14 f(x) =x2−6x and g(x) =8−x
Find (f−g)(x) and (f −g)(2).
(f−g)(x)=(Simplify your answer.)
(f−g)(2) =
15. Let
f(x)=x2+4x and g(x) =2−x. Find (fg)(−3).
(fg)(−3)=(Simplify your answer.)
16. Let f(x) =x2+7x and g(x) =5−x.
Find fg(x) and fg(8).
fg(x)=(Simplify your answer.)
fg(8)=(Type an integer or fraction.)
17. For f(x)=4x−3 and g(x)=3x2−4 find the following.
a. What is (f◦g)(x)?
(f◦g)(x)=(Simplify your answer.)
b. What is (g◦f)(x)?
(g◦f)(x)=(Simplify your answer.)
c. What is (f◦g)(2)?
(f◦g)(2)equals=(Simplify your answer.)
Find the inverse of the one-to-one function.
f(x)=9x+5
f−1(x)=(Use integers or fractions for any numbers in the expression.)
