Basic Math Questions and Answers

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 +

Find the x- and y-intercepts of the graph of 2x – 10y = 36. State your answers as whole numbers or as improper fractions in simplest form. x-intercept: y-intercept:

Multiply and combine like terms to write as the sum or difference of monomials. a. 2a(5+ 4a) b.) x³(x+6) +9 C. (x-4)(x + 5) d. Produc (10w-1)(10w + 1) oble edt brs 2tinu x zi ensup2 19gisl adob el nolyot baberiz arito con or

The discriminant of a quadratic function is 5. What does this mean about the solutions? O2 real solutions 1 real solution, 1 imaginary solution O real solution, 2 imaginary solutions 1 real solution

Describe the transformation from f(x) to -3f (x + 1) - 3. Of(x) is reflected over the x axis, stretched vertically by a factor of 3, shifted left 1 and down 3. O f (x) is reflected over the y axis, stretched vertically by a factor of 3, shifted left 1 and down 3. O f (x) is reflected over the x axis, stretched vertically by a factor of 3, shifted right 1 and down 3. Of(x) is reflected over the y axis, stretched vertically by a factor of 3, shifted left 1 and up 3.

Write the quadratic function in standard form. y = −3(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.)

A convention to determine the best cookie is held with 100 voting members. Before the speeches, 4 people are going to vote for Oatmeal Raisin. After the speeches are given 6 people decide to vote for Oatmeal Raisin. The Oatmeal Raisin speaker claims to have a 50% increase in supporters. The Oreo speaker says that's a lie and that Oatmeal Raisin support has only risen 2%. Who is correct? a) How did th Oatmeal Raisin speaker arrive at his claim?

Select all of the numbers that are Integers. J 7/8 -99 1.33333... -8.6 7 √51 0 -8.517324924812...

Manually Graded Question: Make sure to answer all parts of the question and be as detailed as possible. Use correct vocabulary when necessary. Use the given information to decide which equation will be the easiest to use to find the indicated value. Find the value and explain your choice. The value of the 4th term is 80 The sequence is being doubled at each step Explicit equation: y = = 5 (2²) Recursive: now = previous term * 2 Find the 5th term. Explanation:

Solve 7x - xy = -18 for x. Ox X = O X = Ox= O x = -18+18 7 y - 18 7-y 18 7y 18 7+y

Match the function h with the transformation it represents, where c>0 h(x) = f(x) - c* (11 Points) a horizontal shift of f, c units to the right a vertical shift of f, c units down a horizontal shift of f, c units to the left a vertical shift of f, c units up

Which of the following is true for f? (3x + 1, if-9 < x≤-2 f(x)=-5, if-2 < x≤1 (x-6, if 1<x<7 A The domain is -9 < x < -2,-2 < x < 1, and 1<x< 7. B The range is (-26, 1). The function is decreasing over the interval (-2, 1). D The rate of change over the interval (-9, 1] is 3.

Solve the absolute value inequality and write the answer interval notation: 19x + 9 |≥ 54 29 0 (-∞, -7]U[²,00) 5 O [-10, -6] O (-∞, -7] U [5, ∞) O (-∞, 5] U [8, ∞)

Skill Practice 5 Solve the equations. a. 512-4t = 50 b. 5 = 6c 7 +9

Find the equation of a line that contains the point (2,7) and is perpendicular to the line x - 4y = 8 y = -4x + 15 y = - 4x -2 y = 4x+8 y = 1/4 x + 8 y = 1/4 x-2

Which equation represents a line that passes through the point (-2, 1) and has a slope of 2 in point slope form? Oy-2=(x-1) Oy-1 = ²(x-2) 3 y + 2 = ²(x - 1) Oy-1 = ²(x+2)

3. Shandra is on vacation and wants to buy souvenirs for at least eight friends. A postcard book costs $2.50 and a magnet costs $4.00. She can spend up to $30 altogether. Write a system of inequalities to represent the situation. Number of magnets 06 8 42 to 01 8 10 12 Number of postcard books X

Jed is standing 10 meters from a maple tree that is 14 meters from a willow tree, as shown in the figure below, in which the measure of an angle is given. Which of the following equations, when solved for x, gives the distance, x meters, between Jed and the villow tree?