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# Basic Algebra

### Exponential and Logarithmic Equations.

Solve each exponential equation. Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 24. 10^x = 8.07 26. e^x = 0.83 28. 19^x = 143 30. 9e^x = 107 32. 4e^7x = 10,273 34. e^(1-8x) = 7957 36.

### Solution of Exponential Equations

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. 2. 3^x=81 4. 5^x =625 6. 3^(2x+1) =27 8. 5^(3x-1) =125 10. 4^x =32 12. 125^x =625 14. 5^(2-x) = 1 125 16. x-2 = sqrt 7 7

### Algebra - Developing and Solving Problems

Harry has \$2.25 in Nickels, Dimes and quarters. If he had twice as many nicels, half as many dimes .... The sume of the digits of a three digit number is 11. If the digits are reversed ... Find the Vertex, Focus and ... Find the equation of the parabola .... Write each equation in the form ... Find the Vertex, Foc

### Mathematics

The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was approximately 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio?

### Algebra word problems

Supplementary angles are angles whose measures have a sum of 180degrees. Complementary angles are angles whose measures have the sum of 90 degrees. Find the measure of an angle whose supplement is 10 degrees more than twice it's complement. Let 90- x equal the degree measure of it's complement and 180 -x equal the degree measure

### Polynomial -- word problem.

If a ball is thrown downwards from a height of 128 feet with an initial velocity of 32 feet per second and its height above the ground is given by the formula S = - 16t2 - 32 t + 128. How long will it take the ball to reach the ground?

### Algebra: Example Word Problem

At 10:00 a.m., train A leaves the station heading east at 40 m.p.h. At 11:00 a.m., train B leaves the same station heading North 30 degrees W (theta = 120 degrees) at 70 m.p.h. How fast is the distance changing at 12:00 noon. Give both the exact answer and a one decimal place approximation. You may find it helpful to plot th

### Physical science 8th edu by Bill W. Tillery (need to see how each problem is worked out to produce a correct answer to each problem)

1. A water wave has a frequency of 6Hz and a wavelength of 3m. (a) What is the period of these waves? (b) what is the wave velocity? 2. The lower frequency limit for human hearing is usually considered to be 20.0 Hz. What is the corresponding wave length for this frequency if the air temperature is 20.0 C? 4. The

### Algebra Express Terms

1. Express in terms of i: -sqrt(-297) 2. Rewrite with positive exponents. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. 8-1/3ax-7/8z^8 3. Simplify. Assume that no radicals were formed by raising negative numbers to even powers. sqrt(20)k^7q^8 4. Simplify: (-3a^2)^3

### Algebra

1. A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 15. Find the length of a side. 2. One side of a rectangle is 12 inches and the other side is x inches. What values of x will make the perimeter at most 44? 3. The equation y = 0.004x - 0.40 can be used to determine the approx

### Algebra: Order of Operations

1.Apply the Order of Operations to simplify the following expression: 9x[(2x2 - 3x + 7) - (9x3 - 3x2)/3x2] 2.Subtract. 3x4 + 4x3 + 7 - (x4 - 2x3 - x2 - 9x) 3.Simplify the expression, and identify the constants, coefficients, and variables in the simplified expression. (8w^4 - 6wz + 6wz^2) - (2w^4 + 7wz -

### Algebra - Understanding Functions

Determine whether each relation is a function. In addition, provide reasons for identifying a relation as a function.1. {(3, 4), (5, 9), (9, 9), (2, 3)}2. {(0, 0), (0, 1), (1, 4), (2, 4)} 3. {(2, 1), (4, 5), (8, 4), (1, 0)} 4. {(8, 3), (8, 0), (7, 7), (4, 7)}

### Algebra Word Problem of Speed Time and Distance

A family makes a 43.25 km trip in 5.5 hours. On the first part of the trip they crossed a lake in a canoe paddling at 12 km/h. For the rest of the trip, they hiked on a scenic trail. If their average walking speed was 5 km/h, how far did they walk?

### Percent: How Many Questions Were on the Test

A student got 50% of the questions on an algebra test correct. If he answered 10 out of the first 12 questions asked correctly but missed 3/4 of the remaining questions, how many questions were on the test?

### Algebra - Finding dimensions of a shape

A rectangular swimming pool is twice as long as it is wide. A small walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.

Please see attached for the details of the problems.

### Solving Simultaneous Equations by Substitution Method

Solve each system of equations by substitution method. Show work by step by step solutions. 1) x + 3y = 2 3x + 9y = 6 2) 4x - 2y = 2 2x - y = 1 3) x/4 - y/4 = -1 x + 4y = -9 4) x/6 - y/2 = 1/3 x + 2y = -3 5) 2x = 3y + 4 4x = 3 - 5y 6) 4x = 3y + 8 2x = -

### Barn Painting Rational Expression

Barn painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x = 5.

