MATH - Questions for Exams 1 and 2
Complete the task below describing the right and left graphs. *2 different pictures next to each other!* Note: m1 relates to line l1 and m2 relates to line l2 m3 relates to line l3 and m4 relates to line l4
1. l1 and l2 are parallel 2. l3 is perpendicular to l4 3. m1 is = to m2 4. l1 and l2 form no angle 5. m3 * m4 is -1 6. l3 and l4 form a right angle
Compute the standard deviation of the following amounts of rainfall given in the sample below. *Picture* Months | Rainfall in Inches 1 | 3 2 | 3.5 3 | 4.5 4 | 4 5 | 4.9 6 | 6.7 7 | 6.9 8 | 7.3 9 | 4.7 10| 4.6 11 | 4.8 12 | 3.5
1.4
Find the product and write the answer in standard form. (6+i)(2-5i)
17 - 28i
Solve the following exponential decay problem using the exponential growth and decay function (y = y_0 (e^kt). If 600 pounds of a radioactive substance are present initially and 2 years later only 400 pounds remain, how much of the substance will be present after 6 years?
178 pounds
A bucket contains 4 red balls, 3 white balls, 6 blue balls, and 5 yellow balls. If one ball is picked at random from the container, what is the probability that it will be yellow?
5/18
Read the stimulus material below that relates to the question that follows. Two airplanes are spotted on a radar map located at the coordinates (sqrt(2), -sqrt(5)) and (3sqrt(2), 5sqrt(5)). Assume the planes are flying in exactly the same direction. The plane behind is flying at 1050mph and at an altitude 2500ft., and the other plane is flying at 850mph and at an altitude of 3500ft. As the air traffic controller, you are given the task to determine how many miles it will take for the plane behind to be directly below the plane flying at 3500ft.
71.925 miles
Select all of the triangles that match the SAS theorem of triangle congruency. *PICTURES of sets of 2 triangles* set a, b, c, d, e, f, g, h, i
A, F, G
Use the information below to answer the two questions that follow. At a school district's ag farm, all newborn pigs and calves are weighed and their weight recorded. Assume that an equal number of pigs and calves have been weighed so far for the year, which distribution would best describe the weights of these baby animals?
Bar graph that looks similar to this: | | | | | | | | | | | | | | | | | | ----------------------
Determine the best choice to assess each student's comprehension of a concept. A. Quiz B. Clickers C. Group Work D. Both A and B
Both A and B
Which of the following concepts or procedures best describes how to find the following retail solution? A $100 pair of shoes is on sale for 25% off. The department store offers a one day special on Saturday; taking an additional 20% off. What is the price of the shoes if purchased on Saturday?
Composition of functions
The geometric example below represents which algebraic property? S=square T=Triangle 3(S+T)=SSSTTT
Distributive
Integers are not closed under which operation.
Division
Determine the correct choice of the mathematician(s) that proved two well known theorems: the Pythagorean theorem and that the sum of the angles of a triangle is 180 degrees.
Euclid
Which measure of central tendency is most sensitive to extreme values?
Mean
Given: L = sqrt(2) M = 3sqrt(3) N = sqrt(16) P = sqrt(9)
N + P
Given: -MK_|_-JL, -LP_|_-JM, -JK~=-JP Prove: (triangle)JMK ~= (triangle)JLP *PICTURE* -2 right triangle overlapping -2 congruent lines next to K and P -values are K=1 and P=2 Statement: 1. -MK_|_-JL, -LP_|_-JM 2. Angles 1 and 2 are right angles 3. <1 ~= <2 4. -JK ~= -JP 5. <J ~= <J 6. (triangle)JMK ~= (triangle)JLP
Reason: 1. Given 2. Perpendicular lines intersect to form right angle. 3. All right angles are congruent. 4. Given. 5. Reflexive property of congruency. 6. ASA postulate.
Determine the answer below that best describes the symmetry of the graph of y=x^3.
