Math Questions

To demonstrate your understanding of the "mathematical language" used in this course, give an example of each of the following. (a) a square root function that has been vertically stretched by a factor of 4, reflected in the y-axis, horizontally stretched by a factor of 2, and translated 3 units left and 5 units up.

Subtract and simplify your answer. 7/X-6 - 6/X+5

Last summer, a group of high school students farmed a plot of land. They harvested 13 bushels of vegetables to give to a food pantry. Next year the students will use a larger, similar plot of land. The ratio of the dimensions of the original plot to the new plot is 2:5. How many bushels of vegetables can the students expect to harvest next year? A. about 81 bushels B. about 65 bushels C. about 33 bushels D. about 114 bushels

Factor by using the perfect-square trinomial formula. 25x² +20xy+4y²

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 101 pounds and a standard deviation of 39.4 pounds. Random samples of size 17 are drawn from this population and the mean of each sample is determined.

Find all the roots and check the answer. 7x² +78x+11=0

If the coordinate of A is (0, -2) and the coordinate of B is (10, -6), the then midpoint of AB is: Part A The X portion of the midpoint is Part B The Y portion of the midpoint is

A population has a mean = 71 and a standard deviation a=36. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=81. H = (Simplify your answer.)

Find the inverse of f(x) =5x- 3/x-1

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $7000 deposit in an account with an APR of 3.5%. The balance in the account after 1 year is approximately $

Find the area of each. Use 3.14 for the value of л. Round your answer to the nearest tenth. 5) circumference = 62.8 km 6) circumference = 24.5 mi 7) circumference = 18.8 in 8) circumference = 37.7 mi

2x-y-4-0 3x+y-9-0 What is the solution set of the given system?

$8,000 is invested in two different accounts earning 3% and 4% interest. If the two accounts earn a total of $295 in interest, how much money was invested at 3%? $2.500 $3,500 $5.500

The sum of Pete's and Sam's ages is 30. Five years ago, Pete was 3 times as old as Sam. How old is Sam? Let P Pete's age, S-Sam's age, and PS= 30. Which of the following equations would complete the system? P-5=35-5 P-S=35-15 P-5=35

What are the domain and range of the relation? Is the relation a function? F=((85,-16), (15,2), ( – 109,2), (70,42)}

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction. Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"? (Hint: cross products) 4n+ 12 = 3d 3n 9-40 4n+3=30

5x + 2y = 7 y=x+1 What is the solution set of the given system? (16/7, 9/7)) (5/7, 12/7)) ((12/7, 5/7) ((9/7, 16/7)

y-2x+3 2y-4x+6 The system of equations has solution(s). one Infinite no

Let ƒ(x) = (x + 6)². Restrict the domain off to a non-decreasing interval. Now find the inverse of f

Solve the following system by graphing. x+y-6=0 x-y=0 What is the solution of the system? (3,3) (-3,3) (3,-3)

Find a slope that is parallel and one that is perpendicular to the given equation. y = 1/4 x + 3

The 13 players on a volleyball team are to line up for a team photograph. The seven shortest players will be in the front row. The remaining players will be in the back row. The coach will be in the back row on either the left or right end or in the middle. How many different arrangements are there for the team photo?

The similarity ratio of two similar parallelograms is 4/5 . The area of the smaller parallelogram is 64 in². Find the area of the larger parallelogram. A. 92 in² B. 88 in² C. 100 in² D. 96 in²

A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in. squares from each corner and folding up the sides. The box is to hold 10368 in³. How big a piece of cardboard is needed?

2y = x + 3 5y = x - 7 What is the solution set of the given system? ((-29/3, -10/3)] [(29/3, 10/3)]} ((-1/3, -4/3)] ((1/3, 4/3)]

What is the x-coordinate of the solution of the following system of equations 3x + y = 6 x-y=6 -3 0 3

Find the equation of the line that passes through the given point and has the given slope. Express your answer in slope-intercept form. (-6,-5), m= 4 What is the slope-intercept form of the equation that passes through (-6, -5) and has a slope of 4?

