For any real number a, the equation |x - a| = 7 can be thought of as meaning “the distance on the real number line from x to a is 7 units.” How far apart are the 2 solutions forx?

Three distinct lines, all contained in a plane, separate the plane into distinct regions. What are all of the pos- sible numbers of distinct regions of the plane that may be separated by any 3 such lines? (Note: Do NOT include any of the points on the 3 lines in your count of distinct regions.)

The Recreation Department wants to build a circular wading pool in the city park. The area available for the pool is a fenced-in rectangular region 12 meters by . 18 meters. If the Recreation Department wants the wading pool to be as large as possible, and the edge of the pool must be at least 2 meters from the fence all around, how many meters long should the radius of the pool be?

For real numbers a and b such that 0 < ab

The quantity n√2^p is defined when n is an integer greater than 2 and p is any nonzero real number Which of the following is a relationship between n and p that will always make n√2^p a positive integer ?

One hot-air balloon is 10 kilometers (km) east and 3 km north of an airport tower while a second hot-air balloon at the same altitude is 2 km west and 5 km . south of the same airport tower. Approximately how many kilometers separate the 2 hot-air balloons?

A movie projector emits light as shown in the top-view diagram below. To make the light projection cover the full width of a 12-foot screen without extending mys beyond the screen, the projector must be placed a certain distance from the screen. Assuming the screen is positioned directly in front of the projector as shown, which of the following expressions could be used to calculate the distance, in feet, from the projector to the screen?

To make a piece of jewelry, Aaron cuts out a circular piece of metal from a larger circular piece, as shown below. The radius of the larger circle is 2 inches. If the area of the cutout is to be the same as the area of the piece that remains, what should be the radius, in inches, of the inner circle?

The operation A is defined by the following: a ∆ b=3+a+b-axb For-example, 4 ∆ 6=3+4+6-4x6=-11. If a ∆ b=b ∆ a, then which of the following describes all the possible values of a and b?

In the figure below, a square is inscribed in a.circle of radius r. What is the perpendicular distance from the center of the circle to-a side of the square, in terms of r?

A wheel 29 inches in diameter rolls along a: line without slipping. How many inches does the wheel roll along its path in 25 revolutions?

Phuong rode his bike, mostly uphill, to visit Brad. The , trip to Brad’s house took t minutes. Returning home, mostly downhill, Phuong was able to travel at an average speed twice that of his trip to Brad’s. Which of the following is an expression for the total number of minutes Phuong bicycled on the entire trip?

The. volume, V, of the right circular cylinder below is given by the formula V.=πr^2 h, where r is the radius of” the base, and A is the height of the cylinder. If'r is doubled and h.is halved, the new cylinder’s volume, V, will be:

If b ≠ c, what are the real values of a that make the following inequality true? (ab -ac) / (2b-2c) < 0

Whenever ( tan θ ) / ( sin θ ) is defined, it is equivalent to:

What is the solution set of |2z-1| >= 5 ?

The value of x that will make (x/2) +1= 3 a true statement lies between which of the following numbers?

Which of the-following operations will. produce the largest result when substituted for the blank in.the expression: 2 _____ (-1/3)

In the figure below, cos θ =?

In the standard (x,y) coordinate plane, which of the following lines goes through (0,2) and is parallel to y=3x+1 ?

A circular fountain with a diameter of 20 meters is to be placed entirely within a rectangular plaza, 40 by 60 meters. Bricks will be laid on the entire plaza a 5 around the fountain (but not under it), making it acces sible to pedestrians. What is the approximate area, in aa ee . square meters, of the plaza that will be brick?

If 0° <= x° <= 90°, and 2 sin^2 ’x° + 1 = 0, then x° =?

What value of n will satisfy the equation 0.1(n + 1,350) =n?

The points A(1;1) and B(5,2) in the standard (x,y) coordinate plane below are 2 vertices of ABC, which has a right angle at B. Which of the following points could be the third vertex, C ?

The Environmental Club selects its 3 officers by first selecting the president, then the vice president, and finally the secretary. If there. are 20 members who are eligible to hold office and no.member can hold more than 1 office, which of the following gives.the number of different possible results of the election?

