Basic Math Questions and Answers

Diane invested her savings in two investment funds. The $3000 that she invested in Fund A returned a 3% profit. The amount that she invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 7% profit? Amount invested in Fund B: $

Set up the problem below and calculate the number of days that are equivalent to exactly 21600 minutes. Place your conversion factors in order such that "minutes" cancels first. 21600 minutes

Solve the system by substitution. -9y+ 2 = x -x-3y = -8

Write an algebraic equation for the following problem and then solve it. A landscaping company needs 180 gallons of 24% fertilizer to fertilize the shrubs in an office park. They have in stock 30% fertilizer and 20% fertilizer. How much of each type should they mix together? Let x = the number of gallons of 30% fertilizer to be used. Write an expression, in terms of x, that is equal to "180 gallons of 24% fertilizer". (Use integers or decimals for any numbers in the expression.) They should use ______gallons of 30% fertilizer and______ gallons of 20% fertilizer.

The patient's chart indicates that he weighed 175 pounds at the end of September. He then gained 2½ pounds in October and lost 3/4 pound in November. He weighed at the end of November.

Solve for u. -1/ u+5=- 7 /3u+15 - 1 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Consider just the first sentence of this multistep word problem. Sentence 1: The sum of the ages of a brother and sister is 26. Give an equation that represents this statement using b as the age of the brother and s as the age of the sister. Express your answer in terms of the symbols b and s.

y = f(3x) Shift the graph 3 units upward. Stretch the graph horizontally and vertically by a factor of 3. Shift the graph 3 units to the left. Stretch the graph vertically by a factor of 3. Shrink the graph horizontally by a factor of 3.

Greg invested his savings in two investment funds. The amount he invested in Fund A was 4 times as much as the amount he invested in Fund B. Fund A returned a 8% profit and Fund B returned a 2% profit. How much did he invest in Fund B, if the total profit from the two funds together was $3400? Amount invested in Fund B:

The angle of depression from the top of a building to a point on the ground is 45 degrees. How far is the point on the ground from the top of the building if the building is 280 m high? Round your answer to the nearest whole number.

Find the length of each side of the triangle determined by the three points P₁, P2, and P3. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P₁ =(4,4); P₂=(2,3); P3 = (6,0) The length of side P₁ P₂ is (Type an exact answer, using radicals as needed). The length of side P₁P3 is (Type an exact answer, using radicals as needed).

Write the quadratic in vertex form (fill in the "a", "h", and "k" values) y = x² - 2x + 3 y =

Write an equivalent expression by distributing the "-" sign outside the parentheses: -(-3k-4.7)

A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 110 units of A per day. Both products use one raw material, of which the maximum daily availability is 300 lb. The usage rates of the raw material are 2 lb per unit of A, and 4 lb per unit of B. The profit units for A and B are $40 and $90, respectively. Determine the optimal product mix for the company.

A football is kicked vertically upward from a height of 5 feet with an initial speed of 75 feet per second. The formula h=5+75t-161² describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to find the ball's height 3 seconds after it was kicked.

Evaluate the function f(x)=x² + 4x+6 at the given values of the independent variable and simplify. a. f(-6) b. f(x+3) c. f(-x)

Final grades are often computed using weighted averages. Some college professors use complicated weighted averages. Your college professor tells you he will give a 33% -67% split on grades between tests and homework where whichever average is higher will be the 67%. What will your final grade be if your homework average is 85 and your test average is 62?

Write the quadratic function in standard form. y = 3(x - 2)² +1 (fill in the blanks with the correct coefficient. If the coefficient has a "minus sign" in front make the number negative that you enter. Do not enter a "+" for positive numbers.)

Solve the system by substitution. y = -10x +9 2x 10y = 12

Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inches of cord for each necklace. Use matrices to find the number of bracelets and the number of necklaces that Philip made.

Find all numbers for which the rational expression is undefined. If the rational expression is defined for all real numbers, state this. y+2/y²-4 Type the values for which the rational expression is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. (Use a comma to separate answers as needed.) B. The rational expression is defined for all real numbers.

You are looking at your power bill for the month, you pay 13 cents per kilowatt-hour. Your power bill came out to $97.66 how many KWH of energy were used in your house this month?

Solve for all values of x by factoring. x² - 5x -56 = -2x - 2

Yoko borrowed a total of $19,000 from two different banks to start a business. One bank charged the equivalent of 4% simple interest, and the other charged 2.5% interest. If the total interest after 2 years was $1460, determine the amount borrowed from each bank. Yoko borrowed S at 4%. Yoko borrowed S at 2.5%.

Last year, Melissa invested her money in two purchases. She purchased a certificate of deposit for $1000 that paid 2% interest per year and purchased $3000 in corporate bonds paying 7% interest per year. Answer the questions below. Do not do any rounding. (a) What was the total interest earned at the end of 1 year? (b) What was the percent interest for her total investment?

a) What is the average velocity of the hammer between 2 and 6 seconds? b) What is the instantaneous velocity of the hammer at 5 seconds? c) After how many seconds will the hammer hit the ground? d) What is the instantaneous velocity of the hammer as it hits the ground?

Evaluate logs 27 Recall the first step to evaluate a logarithm is to rewrite the logarithm into an exponential. Remember what type of exponent can get values close to 0.