The graph is symmetric with respect to the origin.
Which choice best describes an explanation a teacher could give a student to help him/her judge the reasonableness of the solution in the following scenario. Evaluate: -7 - 12 The student gives an answer of 5.
Think of your checking account being overdrawn by $7 and you write another check for $12. How much would be in your checking account?
Percentiles are commonly used to describe the measure of position rather than the measures of central tendency such as in standardize test scores. A student makes 530 on the Scholastic Aptitude Test (SAT) and the score is reported to be in the 79th percentile. Determine the choice that best describes what this means.
This student scored better than 79% of all the others taking the test.
is the method of obtaining the correct number of significant digits for any number without changing the last digit. For example, if a teacher asked for pi to be written to the ten-thousandths place using this method, the result would be 3.1415.
Truncation
Perform the following transformation by scalar multiplication. -3 [ 0 1] [ 4 5]
[ 0 -3 ] [-12 -15 ]
Given the following set of data, predict the correlation coefficient. {(1, 2), (2, 4), (3, 4), (4, 5), (5, 8), (6, 9)}
close to 1
Determine the equation of the translation. *2 GRAPHS* Figures look like this for f(x) and g(x): ---- | --|
g(x) = (x-5) + 3
Three coins are tossed. Determine the correct probability distribution of the number of tails appearing on each toss of the 3 coins.
x | 0 | 1 | 2 | 3 D| 1/8 | 3/8 | 3/8 | 1/8
Select all that apply for describing the circle below. *PICTURE* -A circle with a diameter = 4
x^2 + y^2 - 8x - 6y +21 = 0 (x-4)^2 + (y-3)^2 = 4 Center (4,3) and radius = 2
An investment of $1000 at 4% compounded semi-annually is made for 10 years. Using the formula A = P(1 + r/n)^tn where P = dollars deposited, r = annual rate, n = periods of compounding per year, A = total dollars in account, and t = years; calculate the interest earned in the second compounding period.
$20.40
Determine the solution set of x^2 - 3x >= 10.
(-inf, -2] U [5, inf)
What is the quotient of Z1/Z2? Z1= (12,60 degrees) Z2= (6,15 degrees)
(2, 45 degrees)
Which equation has the same solution as x^2 - 6x -12 = 0?
(x-3)^2 = 21
A ninth-grade class is doing a lesson on synthetic division today. Their teacher asks them to use synthetic division to perform the division. (x^5 + 9x^4 - 2x^2 + 19x - 5)/(x-3) As the teacher walks around the room checking for proper setup of the problem, she discovers that one student has the following. Which number is incorrect? -3 | 1 9 0 -2 19 -5 L______________________________________
-3
Find the determinant of the following 2x2 matrix. [ 0 1] [ 4 5]
-4
Use a graphing calculator to find the relative minimum of the function f(x) = 4x^3 + 6x^2 - 10x - 3 on the interval [-10, 10].
-6.021
Using mathematical probability, what is the range of a situation where it is impossible for an event to occur, to absolutely certainly that the event will occur?
0 to 1.
At Leslie's beauty shop, she has found that a customer will want a color with a probability of 0.53, a haircut with a probability of 0.4, and both with a probability of 0.17. What is the probability that a customer will require a color and not a hair cut?
0.36
What is the probability of getting at least two tails in tossing three coins?
0.5
Now, determine the value for each of the trigonometric functions listed below using a calculator when needed. Consider which choice below is most accurate: sin 30 degrees, sin 45 degrees, sin 60 degrees, and sin 80 degrees
0.5, sqrt(2)/2, sqrt(3)/2, 0.985
Match the phrase to the correct logical statement. 1. Converse, q -> p 2. Inverse, ~p -> ~q 3. Contrapositive, ~q -> ~p 4. Biconditional, p <-> q
1. Interchange p and q. If q, then p. 2. Negate both p and q. If not p, then not q. 3. Interchange and negate p and q. If not q, then not p. 4. Connect p and q with "if and only if". p if and only if q.
