A scale model, where 1 coordinate unit represents 1 mile, is drawn in the standard (x,y) coordinate plane. Angelo’s house is at (4,−3) , Ella’s house is at (4,7) , Troy’s house is at (−2,7) , and Yoko’s house is at (−2,−3) . Which of the following is closest to the area, in square miles, of the rectangle whose vertices are the real locations of the 4 houses?
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Let the function f be defined as f (x) = −9 x . In the standard (x,y) coordinate plane, the graph of y = f (x) undergoes a transformation such that the result is the graph of y = f (x) − 4 . Under this transformation the graph of y = f (x) is:
Which of the following expressions equals the height, in feet, of the tree shown? ? 40° 18 feet
As shown, the number line between 0 and 8 is divided into 6 segments of equal length by points A through E . _ Which of the following statements about √ 8 is true? 0 A B C D E 8 _
Deon often flies his kite. He can only fly his kite on days with wind. He does not fly his kite on every day with wind. For any given day, let Event A be that there is wind and let Event B be that Deon flies his kite. Which of the following values can P (A and B) be?
Whenever is defined, it is equivalent to: 3 2 x − x − 6x
The roots of a polynomial equation are 0 , 2 , and −5 . Which of the following is a factored form of the equation?
If = , then = ? x + y 8 y _ 2
Let the slope of 3x + 2y = 5 be m 1 , and the slope of x + 4y = 7 be m 2 . Which of the following is true?
The piecewise functions f and g are given. − x for x < 0 f (x) = { 1 − x for x ≥ 0 ⎪x⎪ + 7 for x ≤ −1 g (x) = { x − 3 for x > −1 What is the value of f (g ( − 1) ) ?
Let f be defined by f ( x ) = 4x + 7 . Let g be defined by g ( x ) = −2 x + 11x + 1 . The graphs of y = f ( x ) and y = g ( x ) intersect at one of the following ( x,y ) points. Which one?
A tourism organization randomly selected 100 tourists finishing their summer visit to Spain. The organization asked them how many cities they had toured in the country. The table shows the results. Based on these data, for the population of tourists that visited Spain during the summer, what is the best estimate of the mean number of cities toured? Number of cities 1 2 3 Number of tourists 10 40 50
Given that i is the imaginary unit, which of the following numbers is equal to (7 + 4i) ?
The product of 2 complex numbers, x and y , is a real number that is irrational. Which of the following statements cannot be true?
The real solution of the equation 3 e = 12 is:
The figure shows nABC , a right isosceles triangle, inscribed in a circle with center O and radius 10 cm. ⏜ What is the length, in centimeters, of arc A B shown as the thick curved line? A B 10 cm O C
It took Sam x minutes to bike the d miles from home to work. Returning home on the same route, it took Sam y minutes. On the way home his average speed was 2 times his average speed on the way to work. Which of the following equations gives y in terms of x ? _ x
The hyperbolas − = 1 and − = 1 are graphed 9 4 36 25 in the standard (x,y) coordinate plane. Which of the following equations is an ellipse that intersects all 4 vertices of the hyperbolas? y x O _ x 2 _ y
Given that f (x) = √ 2x − 1 , which of the following −1 expressions is the inverse function, f (x) ? _ 1
In the Venn diagram, circles S, C, and P represent farms raising sheep, cows, and pigs, respectively. How many of the 47 farms represented in the diagram do not raise cows?
Figure 1
The image is a Venn diagram of 3 intersecting circles. The top left circle is labeled S, 12. The top right circle is labeled C, 10. The bottom middle circle is labeled P, 5. Where only circles S and C overlap is labeled 13. Where only circles C and P overlap is labeled 4. Where only circles P and S overlap is labeled 2. Where all 3 circles overlap is labeled 1.
×In rectangle ABCD shown, segments line segment B E and line segment CE partition the rectangle into 3 triangles. Given DE=7 centimeters, BE=26 centimeters, and CE=25 centimeters, what is the length, in centimeters, of line segment BC?
Figure 1
The image is a rectangle labeled, clockwise from the top left, A, B, C, D, and E. Line segment DE is labeled 7, line segment BE is labeled 26, and line segment CE is labeled 25.
× Which of the following diagrams best shows the location of the basal cavity as described by Student 3?