![]() ![]() Let us find the x and y intercepts of the line whose equation is given. Which one of the graphs is closet to the graph of y = -2x + 2? If each person eats at least 3/4 of a pizza, then the 7 will eat at least.Īll axes in the graphs below have the same scales. What is the smallest number of whole pizzas needed for lunch? Each person eats at least 3/4 of a pizza. X = - 3 and x = - 1 and the smallest is - 3Ī group of 7 friends are having lunch together. The left side of the above equation may be factored as follows. What is the smallest value of x that satisfies the equationĮxpand and write the given equation with the right side equal to 0. Size of angle ABC = 180° - (26° + 131°) = 23°Īngles ABC and CBD are supplementary. Let us first find angle ABC using the sum of the angles in triangle ABC. In the figure below, B is on AD, ∠ BAC and ∠ ACB measure 26° and 131° respectively. The slope is the coefficient of and is equal to - 4 / 3. We first need to write the given equation in slope intercept form y = m x + b and then identify the slope and its value. The graph in C is all below the x axis and is therefore the closet to the graph of y = -2 / |x - 3| Hence - 1 / |x - 3| is always negative except at x = 3 where it is not defined. The graph of y = 2 / (x - 3) is shown belowĪmong the following, which is the best possible graphical representation of y = -2 / |x - 3| We first find the hypotenuse BA and use it to find cos(A).Ĭos(A) = adajacent side / hypotenuse = 3/5 In the right triangle ABC below, what is the cosine of angle A? Using the values x = 1.8 and y = 2.1, it can easily be shown that B) C) D) and E) above are not true. X < x y / 2 < y, which correspond to the answer in A) above. The above inequality may also be written as. Multiply all terms of the above inequality by x y and simplify to obtain. Which means a must be negative and b + 4 not equal to 0 or b not equal to - 4. What are the values of a and b, if any, where - a|b + 4| > 0?įor - a |b + 4| - a must be positive and |b + 4| must also be positive. Solve for cos(A) and select the positive value since A is an acute angle Substitute sin(A) by 11/14 in the above equation The radius is given by the distance between the center of the circle (4, - 5) and the y axis which is 4Īngle A is an acute angle and sin(A) = 11/14. The above equation has two solutions + √7 and - √7Ī circle with center (4,-5) is tangent to the y-axis in the standard (x,y) coordinate plane. How many solutions are there to the equation x 2 - 7 = 0? The radius of the circle is 4 and therefore the circumference is given by What is the circumference of the circle, expressed in coordinate units? In the standard (x,y) coordinate plane, the graph of (x + 3) 2 + (y + 5) 2 = 16 is a circle. Let x be the length of second leg and apply Pythagora's theorem as follows If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg? We first factor 2x 2 + 2x - 12 as follows If the width is 5 in and the length is 3 times the width, then the length isįor all x >2, (2x 2 + 2x - 12) / (x - 2) simplifies to If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches? The length of a rectangle is 3 times its width. ![]() If one ball is selected at random, the probability that it is blue is given by If 1 green and 1 blue ball are taken from the box, then there are 7 green, 3 blue and 3 white balls, a total of 13 balls. What is the probability that a blue ball is selected at random from the box? ![]() ![]() Then 1 green and 1 blue balls are taken from the box and put away. There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Which of the following is equivalent to (x)(x)(x)(x 3), for all x? ![]()
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