What is the probability that both a couple's last two children will be girls?
1/4
Use the entry box given to answer the question below. Please use the format "N (operator) N = N". Use the f(x) to enter a numerical value, formula, or equation. Use the omega symbol to enter special characters that do not appear in the formula feature. (Do not type directly into the box unless directed.) Translate the following scenario into an equation: Mario has a job at a pet-sitting business that he works after school, at which he earns approximately $125 a week. He needs new lashes, pet toys, and clothes so that he can walk the dogs. If he spends $55 on the clothes, how many leashes, at $10 each, and pet toys, at $5.50, can he purchase?
10l + 5.5t = 70
A city in North America located on latitude 49 degrees N and a city in South America located on latitude 55 degrees S lie on the same north-south line, thus having the same longitude. Use 6400km for the earth's radius. Find the distance between the two cities.
11,617 km
Use the information below to answer the three questions that follow. Two airplanes are spotted on a radar map located at the coordinates (sqrt(2), -sqrt(5)) and (3sqrt(2), 5sqrt(5)). Determine the distance the airplanes are apart using a calculator to state your answer in decimal form to the nearest hundreds. Assume the coordinates are given so that the distance is in units of miles.
13.71 miles
Now, calculate the difference in the areas under the two curves f(x) = sqrt(x) and f(x) = ^4 sqrt(x) between x=0 to x=16.
17.07
Find the length of the minor axis of x^2 + 16y^2 = 16.
2
Find the difference and write the answer in standard form. (4+i) - (2-3i)
2+4i
A ball is thrown into the air from the edge of a 48-foot-high cliff so that is eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds. *GRAPH* starts at 48 and curves up till (2.5,14?), then down, landing on 5.5. For which interval is the ball's height always decreasing?
2.5 < x < 5.5
Which of the following represents the prime factorization of 5616?
2^4 * 3^3 *13
Given that a circle is inscribed within a square and a smaller square is inscribed within the circle. Determine the range between the upper and lower bounds of the area of the circle. *PICTURE* A small square within a circle and a circle within a large square.
2r^2 < area of circle < 4r^2
Read the stimulus material below that relates to the question that follows. Two airplanes are spotted on a radar map located at the coordinates (sqrt(2), -sqrt(5)) and (3sqrt(2), 5sqrt(5)). Assume the planes are flying in exactly the same direction. Now as the air traffic controller, you are given the task to determine how many minutes it will take for the plane behind to be directly below the plane flying at 3500ft.
4.11 minutes
Find the mean of rainfall for 2011. *Picture* Months | Rainfall in Inches 1 | 3 2 | 3.5 3 | 4.5 4 | 4 5 | 4.9 6 | 6.7 7 | 6.9 8 | 7.3 9 | 4.7 10 | 4.6 11 | 4.8 12 | 3.5
4.87
Now solve the following problem. Notice the difference in this problem and the previous problem. The previous problem is of the format log_b x = log_b y whereas this problem is in the format y = log_b x. Solve for x. log_10 (x+2) - log_10 (x-1) = 1
4/3
The city of Austin needs to know the distance across a pond of water after a large rain. They hire a surveyor to calculate the distance. The surveyor sets his equipment up due east of the pond at point B with measure of angle B being 35*20'. He measures the length from A to B which is 59.1 yd. ( * means degrees) Given this information find the length of AC(the pond) using a graphic calculator. -PICTURE of triangle in pond.
41.9 yd
Find the area of a regular octagon stop sign that has side lengths of 10 inches. *PICTURE of octagon with a side of length = 10
482. 8 in^2
Given the recursive function defined by f(2) = 1 f(3) = 2 f(n) = f(n-2) + f(n-1) for n>=3 What is the value of f(5)?
