Coordinate system Questions and Answers

A circle with circumference 12 has an arc with a 330° central angle. What is the length of the arc?

If DE = 4x-1, EF = 9, and DF = 9x-22, find the value of x.

The number of branches on a tree demonstrates the Fibonacci sequence. How many branches would there be on the next two levels of this tree? 13 8 2 5 3 2 1 branches A. 34, 55 B. 21,34 C. 18, 28 D. 21, 29

A circle is inscribed in a square with a side length of 94. If a point in the square is chosen at random, what is the probability that the point is inside the circle? Round your answer to the nearest tenth of a percent. ______ %

CONSTRUCTION The frame for the roof of a house is designed so that the ratio of the rise to the run is in a constant ratio of 5/12.What is the measure of angle A to the nearest degree? A) 23° B) 25° C) 65° D) 67°

At her party, Emily wants to serve each of her friends a hotdog and a bun. There are 8 hotdogs in a package but only 6 buns in a bag. What is the least amount of hotdogs Emily must buy so that she has the same amount of hotdogs and buns? A. 48 B. 16 C. 8 D. 24

Use the Parabola tool to graph the quadratic function. f(x)=2x² + 12x + 15 Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

3. A rectangle has side lengths of 3 cm and 6 cm. a.)What is the area of this rectangle? b.)What is the area of this rectangle after it has been dilated by a scale factor of 5? 4. Find the area of the shaded region in the figure at left.

An insurance company claims that for x thousand policies, its monthly revenue in dollars is given by R(x) = 225x and its monthly cost in dollars is given by C(x)= 180x + 16,200. a). Find the break-even point. b). Graph the revenue and cost equations on the same axes. c). From the graph, estimate the revenue and cost when x = 180.

Given the following diagram, find the required measure. Given: /11 m m∠1=140° m ∠ 3=50° m∠4= 90 40 130 140

Solve each equation by completing the square. 2) x²-(18x) + 17 =-10

Solve each equation by factoring. 4) x² + 16 = 10x

Two angles whose sides are opposite rays are called_______ angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called _____ angles. vertical; adjacent adjacent; complementary adjacent; vertical vertical; supplementary

What are the names of three collinear points? Points D, J, and B are collinear. Points A, J, and B are collinear. Points L, J, and K are collinear. Points D, J, and K are collinear.

Find the coordinates of the midpoint of the segment whose endpoints are H(6, 4) and K(2, 8). (4,4) (4,6) (2, 2) (8, 12)

Name an angle vertical to ∠EGH. ∠EGF ∠HGJ ∠IGF ∠HGI

In September 2016, the cost of gasoline in Berlin was around 1.2 euros per litre What would the equivalent cost be in U.S. dollars per gallon? 1 U.S. dollar ≈ 0.876 euros 1 gallon ≈ 3.785 liters The equivalent cost would be $ _____per gallon.

Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. 11 61 7.8 14.9

In pentagon ABCDE, m∠A= m∠C=m∠D = 90° and ∠B=∠E. What is m∠B, in degrees?

8.) Give 3 example problems with solutions using the point of division.

A line segment has endpoints of (-2,4) and (5,-3). Find its length and midpoint

28. The sides of a square are 3 cm long. One vertex of the square is at (2, 0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square? A. (-4,0) B. (0, 1) C. (1,-1) D. (4,1) E. (5,0)

Which of the following statements is false? A. The base angles of an isosceles trapezoid are congruent. B. The bases of an isosceles trapezoid are congruent. C. A rectangle is an equiangular quadrilateral. D. The diagonals of a rhombus are perpendicular and bisect each other.

Graph the following function: y = -2-3cot(x)/2 Step 1 of 2: Identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.

Graph the following function: y = -5sес(πx + 3π)/2 Step 1 of 2: Identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.

Graph the set (x|-5<x<5) on the number line. Then, write the set using interval notation.

Consider the following exponential functions for -3 ≤ x ≤ 3: f(x)= 3x g(x)=(1/3)x a. Determine f(x) and g(x) and graph each after the given transformation is applied to both (graph together on the same graph and label each function clearly): k=-1 a=3 d=-1 c=-3 b. Explain two observations that you can make from your graphs that connect transformational parameters as potentially equivalent to each other.

What rotation about the origin is equivalent to R-200? A. R560 B. R-160 C. R200 D. R160

Determine the domain and range of each exponential function. a. y = -5(1.2)x-7+ 10 b. y=13(0.7)-2x+11-99

How much money in commission does a real estate agent who works on a 2.5% commission rate earn from a $260,000 sale? A. $1,040,000 B. $10,400 C. $65,000 D. $6,500

Find the inverse of the function f(x) = -2/5 x - 4 Draw the functions f and f-1(x)

For a given interest rate, simple interest varies jointly as the principal and time. If $1000 left in an account for 6 years earned interest of $420, then how much interest would be earned in 7 years? The amount of interest earned in 7 years would be $ (Type an integer or a decimal.)

