### Solve the equation y = x2 - 6x + 8 = 0

Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a)Solve by factoring, b)solve by completing the square, c)solve by using the quadratic formula

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Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a)Solve by factoring, b)solve by completing the square, c)solve by using the quadratic formula

1. Write an equation for the circle that passes through the points: (1, -1), (-5, 7), and (-6, 0). 2. Express the polar equation in rectangular form. 3. Find the total area enclosed by the graph of the polar equation r = 1 + cos 2θ. 4. Write the equation of the line tangent to the parametric curve x = tcos t, y

Brackets [ ] are used to indicate a subscript, so a[n] means the nth term of a sequence. 1. Write the first four terms of the sequence defined by a[n] = 2n + 3. 2. Write the first four terms of the arithmetic sequence with a[1] = -6 and d = 4. 3. What is the common ration in the geometric sequence 4, -12, 36, -108, . .

Show and explain. [(3x)/(x^2+2x-8] - [1/(x-2)]+[1/x+4]

Show and explain. [(2x2+6x)/(4x)]*[(6x+12)/(x2+2x-3)] /[(x2-4)/(x2-3x+2)]

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1. Complete table for savings in which interest is compounded continously. Initial investment Annual rate Time to double total $1000 ? ? $2281.88 2. Complete table for radioactive isotope Isotope Half-life(years) Initial quantity Amt after 1000 years 5715 ? 3.5g 3. The population of P of a city is given by P=

1. Graph the inequality. y  1 2. Graph the inequality. y  3x 3. Given f(x) = 4x + 1, find f(3). 4. Given f(x) = 5x2 - 3x + 1, find f(-2). A) -13 B) 15 C) -25 D) 27 5. Given f(x) = x2 + 5x + 3, find f(0). 6. Rewrite the equation 4x - 10y = 11 as a function of x. A) B) C)

Please answer the following questions: 1. Find the domain of the function f(x) = ln(x - 7). 2. Simplify: log 1000 3. Write as a single logarithm (DO NOT find approximations): 2 log 4 + log x - log2. 4. Expand and simplify: ln(e^x). 5. Solve for x: log(x - 4) + log 2 = 1.

Solve the inhomogeneous second order linear equation by variation of parameters. See attached file.

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign. ADDITIONAL INSTRUCTOR COMMENTS/REQUIREMENTS For unit

A. what is d, the difference between any 2 terms? answer: show work in this space. b. using the formuls for the nth term of a arithmetic sequence, what is 101st term? answer: show work in this space. c. using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? answer: show work in

Solve for x in the following equations: 1. 2 + 4(x + 2) = 3x - 2(x + 1) 2. |5x - 3| + 4 = 11 3. Solve for x: 3/x - 1/(x+2) = -2/(3x + 6) 4. Solve for y by completing the square: y^2 + 8y + 5 = 0 5. Use the quadratic formula to solve for x: x^2 - 4x + 2 = 0 6. Solve for x by factoring. x^3 + x^2 - 6x =

Find a primitive root modulo 17 if it exists.

(See attached file for full problem description) 1. Which of the ordered pairs (3, 1), (0, -4), (-4, 0), (-3, -7) are solutions for the equation x - y = 4? A) (0, -4), (-4, 0), and (-3, -7) B) (-4, 0) and (-3, -7) C) (0, -4) and (-3, -7) D) (3, 1) and (-4, 0) 2. Give the coordinates of the point graphed below.

(See attached file for full problem description with proper symbols) --- 1/ If the amplitude ratio, N in decibels, of an electrical system is given by the formula. N = 10log And the power is given by P = Show that for matched input and output resistances the output voltage Vo is related to the input voltag

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P [1+r/n}^nt, let r = 10%, P=1, and n= 1 and give the coordinates (t,a) for the points where t= 0,1,2,3,4. Round the A value to the tenth's place. a. show coordinates in this space.

Explain an advantage of rational exponents over the radical sign and give an example.

(See attached file for full problem description with all symbols) --- 2.34 (I) How many elements of order 2 are there in and in ? Show work. (Answer: 25, 75 respectively) (II) How many elements of order 2 are there in ?

(See attached file for full problem description) 2.22 Define f: {0,1,2,...,10} {0,1,2,...,10} by f(n)= the remainder after dividing by 11. (I) Show that f is a permutation. (II) Compute the parity of f. (III) Compute the inverse of f.

Prove or disprove: If m|n, then ø(m,n)=mø(n).

1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer b) Graph this fun

Find all real or imaginary solutions to each equation. 1. 49x2 + 9 = 42x 2. 6x = - 19x + 25 X + 1 3. x - 1 = 2x - 3 4. (w2- 1)2 + 2(w2- 1) = 1

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include an example of an equation easier to solve as a rational exponent rather then a radical sign. 2)The loudness of sound is based on intensity level measured in decibe

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. How do I create three unique equations where the discriminant is positive, zero, or negative. For each case, Please help me explain what this value means to th

1. Graph the solution to the system of inequalities y>= -2x-3 y > 3x-2 2. y<= -2x-5 y< 7x-2 3. x>8 4. x>=-2 5. -3x-5y<7 6. 10x-7y>=68

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