5
These two triangles are similar. Determine which statement is not true in using ratios for the proportions. *PICTURE of two similar triangles(right)* SIDES: -Bigger triangle: 3, x, 5 -Small triangle: y, 1.5, 4
5/4 with 1.5/x
Cherry harvest in James' orchard follows a particular pattern of producing pounds of good quality cherries per day. The number of pounds F of quality cherries harvested x days after the harvest begins is given by F(x) = -22.68(x-22)^2 + 10977.12, where 0 < x < 22. At what rate, in pounds per day, are the cherries being harvested 10 days after the start of harvest?
544.32
Compute the varience of the age of the fathers of the 11 basketball team members of a freshman team. 31, 42, 38, 34, 37, 38, 60, 37, 39, 47, 49
60.45
The city of Austin needs to know the distance across a pond of water after a large rain. They hire a surveyor to calculate the distance. The surveyor sets his equipment up due east of the pond at point B with measure of angle B being 35*20'. He measures the length from A to B which is 59.1 yd. Find the length of BC using a graphic calculator. ( * means degrees) -PICTURE of triangle in pond.
72.45 yd
What is the mean of the following grades for a math test? 45 85 95 83 82 76 76 92
79.25
Determine the answer that does not correctly identify the ray starting at C and going through A. *PICTURE looks similar* | | --|----|-----|-----------|-- Z A B C
<--CA
The graph y = f(x) is shown below. *GRAPH* Points: A: (2, 0) B: (0, 2) C: (-2, 0) D: (-1, -2) Which point could be used to find f(2)?
A
Determine the operation that is NOT true with matrices.
AB=BA
Which of the following would be the least effective approach in teaching a lesson of algebra?
After a lecture-based instructional teaching model, have students complete a worksheet on the topic before leaving class.
Determine the statement below that is NOT true.
All quadrilaterals are parallelograms.
Determine which, if any, of the graphs below are discontinuous. Graph 1 has a closed and open circle/point. Graph 2 has two open points.
Both 1 and 2
Before a quiz can be given on finding the center of the following circle x^2 + 6x + y^2 + 8y = -9 , what concept must be taught?
Completing the square
Grab the correct answer and drag it to the appropriate response box. For a deck of cards: Let^A = spades Let^B = hearts 1. Key Word associated with union and intersection: 2. Symbol: 3. Symbolical: 4. Venn Diagram:
Describe the union of these sets: 1. 'or' 2. C 3. A C B 4. Both circles shaded, including middle. Describe the intersection of these sets: 1. 'and' 2. E' 3. (A E' B) 4. Only middle shaded in A&B(circles)
We realize that if we toss a "fair con" twice, it may not land heads up exactly once. However intuitively, we are pretty sure that the probability of this fair coin landing heads up is 1/2 if it is tossed many times. Determine the choice below that does not relate to this scenario.
Descriptive statistics
The table below represents the function F. x | 3 | 4 | 6 | 7 | 8 F(x) | 9 | 17 | 65 | 129 | 257
F(x) = 2^x + 1.
A student uses the following two t-charts to develop a graph of perpendicular lines using the line chart function in Excel. *Chart* X | Y | Y | | -2 | -2 | 11.5 1 | 5 | 10 3 | 9 | 9 5 | 13 | 8 The student is confused when the graph looks like the following and the lines do not appear perpendicular. *GRAPH with green and yellow line intersecting* As a teacher, you will need to help the student use critical thinking to understand why their graph does not look like the lines are perpendicular. The student has informed you that she has checked her t-charts and know that their values are correct for the two perpendicular lines y = 2x + 3 and y = -1/2x + 21/2. Which choice below will inspire the most critical thinking?
First suggest the student look at the graph and ask "Do you see anything that might change the shape of the angle where the two lines cross?" If the student needs more input after having some time to observe, suggest she look at the scale of the x and y-axis.