If AB = 15 m, BC = 18 m and CA = 24 m, find the point of intersection of the angular bisector from the vertex C. (i know how to get the incentre but i can't get the distance of incentre to vertex C)

(x³ + 2x² - 6x+5)-(2x³+4x² -5x+10) is equivalent to: A. 3x³ +6x² -11x+15 B. -x³ +6x²-11x+15 C. -x³-2x²-x-5 D. -2x³-2x²+x+5 E. x³ +6x²-2x+15

Which expression would be appropriate to complete the following equation in order for the equation to illustrate the Associative Property of Addition: 5+(7+0) = ? A. (7+0)+5 B. 5+ (0+7) C. (5+7)+0 D. 5+7 E. 12

You can use your own graph paper or download and print this graph paper (PDF, 15kb). For each problem, complete the translation, reflection, or rotation given the coordinates.

Consider the following three straight lines. D₁: (x, y, z) = (2,4, − 1) + s(2, − 1,3) x = -1 + 2k D₂: y = 1+ 3k Z=-6+4k D3: (x, y, z) = (–7,8, − 14) + t(−4,2, − 6)| Using these lines, form: a) a pair of parallel lines; (b) a pair of intersecting lines (indicate the point of intersection); c) a pair of left lines. Justify your answers.

Determine algebraically whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or, the origin. Confirm graphically. y=11/x Select all that apply. A. The graph is symmetric with respect to the origin. B. The graph is symmetric with respect to the y-axis.. C. The graph is symmetric with respect to the x-axis. D. None of these

Choose all the statements that are TRUE about the vertical line through the point (1,4). The graph is located 1 unit to the above the x-axis. It has an equation of y = 4. It has an x-intercept of (1, 0). The equation is x = 1.

What value of A will produce the output (in degrees) in the graphing calculator screen? A= (Type an integer or decimal rounded to seven decimal places as needed.)

A vehicular tunnel has a length of 7165 feet. Use the concept of accuracy and significant digits to determine the range of this number. The range is from to feet. (Type an integer or a decimal.)

The number of sides of a regular polygon is given. Find the measure of the sum of the interior angles and the measure of each interior angle: a) 5 sides Sum of interior angles: Individual interior angle: b) 8 sides Sum of interior angles: Individual interior angle: c) 15 sides Sum of interior angles: Individual interior angle:

A parallelogram has four points at (1, 6), (7, 8), (1, 1) and (7,3). At what point will the diagonals intersect? (1,2) (4,4.5) (2.2.25) (8,9)

Graph the function. 9) y = -6 csc(x + π/2)+1 Step:1 Find the period Step:2 Find the interval Step:3 Divide the interval into four equal parts and then complete the table Step:4 Graph the function over one period

A certain stylist charges $15 for a haircut and $30 for hair coloring. A haircut takes on average 30 minutes, while coloring takes 2 hours. The stylist works up to 8 hours in a day, and she needs to make a minimum of $150 a day to pay for her expenses. a. Create a system of inequalities that describes the constraints in this situation. Be sure to specify what each variable represents. b. Graph the inequalities and show the solution set. c. Identify a point that represents a combination of haircuts and and hair-coloring jobs that meets the stylist's requirements. d. Identify a point that is a solution to the system of inequalities but is not possible or not likely in the situation. Explain why this solution is impossible or unlikely.

Sketch a graph of f(x) = 0 if x≤-2 2 if -2 < x≤1 0 if x>1

An electron fired as a straight line from point A, located at 30μm from the center of a spherical atom of radius 10µm and travelling towards it at the rate of 1 m/sec barely grazes the periphery of the atom. How much time is needed for the electron to move from point A till it tangentially grazes the atom?

Make a table for r = 2cos(3 thetas) with theta= 15degree+ 30 degrees k with k going from 0 to 11 along with theta=90 degree k with k going from 0 to 4 and plot these points (by hand). Use these points to help you sketch a graph of r=sin2(theta). Theta =0 please show neat work

A triangle has vertices (-4,3), (2,-5) and (6,5). What kind of triangle is it?

An Elongated Pentagonal Orthocupolarotunda is a polyhedron with exactly 37 faces, 15 of which are squares, 7 of which are regular pentagons, and 15 of which are triangles. How many vertices does it have?