The ellipse shown .below intersects any different ellipse in, at most how many points?

ne route. along flat terrain from Red Deer to Vegreville:is to drive north from Red Deer to Edmonton about 150 kilometers, then, at Edmonton, to drive east for about 100 kilometers to Vegreville. If a straight, flat road existed between Red Deer and Vegreville, about how many kilometers long would it be?

1/3 ∙ 2/4 ∙ 3/5 ∙ 4/6 ∙ 5/7 ∙ 6/8 ∙ 7/9 ∙ 8/10 ?

Which of the following is the least common denominator for the expression below? ( 1/ (13^2 ∙ 17 ∙ 23) ) + ( 1/ (17^2 ∙ 23) ) + ( 1/ (17 ∙ 23^3) )

In the standard (x,y) coordinate plane, what is the slope of the line given by the equation 5x- 4y=3?

If (x^a) / (x^b) = x^3 for all x ≠0, which of the following must be true?

As a salesperson, Onawa travels to a variety, of locations during a day. The graph shows the relationship between time and total distance traveled on a particular day. What was Onawa’s average speed, in miles per hour, for the parts of the day when she was traveling fromone place to another?

In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoints (-1,3) and (2,7) ?

The domain of a function f is the set of all values of x for which f(x) is defined. One of the following sets is the domain for the function graphed below. Which set is that domain?

What is the center of the circle with equation (x-2)^2 +(y+ 2)^2 = 2 in the standard (x,y) coordinateplane?

In the standard (x,y) coordinate plane, what is the slope of the line joining the points (2,-7) and (5,4) ?

A rectangular room that is 2 feet longer than it is wide has an area of 120 square feet. How: many feet long is the room?

All sides of a rhombus are the same length, as illustrated below. If one diagonal is 10 inches long and the other is . 24 inches long, how many inches long is a side of the rhombus?

For a certain quadratic equation, ax^2 +bx+c=0 the 2 solutions are x = 3/5 and x = 1/2. Which of the following could be factors of ax^2+ bx +c?

The area of a trapezoid may be found by using the formula A = (1/2)h (b1 + b2), where h is the height and . b1, and b2, are the lengths of the parallel bases. What is the area, in square inches, of the isosceles trapezoid below?

How many minutes would it take a train to travel 90 kilometers at a constant speed of 120 kilometers per hour?

When x = 1/2, what is the value of (3x - 3) / x ?

Which of the following expressions is NOT a polynomial factor of x‘ - 4?

What is the sum of the 2 solutions of the equation . x^2 +2x-15=0?

The area of a square is 36 square inches. What is its perimeter, in inches?

What is the 311th digit after the decimal point in the repeating decimal 0.51246 ?

(x^5)^12 is equivalent to:

For all x, 5-3(x-4)= ?

For all x and y, (x-y)(x^2 +y) =?

What is the value of |3 - x| if x = 6?

Carlotta had 2 more CDs (compact discs) than Mario. Then she bought 3 CDs from Mario. Now how many’ more CDs does Carlotta have than Mario?

Sherry won a cash settlement for a suit she had filed . in court. Sherry paid her lawyer 25% of the original . settlement and had $12,000 remaining. How much was the original settlement?

When a triangle-is isosceles, its parts are given special names, which are shown below for ABC where AB ≅ CB. If 2 isosceles triangles are similar, which of the following must be equal?

A package of 10 ballpoint pens is priced at $1.50 now. If the pens go on sale for 20% off the ‘current price‘ what will be the sale price of the package?

In the figure showing ABC below, line m is parallel to line n.. Which one of the following angles must be congruent to

The daily totals of lunch customers served at the Sunshine Cafe last Monday through Saturday were 256, 189, 204, 179, 166, and 218. What was the average number of lunch customers served each day?

Malcolm has 3 striped ties and 4 solid-colored ties a hanging together in his closet. In his haste to get to his appointment, he randomly grabs 1 of these 7 ties. What is the probability the tie that Malcolm grabs is striped?

A Fahrenheit temperature F can be approximated by doubling the Celsius temperature C and adding 32. Which. of the following expresses this approximation method? (Note: The symbol ≈ means is approximately equal : to.)

Given right triangle ABC below, how many units long is BC ?

Ona real number line, point S has coordinate -5 and point T has coordinate -7. What is the coordinate of the midpoint of ST ?