### Rational expression for his average speed

Driving Marathon. Felix drove 800 miles in x hours on Monday. 1) write a rational expression for his average speed. 2) On Tuesday he drove for 6 hours at the same average speed. Write a rational expression for his distance on Tuesday.

### Quadratic formula and Completing the square.

Solve the equation x2 + 8x - 2 = 0 using both 1) The quadratic formula 2) Completing the square Write a paragraph or two comparing and contrasting the two methods. Explain which method you prefer and why.

### Algebra word problems

Marginal revenue. A defense attorney charges her client \$4000 plus \$120 per hour. The formula R =120n + 4000 gives her revenue in dollars for n hours of work. What is her revenue for 100 hours of work? What is her revenue for 101 hours of work? By how much did the one extra hour of work increase the revenue? (The increase i

### Complete each ordered pair so that it satisfies the given equation. 1---- y = 2x + 5: (8, ), (-1, ), ( ,-1) Use the given equations to find the missing coordinates in the following tables. 2------ y= -x+4 X Y -2 0 2 0 -2 3-------------Graph each equation. Plot at least five points for each equation. x - 2y = 6 4--------------find the slope of each line. 5--------------- 6---------------Graph the line with the given point and slope. The line through (-2, 5) with slope -1 7--------------- Draw l1 through (-4, 0) and (0, 6). What is the slope of any line parallel to l1? Draw l2 through the origin and parallel to l1. 8-----------------Write an equation for each line. Use slope-intercept form if possible. 9------------ 10-------------Find the slope and y-intercept for each line that has a slope and y-intercept. X+2y=3 11----------- Y+4x=8 12----------determine whether the lines are parallel, perpendicular, or neither. Y=x+7 Y=-x+2 13------------Write each equation in slope-intercept form. Y+3=-3(x-6) 14------------Find the equation of the line that goes through the given point and has the given slope. (-1, -5), -8 15-------¬Find the equation of each line. Write each answer in slope intercept form. The line is parallel to -3x + 2y = 9 and contains the point (-2, 1). 16------------Find the equation of each line in the form y = mx + b if possible. The line through (3, 2) with undefined slope 17----------------Write a formula that expresses the relationship described by each statement. Use k for the constant in each case. m varies directly as p. 18------------ Write a formula that expresses the relationship described by each statement. Use k for the constant in each case. u varies inversely as n. 19-----------------Find the variation constant, and write a formula that expresses the indicated variation. c varies inversely as d, and c = 5 when d = 2. 20-------------------- Solve each variation problem n varies directly as q, and n = 39 when q = 3. Find n when q = 8.

Complete each ordered pair so that it satisfies the given equation. 1---- y = 2x + 5: (8, ), (-1, ), ( ,-1) Use the given equations to find the missing coordinates in the following tables. 2------ y= -x+4 X Y -2 0 2 0 -2 3-------------Graph each equation. Plot at least five points for each equation.

### laws of vector algebra

Draw appropiate figures to give geometric proofs for the following laws of vector algebra: (a+b)+c = a +(b+c) lambda(a+b) = lambda(a) + lambda (b) : lambda is any scalar a(b+c) = ab + ac .................................................................... a,b,c do not need to be coplanar. Full solution please

### Time Card & Net Pay Calculation

Practice Questions Complete the following time card. Janice earns time and a half overtime when she works more than eight hours on a weekday or on Saturday. She earns double time on Sundays and holidays. Calculate Janice's net pay if she earns \$9.75 per hour, is married, and claims one withholding allowance. Challenge Proble

### Average Annual Return Equation

Venture capital. Henry invested \$12,000 in a new restaurant. When the restaurant was sold two years later, he received \$27,000. Find his average annual return by solving the equation 12,000(1 + r)2 = 27,000.

### linear equation mathematical models

A butcher charges \$2.80 for 2.5 pounds of hamburger. How do I write a mathematical model (linear equation) that allows the calculation of the cost of the hamburger based on buying any number of pounds?

### Solving Quadratic Equations and Substitutions

1. An interesting method for solving quadratic equations came from India. The steps are: (a) Move the constant term to the right side of the equation (b) Multiply each term in the equation by four times the coefficient of the x2 term (c) Square the coefficient of the original x term and add it to both sides of the equation (d)

### "Squares everywhere" Determine the Perimeter

The figure has been divided into nine squares, the smallest one, darkly shaded, has sides of length one and the lightly shaded squares has side of length x. Determine x and also determine the perimeter of the large figure. See Attached