Solve for all values of x by factoring. x² - 36 = 0

Using the Pythagorean Theorem (a² + b² = c²), find the altitude of a right square pyramid that has a square base that has a side length of 25.7 cm and a slant height of 20.2 cm. Round to three decimal places, if needed. Your Answer:

The half-life of an over the counter pain medication is 2 hours. If the initial amount of pain medicine is 200mg how much of the pain medicine would remain in your body after 5 hours? 55.36mg 35.36mg 151 mẹ 25mg

A geometric sequence h starts with 10, 5,... Explain how you would calculate the value of the 100th term.

Which function below represents the inverse function of y = 2ln(3x + 2) - 4? y¹ = 100.5-2 +1 y¹ = (e-2) y-¹ = e²+2 y¹=²+2-2 Keep in mind that a natural logarithm has base e so the inverse of that function would be an exponential with base e, also your first step is isolate the exponential first.

For each equation, choose the statement that describes its solution. If applicable, give the solution. 4(v + 1) - v = 3(v − 1) + 3 No solution v = 0 All real numbers are solutions −4(y + 1) + 6y = 2(y + 2) - 8 No solution y = 0 All real numbers are solutions 8 X 20 Ś ?

y = 3f (-1²-x) 3 Stretch the graph horizontally by a factor of 3. Stretch the graph horizontally and vertically by a factor of 3. Stretch the graph vertically by a factor of 3. Shrink the graph horizontally and vertically by a factor of 3. Shrink the graph horizontally by a factor of 3. X

Suppose that you have a piece of string 6 cm long. If one end is held fixed and you draw with a pen at the other end, keeping the string tight, then you will draw a circle. What is the circumference of this circle? Express your answer in centimeters to three significant figures.

The United States did not experience a major unemployment problem among veterans following World War II, as it had after World War I. Which of the following provides one major cause behind this difference?

Ty decided to invest $600 in an account and was able to take out $670 from the account after 8 years. The interest in the account was compounded continuously. What was the interest rate for his account? x=1.37% x-0.014% x-1.12% x=13.7%

Describe the transformations taking place if we transform f(x) to f (x + 2) f(x) is shifted up 2 f(x) is shifted down 2 f(x) is shifted left 2 f(x) is shifted right 2

Write an equation of the line with the indicated slope and y-intercept. Slope = -7 y-intercept = 6 y=0 (Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form.)

Suppose that you needed to make a pen for some small animals. You have 13 m of fencing. You decide to make a circular pen, because if you wish to enclose an area using a given length of fencing, then a circular fence encloses a larger area than a fence of any other shape. What is the radius r of the pen? Express your answer in meters to four significant figures.

In the lab, Eric has two solutions that contain alcohol and is mixing them with each other. He uses 500 milliliters less of Solution A than Solution B. Solution A is 19% alcohol and Solution B is 11% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 115 milliliters of pure alcohol?

a. Use the following information to write an equation in terms of x. Then solve the equation, and find RS and ST. RS= 2x+10, ST=x-4, RT = 21 Equation: = 21 X = RS= ST= b. Use the following information to write an equation in terms of x. Then solve the equation and find RS and ST. RS= 3x - 16, ST = 4x-8, RT = 60 Equation: = 60

Your college professor tells you he will give a 30% -30% -40% split on grades between homework, quizzes, and test. However whichever category you have the highest average in will be the 40% category. What will your final grade be if your homework average is 51, you quiz average is 73, and your test average is 93? Type your answer....

The temperature on Monday is -24°C. The temperature on Tuesday is -21°C. Circle the inequality that makes a correct comparison. Then write a sentence to tell what the inequality means in this situation. a. -24 < -21 b. -24 <1-21| |-24|<|-21| |-24|>|-21|

Trevor purchases a car. The value of the car is modeled by the function y= 22000(0.86). Which statement below best describes the value the base 0.86? The car that Trevor purchased appreciates at a rate of 14%. The car Trevor purchased depreciates at a rate of 14%. The car Trevor purchased depreciates at a rate of 86%. The car that Trevor purchased appreciates at a rate of 86%.

A football is kicked vertically upward from a height of 6 feet with an initial speed of 55 feet per second. The formula h = 6 + 55t-16t² describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to find the ball's height 3 seconds after it was kicked. The ball's height, 3 seconds after it was kicked, was feet.

Because of the difficulty of weighing a bear in the woods, researchers caught and measured 54 bears, recording their weight, neck size, length, and sex. They hoped to find a way to estimate weight from the other, more easily determined quantities. Which of the following are quantitative variables for this study? Neck Size Length Bear Weight Sex

Evaluate the given algebraic expression for x = 7 and y = -2. |x | + lyl The answer is (Type an integer.)

10. Jerry is making baked garlic. The recipe calls for 5 large heads of garlic. However, Jerry has only small heads of garlic. If a large head of garlic has about 15 cloves, while a small head has about 7 cloves, how many small heads should he put in the roasting pan to end up with a similar number of garlic cloves? a. 3 garlic heads b. 75 garlic heads c. 20 garlic heads d. 11 garlic heads continued

Write the quadratic function in standard form. y = 2(x + 3)² + 2 (fill in the blanks with the correct coefficient. If the coefficient has a "minus sign" in front make the number negative that you enter. Do not enter a "+" for positive numbers.) y= x² + X +