A teacher gives her class the following project to work during a class period. She explains the problem requires several steps and asks the class to support their answers by checking them in a way other than just giving the answers derived from the formulas. She takes her class to the computer lab, so they can also use other means of technology as well as their calculators. Problem: A bridge for bike riders and pedestrians is built over the Concho River that goes through downtown San Angelo Texas where the river bottom is V-shaped. If the supports are 2 feet long at each end, the center support is 401 feet long, and the supports increase in length by 3 feet with each support going from 2 feet to 401 feet, what is the total length of all the supports? The students can first use the formula for calculating the nth term of an arithmetic sequence [a_n = a_1 + (n-1)d] to calculate the value for n. If n is miscalculated the rest of the answers will be incorrect even if the students use the correct processes. Next the students can use the formula to calculate the sum of the first n terms of an arithmetic sequence [ S_n = n/2 (a_1 + a_n)] once with the value for n, and again for n - 1. The teacher wants the grade for this project to reflect different levels of performance of arithmetic skills, well-defined processes in solving the problem and checking the answer, use of quantitative language in writing that supports their answers, and their applications of the mathematics to the real-world problem. What method of assessment would be best for this project?
Form a rubric using the different items to be evaluated for the columns of the rubric and rows progressing with levels (1 to 4) of understanding and predetermined points associated with each level of understanding. With the rubric, students can get full credit for calculating the sum of the first n terms as long as the sum is correct with the n-value they use.
A parked oil barge off the Atlantic Coast is leaking oil. The oil is spreading over the water's surface in the shape of a circle. At any time t, in minutes after the start of the leak, the radius of the oil slick is r(f) = 4t feet. Let A(r) = p r^2. The following table was created using the composition of functions method (A o r)(f) = A(r(f)) to solve for A at t. t | r(t) | A(r) ------------------------------ 1 | 4 | 50.265 3 | 12 | 452.389 9 | 26 | 4071.504 27 | 108 | 36643.537 81 | 324 | 329791.830 Which method below could also be used to find A(r) for t = {1, 3, 9, 27, 81}?
Geometric sequence with a ratio of 9.
If f(x) = 1/3x + 9, which statement is always true?
If x>0, then f(x)>0.
Determine the intervals of increase and decrease of the function. *PICTURE of graph curving at x = 2.
Interval of increase (2, inf). Interval of decrease (-inf, 2].
In mathematical reasoning. <-> (If and only if), -> (If-then), v (OR), ^ (AND) are all symbolic representations of the relationship between the first part of the logic statement (p) and the second (q). Match the correct words and rules to the appropriate logical statements. Logic Rules: 1. Conjunction, p ^ q 2. Disjunction, p v q 3. Conditional, p -> q 4. Biconditional, p <-> q
Logical Statements: 1. True when p and q are both true. 2. True when p is true, or q is true, or both are true. 3. Always true except when p is true and q is false. 4. True when p and q have the same truth values.
Determine the choice below that is not a truth of the comparison of Euclidean, elliptical, and hyperbolic geometry.
Many theorems hold true for all three geometries such as the theorem concerning the sum of the measures of the angles of a triangle.
Mr. Wilson and his eighth graders are learning about congruent triangles and how congruency relates to angles of triangles. Drag and drop the triangles to show which ones are congruent.
Match similar triangles
Determine the recursive definition of the Fibonacci sequence. {1, 1, 2, 3, 5, 8, 13, 21,...}
N_i = N_(i-1) + N(i-2)
Which of the following approaches and initiatives used by a math teacher will best assist with planning, delivery, and reevaluating instruction to ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics?
Observing, listening to and gathering other information about the students to assess what they are learning.
Which of the following is a reflection the teacher of mathematics should engage to ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics?
Observing, listening to and gathering other information about the students to assess what they are learning.
