For a certain rectangular region, the ratio of its length to its width is 35 to 10. If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?
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Square P has a side length of x inches. Square Q has a perimeter that is 176 inches greater than the perimeter of square P. The function f gives the area of square Q, in square inches. Which of the following defines f?
(14 x)/(7 y) = 2 w + 19 The given equation relates the distinct positive real numbers w, x, and y. Which equation correctly expresses w in terms of x and y? f
What percentage of 300 is 75?
Point O is the center of a circle. The measure of arc RS on this circle is 100°. What is the measure, in ROS degrees, of its associated angle?
5 The expression 6^5 3 x^45 ·^8 2^8 x is equivalent to ax^b, > 1 where a and b are positive constants and x. What is the value of a + b?
A right triangle has sides of length 2 2, 6 2, and 80 units. What is the area of the triangle, in square units?
4x^2 + − 45 The expression bx, where b is a constant, can be rewritten as (hx + k)(x + j), where h, k, and j are integer constants. Which of the following must be an integer?
y = 2x^2 − 21x+ 64 y = 3x+ a In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point, (x,y),inthex y-plane. What is the value of x?
An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?
In the xy-plane, a parabola has vertex (9, −14) and intersects the x-axis at two points. If the equation of the parabola is written in the form y = ax^2 + bx+ c, where a, b, and c are constants, which of the following could be the value of a+b+c?
f(x) Function f is defined by = −a^x + b, where a and b are constants. In the xy-plane, the graph of ⎛ ⎞ f(x) ⎜ ⎟ y = − 15 has a y-intercept at ⎜ 0, − ⎟. The ⎝ 99/7 ⎠⎟ product of a and b is 65/7. What is the value of a?
- (x^2)/25 = 36 What is a solution to the given equation?
3 more than 8 times a number x is equal to 83. Which equation represents this situation? (3)(8)x
Hana deposited a fixed amount into her bank f(t)= account each month. The function 100 + 25 t gives the amount, in dollars, in Hana’s bank account after t monthly deposits. What is the best interpretation of 25 in this context?
A customer spent $27 to purchase oranges at $3 per pound. How many pounds of oranges did the customer purchase?
Nasir bought 9 storage bins that were each the same price. He used a coupon for $63 off the entire purchase. The cost for the entire purchase after using the coupon was $27. What was the original price, in dollars, for 1 storage bin?
x f(x) 0 2 9 1 3 2 2 3 5 For the linear function f, the table shows three values f(x) of x and their corresponding values of. Which f(x) equation defines? f(x)
Q S~: P ___....._.R Note: Figures not drawn to scale. Right triangles PQR and STU are similar, where P corresponds to S. If the measure of angle Q is 18°, what is the measure of angle S?
The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999. I \ I '\ I / I ' ' - Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?
- To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49, with an associated margin of error of 0.04. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?
- A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of 500 pounds if each box weighs 120 pounds?
- −4x^2 −7x = −36 What is the positive solution to the given equation?
- The table summarizes the distribution of color and shape for 100 tiles of equal area. Red Blue Yellow Total Square 10 20 25 55 Pentagon 20 10 15 45 I I I I I I Total 30 30 40 100 If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.) -
- f(x) = 2x +3 () For the given function f, the graph of y = f x in the xy -plane is parallel to line j. What is the slope of line j?