Which equation models the same quadratic relationship as function ? f(x) = 2x² - 12x + 11 A. y = 2(x + 6)² + 2 B. y = 2(x − 6)² + 5 C. y = 2(x - 3)² - 7 D. y = 2(x + 3)² - 7

2x + y = -2 x+y=5 The x-coordinate of the solution to the system shown is -3 7 3 -7

Solve the following system of equations by the substitution method. 8x = 2y + 5 3x = y +7 What is the solution set?

Find the sum and classify the polynomial based on degree and number of terms. 3n2(5n22n + 1) + (4n² - 11n4 -9) A 4th degree polynomial with 4 terms B. 3rd degree polynomial with 3 terms C. 3rd degree polynomial with 4 terms D. 4th degree polynomial with 3 terms

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. A Side-Side-Side (SSS) Congruence Postulate B Side-Angle-Side (SAS) Congruence Postulate C Angle-Angle-Angle (AAA) Congruence Postulate DSide-Side-Angle (SSA) Congruence Postulate

What are the solutions of this quadratic equation? x² =16x- 65

Against the wind a small plane flew 175 miles in 1 hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air? The speed of the plane in still air was___mph. The speed of the wind was__mph.

Select the best method of finding an accurate solution to a system of linear equations. algebraic methods graph the lines guess and check

NASA launches a rocket at t= 0 seconds. Its height, in meters above sea-level, as an equation of time is given by h=- 4.9ť² + 139t + 269. How many seconds does it take for the rocket to reach its maximum height?

When solving a system of linear equations, try to algebraically form one equation that has only one variable. True False

Board feet is a measurement of lumber volume. A board foot is equal to 144 in3 of wood. About how many board feet is a piece of lumber that measures 2 in. by 8 in. by 12 ft? 22 board feet 1.3 board feet 6.5 board feet 16 board feet

The demand equation for a certain product is given by p = 124 – 0.065x, where p is the unit price (in dollars) of the product and is the number of units produced. The total revenue obtained by producing and selling z units is given by R Determine prices p that would yield a revenue of 7280 dollars. Lowest such price = Highest such price:

Suppose you have $14,000 to invest. Which of the two rates would yield the larger amount in 2 years: 8% compounded daily or 5.87% compounded continuously? Which of the two rates would yield the larger amount in 2 years? 6% compounded daily 5.87% compounded continuously

x-y=2 0.2x + 0.4y=1 The x-coordinate of the solution to the system shown is 6 3 1

Chose the equation for a line that passes through (2,-3) and has a slope of m=-4 in point slope form. A y-3=-4(x- 2) B y-2=-3(x+4) C y+3=-4(x-2) D y+2=-4(x+3)

Find the point-slope equation of the line with slope -3 that passes through the point (2, -10). Solution: y-y1=m(x-x₁) y-(2)=-3(x-(-10)) y-2=-3(x+10) The equation of the line is y-2=-3(x+10).

Determine the standard form of the equation for the circle with center (h, k) = (-5,1/2) and radius r = 1.

Find the partial fraction decomposition of the given rational expression. 16x + 34/4x² + 12x + 8

You volunteer to help drive children at a charity event to the zoo, but you can fit only 7 of the 14 children present in your van. How many different groups of 7 children can you drive?

Catelyn invested $7000 in an account that earns 5.6% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t. How much did Catelyn have in the account after 4 years? A. $8704.70 B. $8719.36 C. $8568.00 D. $10,920.00

One solution to a quadratic function, h, is given. -4 + 7i Which statement is true? Function h has no other solutions. The other solution to function h is -4 - 7i. The other solution to function his 4 - 7i. The other solution to function is 4+ 7i.

Use identities to simplify the expression. CSC X-1/CSC X Which of the following is a simplified form of csc x- 1/csc x?

Using a sheet of graph paper, solve the following system of equations graphically. Be sure to show any work, use a straight edge, and be neat. When you are finished, enter the solution set in the box below and turn in your graph paper to your teacher. x+y=0 x-y+2=0