The zeros to the following graph are ________ numbers. *Graph* -It curves around (1.5, -1)
Rational or irrational
Given that ABCD is a parallelogram. Prove: KM x LB = LM x KD. *PICTURE* Statement: 1. (parallelogram)ABCD 2. AD||BC 3. (triangle)KMD ~ (triangle)LMB 4. <1~= <2 ; <3 ~= <4. 5. KM x LB = LM x KD
Reason: 1. Given 2. Opposite sides of a parallelogram are parallel. 3. If two lines are parallel, then their alternate interior angles are congruent. 4. AA Theorem 5. The lengths of corresponding sides of similar triangles are in proportion. 6. In a proportion, the product of the means equals the product of the extremes.
What type of distribution would be expected using a histogram to represent the outcomes from rolling a die 300 times?
Rectangular Distribution
What graph technique is used to describe the difference in the graphs of y=x^2 and y=-x^2?
Reflection
If a circle is inscribed in a regular shaped polygon and a smaller regular shaped polygon of the same number of sides is inscribed within the circle resulting in the circle being squeezed between the two polygons, the perimeters of these polygons can serve as the upper and lower bounds in approximating the circumference of the circle. Which set of polygons will result in the narrowest range between the two bounds?
Regular decagon
Use the information below to answer the two questions that follow. Use a graphing calculator to determine how the difference of the area changes under the curves of f(x) = sqrt(x) and f(x) = ^4 sqrt(x) as x goes to infinity.
The difference in the two areas increases.
Divide 0.0000081/27,000,000 without using a calculator.
The easiest method to divide this is to change both numbers to scientific notation. This would result in 8.1x10^(-6)/2.7x10^(7). Answer is 3x10^(-13).
Using the parabola y = 2(x-3)^2 - 6, explain the transformation process from the basic formula of a parabola y = x^2.
The parabola is shifted three units to the right and down six units.
Now, determine the choice that does relate to the following. 10x + 5 = 85
The variable x has one specific value.
Given ax^(2)+bx+c=0. If the discriminant sqrt(b^(2)-4ac)) is negative, which of the following is true?
There are two nonreal, complex solutions.
Using the Present Value Formula, students have calculated a house payment for a loan set up on an annuity. The principle is $127,000 and the monthly payments are $583.56. The students want to know how much interest, over the period of the note (30 years), will accrue. They decide the first step is to calculate the total amount to be invested in the house. For this, they determine the following equation should be used. Payment amount x Number of payments = Total amount invested What should the next step of the algorithm be?
Total amount invested - Principle
In teaching a lesson for the first time on decay function models using the formula [y = y_0 (e^kt)] where y_0 is the amount present at any time t, students are having a hard time understanding how to find the y_0 in the problem given below. They understand that it seems like it would be 700, but are confused at how to derive 700 from the formula. Problem: If 700 grams of a radioactive substance are present initially and 2 years later only 550 grams remain, how much of the substance will be present after 4 years? Which choice below would not be a good approach for the teacher to handle this learning situation if the teacher is trying to stress critical thinking?
Work through an example of this problem with the class changing the numerical values in this problem to other numbers.
Find the sum. [1 2] + [ 9 6] [3 4] [ 7 8]
[ 10 8] [ 10 12]
Find the product. [2 3] [ 1 3 5] [4 6] [ 2 6 7]
[ 8 24 31] [ 16 48 62]
Find the inverse of the following 2x2 matrix. [1 2] [-4 5]
[5/13 -2/13] [4/13 1/13]
Which of the following is NOT associated with the commutative property?
a+(b+c) = (a+b)+c
Which triangle pairs below represent theorems of congruent triangles that include two or more angles? *PICTURES of sets of 2 triangles* set a, b, c, d, e, f, g, h, i
b, d, h
This theorem states that if you have a population with mean "u" and standard deviation "s" and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min (np, n(1-p)) > 5, where n is the sample size and p is the probability of success in the population. What is this theorem?
