Basic Math Questions and Answers

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

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).

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.

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

A vehicle purchased for $27500 depreciates at a constant rate of 7%. Determine the approximate value of the vehicle 13 years after purchase.

Robert invested $200 in a retirement account that had a rate of 20% that compounds annually. If Robert leaves his money in for 3 years, how much money will be in his account rounded to the nearest cent?

Simplify by rationalizing the denominator. √13+√3/√13-√3

Solve the following system of equations graphically. x+y-4 = 0 -x-y=0 The solution lies in quadrant. llI II I IV

NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = -4.9t² +238t+402. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level.

Solve for A. BA+ C = D A=(C-D)/B A (D-C)/B A D-B-C

Find the zeros of the function, and their multiplicities. f(x) = x³ - 6x² -x+6

Dwayne's garden is triangle-shaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is each side? Which equation represents this? 3x+4=49 2x+4-49 2x=49 3x=49

Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between a and b. f(x)=x4-3x²-6; a=3, b=5 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. By the intermediate value theorem, the function does not have at least one real zero between a and b because f(a)= 48 and f(b)= B. By the intermediate value theorem, the function has at least one real zero between a and b because f(a)= C. It is impossible to use the intermediate value theorem in this case. and f(b) = 544. (Simplify your answers.) (Simplify your answers.)

Select the correct answer from the drop-down menu. A company sells its product to distributors in boxes of 10 units each. Its profits can be modeled by this equation, where p is the profit after selling n boxes. p = n² + 300m + 100,000 Use this equation to complete the statement. The company breaks even, meaning the profits are $0, only when it sells boxes.

Concrete can be purchased by the cubic yard. How much will it cost to pour a circular slab 18 ft in diameter by 3 in. for a patio if the concrete costs $40.00 per cubic yard? (1 cubic yard = 27 cubic feet) $4,523.89 $94.25 $1,130.97 $30.00

Simplify the equation. Then solve by the quadratic formula. 3x²2²-6x+5=0 X=

Graph the solution of the following system. x-y 2 -4 - 3x-y ≤ 5 Use the graphing tool to graph the system.

What is the SUM of the angle measures in a nonagon (9 sides) A 900° B) 1080° C 1440° D 1260°

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-Angle-Side (AAS) Congruence Theorem BSide-Side-Side (SSS) Congruence Postulate Angle-Side-Angle (ASA) Congruence Postulate Side-Angle-Side (SAS) Congruence Postulate

For the function f(x)=x9 - 8x³ + 8x - 7, state: a) the maximum number of real zeros that the function can have; b) the maximum number of x-intercepts that the graph of the function can have; and c) the maximum number of turning points that the graph of the function can have.

Which set of integers does NOT represent the lengths of the sides of a triangle? A. {4,7,9) B. (6,6,11} C. {4,8,12) D. (9,10,11)

23 less than twice a number is - 15. Find the number.

A sector of a circle has a central angle of 120°. Find the area of the sector if the radius of the circle is 14 cm.

Suppose on your 21st birthday you begin making monthly payments of $500 into an account that pays 8% compounded monthly. If you continue the payments until your 51st birthday (30 years), how much money will be in the account?

If we angles and the nonincluded side of one triangle are congruent to the corresponding angles and the nonincluded side of another triangle, then the triangles are congruent. Side-Side-Side (SSS) Congruence Postulate Angle-Angle-Side (AAS) Congruence Theorem Angle-Side Angle (ASA) Congruence Postulate Side-Angle-Side (SAS) Congruence Postulate

Tides are coming into the shore twice as far at Groves Point as they are at Harbor Bay. Compare the graphs of the length of tidal movements over time of both shorelines. The amplitude of the graph for Harbor Bay is twice the amplitude of the graph for Groves Point. The amplitude of the graph for Harbor Bay is four times the amplitude of the graph for Groves Point. The amplitude of the graph for Groves Point is twice the amplitude of the graph for Harbor Bay. The amplitude of the graph for Groves Point is half the amplitude of the graph for Harbor Bay.

Phyllis went to the mall and saw a massage chair that she would have to take a loan out for $6500 to purchase. The bank said that she could get a simple interest rate of 5% for 5 years. What is the total amount that Phyllis will pay for the chair?

Which description does NOT guarantee that a quadrilateral is a square? has all sides congruent and all angles congruent is both a rectangle and a rhombus has all right angles and has all sides congruent is a parallelogram with perpendicular diagonals

A man walks 10 miles in x hours. How far does he walk in one hour? Which expression represents this? 10/x miles 10x miles 10+x miles

One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. What are the dimensions of the rectangle? Which of the following equations could be used to solve the problem? 2x-2x-3=54 2x2(x-3)=54 2x-3=54

Where is the center of the largest circle that you could draw inside a given triangle? the point of concurrency of the angle bisectors of the triangle the point of concurrency of the medians of the triangle the point of concurrency of the altitudes of the triangle the point of concurrency of the perpendicular bisectors of the sides of the triangle

Which of the following would not be the result of a substitution 2x + y = 7 y - x = 1 2x+x+1=7 2(y+1)+y=7 7-2x-x=1

2x - y = 2s 2x - 2y = 4s The lines whose equations are shown intersect at which point? (0, -2s) (-2s, 0) (4s, 2s)

Suppose you invest $2500 at an annual interest rate of 3% compounded continuously. How much will you have in the account after 7 years? Round the solution to the nearest dollar. $3592 $3297 $3084 $3025

Solve the following system of equations graphically. y - 4 = 0 2x-y-2=0 What is the solution set? [(-3, 4)) [(-3,-4)) {(3, 4)}

x+y=k x-y=k The solution to the system shown is (2, 2) (k, 0) (0. k)

For the polynomial function f(x) = x(x + 3)(x + 2)2, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept. x = 0, cross; x = -3, cross; x = -2, cross x = 0, cross; x = -3, cross; x = -2, touch x = 0, touch; x = -3, touch; x = -2, touch x = 0, cross; x = -3, touch; x = -2, touch

y = 1/4 x + 7 y = 1/2 x+5 The y-coordinate of the solution to the system shown is 19 111 9

Find the coordinates of a point n (x,y) = with radius 10 corresponding to an angle of 345° Round your answers to three decimal places.