central limit theorem
Given a line y=x + 1, the slope of this line is one. Also, given dots that form a straight line but do not have a slope of 1, what will the correlation coefficient (r) be for the dots? Determine the best choice. *PICTURE of graph with a straight line (y=x+1) and another dotted line underneath going straight.
exactly 1
The table below shows the average yearly balance in a savings account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited. *Picture* Year: | Balance, in Dollars 0 | 380.00 10 | 562.49 20 | 832.63 30 | 1232.49 40 | 1824.39 50 | 2700.54 Which type of function best function best models the given data?
exponential growth function
Use the entry box given to answer the question below. Use the f(x) to enter a numerical value, formula, or equation. Use the omega symbol to enter special characters that do not appear in the formula feature. (Do not type directly into the box unless directed.) The function f(x) = 3x^2 + 12x + 11 can be written in the vertex form as --
f(x) = 3(x+2)^2 -1
Determine the most correct description of the following figure. *picture* f(x) g(x) 1 <-------> 4 2 <-------> 8 6 <-------> 8 3 <-------> 9 5 <-------> 7
f(x) is a function.
Find the inverse of the function f(x) = (x+2)/(x-1).
f^(-1)(x) = (x+2)/(x-1)
Find the inverse of the function f(x) = 3x + 2.
f^-1 (x) = (x-2)/3
Workers at a local factory make $8, $10, or $12.50 per hour. Each receives a $50 weekly gas allowance. Let h = hours and r = rate. Which expression can be used to represent the grass weekly pay of each individual?
hr + 50
Solve the following logarithmic equation. log_3 (4x-3) - log_3 (4) = log_3 (2x-1)
no solution
In finding the values of the trigonometric functions listed below, determine the one that would be the hardest to determine without a calculator.
sin 80 degrees
Use the information below to answer the two questions that follow. In finding the values of the trigonometric functions listed below, determine the one that would be the hardest to determine without a calculator.
sin 80 degrees
Use the information below to answer the two questions that follow. Determine the choice that does not relate to the following: 10x + 5
solve for the value of x
Which of the following expressions is the length of the diagonal of the rectangle in the figure below in terms of L and W? *PICTURE* -A rectangle with a diagonal line crossing from up-left to down-right. -L on top & W on right side
sqrt(L^2 + W^2)
In the following function, the vertical asymptotes are x= -1 and x= 5. f(x) = (x^2 - x - 6)/(x^2 - 4x - 5) Complete the following sentence. The graph of this rational function________.
will never intercept the vertical asymptotes.
Use the following below to answer the two questions that follow. Solve for x. log_b x=3/2 log_b 16 - 2/3 log_b 8
x = 16
Determine the axis of symmetry. *PICTURE of graph curving downward at x=2.
x = 2
What is the geometric representation of x and y? *PICTURE of graph* <| right triangle with: -Hypothenuse = r -Angle below 'r' is theta '0' -Corner upright of 'r' is 5 + 3i
x = r cos '0', y = r sin '0'
Use the List-function on a graphing calculator to enter the list of date. Use the regression features of the calculator to determine the curve of best fit. *Picture* Months | Rainfall in Inches 1 | 3 2 | 3.5 3 | 4.5 4 | 4 5 | 4.9 6 | 6.7 7 | 6.9 8 | 7.3 9 | 4.7 10| 4.6 11 | 4.8 12 | 3.5
y = -0.1x^2 + 1.411x + 1.155
Determine the system of inequalities for the following graph. *GRAPH* -Shaded region in inside the triangle created by an abs. value and a straight line.
y >= |x - 2| + 2 y < 2/3x + 4
A teacher begins a new lesson on absolute value. He works the following three problems with the students in class. |3x + 2| = 9 |3x - 4| <=10 |7x + 9| > 16 The in-class assignment has three more problems with the same type of problems, but different numerical values. Next, he gives the students an absolute value problem as a quiz for the day. Which problem below would not be consistent with what has been taught?
|2x + 9| > -2
