• What should the exponent of the variable b be in Marina’s simplified expression \(-\frac{1}{2}a^4b\) after simplifying the expression \(\frac{-4a^{-2}b^4}{8a^{-6}b^{-3}}\), assuming that \(a \neq 0\) and \(b \neq 0\)?
• Using the words from the word list, name all the parts of an isosceles triangle. Some words may be used more than once.
• Naoya read a book cover to cover in a single session at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let P(t) denote the number of pages left to read as a function of time t (measured in hours). What is the formula for this function?
• What are the expected total number of orange candies and the standard deviation for the total number of orange candies in two independent samples of size 25 each, one from dynamite mints candies, where 10% are orange, and the other from holiday mints candies, where 45% are orange?
• Which statement describes whether there is an extraneous solution to the equation x – 3 = x – 5? A. There are no solutions to the equation, B. The extraneous solution is x = 7, C. The valid solutions are x = 7 and x = 4, or D. The extraneous solution is x = 4.
• In rectangle JKLM, with m‚à†KJM = m‚à†KLM = 90¬∞ and m‚à†KJC + m‚à†MLC, which reason justifies the statement that m‚à†KLC is complementary to m‚à†KJC? 1) Angles that are congruent are complementary to the same angle. 2) Angles that are congruent are supplementary to the same angle. 3) All angles in a rectangle are right angles. 4) Complementary angles are always congruent.
• What do the properties of polynomial addition mean? Complete each statement: The closure property states that the sum of two polynomials is a ___. The commutative property states that changing the order of two or more terms does not change the value of the sum. The associative property states that the way in which two or more terms are grouped in a sum does not change the value.
• Dan uses a compass to draw an arc from point Q, as shown. He wants to construct a line segment through point R that makes the same angle with line segment QR as line segment PQ. Which figure shows the next step to construct a congruent angle at R? Refer to charts 2, 3, 4, and 5.
• A company manufactures video games with a current defect rate of 0.95%. To minimize the number of defective video games delivered, they test each game before delivery. The test is 98% accurate in identifying defective video games. If 100,000 products are manufactured and delivered in a month, approximately how many defective products are expected to be delivered?
• Which graph exhibits the same end behavior as the graph of f(x) = 2x^6 – 2x^2 – 5?
• How does your prediction compare with the total number of pennies in Row 1? How would you adjust your estimate based on this comparison, and were you surprised by the result?
• Which expression is equivalent to the given image mc003-1.jpg?
• Construct the line perpendicular to line segment NO at point P.
• How much longer is the side of a cube with a surface area of 1,200 square inches compared to a cube with a surface area of 768 square inches, given that the formula s = SA/6 squared gives the length of the side, s?
• In an isosceles triangle, two sides of equal length, denoted as a, are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters, which can be represented by the equation 2a + b = 15.7. If one of the longer sides measures 6.3 centimeters, what is the length of the base?
• The descriptive statistics are provided. Analyze the misleading graphs and reports by comparing the measures. What do these measures indicate about the shape of the box-and-whisker plot?
• The scatter plot below shows the number of pizzas sold during weeks when different numbers of coupons were issued. The equation representing the linear model for this data is y = 3.4x + 43. According to the model, how many pizzas will be sold nightly if 15 coupons are issued? Please enter your answer in the box.
• Which of the following statements is true regarding Tim’s situation with the rental car? a. It would be cheaper to refuel the car and return it a day late. b. It would be cheaper to return the car on time and pay the refueling costs. c. It would cost about the same to return the car on time without gas or one day late with gas. d. Tim is not responsible for refueling the car when he returns it.
• The noise in a quiet room is 500 times more intense than the threshold of hearing. What is the decibel measurement for this quiet room?
• What are the x- and y-coordinates of point P on the directed line segment from point A to point B, such that P is located at a specific distance along the line segment? The coordinates of A are (2, -1) and the coordinates of B are (4, -3).
• The area of a rectangle is (x^4 + 4x^3 + 3x^2 – 4x – 4), and the length of the rectangle is (x^3 + 5x^2 + 8x + 4). If the area equals the length multiplied by the width, what is the width of the rectangle?
• Solve the linear equation: 3.4 + 2(9.7 – 4.8x) = 61.2. What are the possible steps involved in solving this equation? Check all that apply: 1. Add 3.4 and 2. 2. Distribute 2 to 9.7 and -4.8x. 3. Combine 3.4 and 19.4. 4. Divide both sides by 22.8. 5. Subtract 22.8 from both sides. 6. Divide both sides by 9.6.
• Given the information T _ _ V; ST || UV, prove that TU || VW by completing the two-column proof.
• How are the functions f(x) = 16x and g(x) = 16(1/2)x related? Are the output values of g(x) one-half, one-quarter, the square root, or the square of the output values of f(x) for the same value of x?
• Which statement explains why triangle ABC is congruent to triangle A’B’C’? You can map triangle ABC onto triangle A’B’C’ by reflecting it across the line y = x and rotating it 90 degrees counterclockwise about the origin, which is a sequence of rigid motions. You can map triangle ABC onto triangle A’B’C’ by reflecting it across the x-axis and then across the y-axis, which is a sequence of rigid motions. You can map triangle ABC onto triangle A’B’C’ by translating it 2 units up and reflecting it across the y-axis, which is a sequence of rigid motions. You can map triangle ABC onto triangle A’B’C’ by translating it 6 units left and reflecting it over the x-axis, which is a sequence of rigid motions. Triangle ABC has vertices A(1, -3), B(5, 3), and C(4, -1). Triangle A’B’C’ has vertices A'(-5, 3), B'(-1, -3), and C'(-2, 1).
• A student wants to check six websites: four social and two school-related. After checking two sites, she has to leave for school. What is the approximate probability that she checked a social website first and then a school-related website? Options: 0.042, 0.267, 0.533, 0.667.
• Evaluate the function g(x) = -2x^2 + 3x – 5 for the input values -2, 0, and 3. What are the values of g(-2), g(0), and g(3)?
• How does unemployment negatively impact an economy? Check all that apply: – Unemployed individuals typically buy fewer goods and services. – Unemployed individuals may struggle to repay their loans. – Unemployed individuals are often not actively seeking employment. – Unemployed individuals do not have increased buying power. – Unemployed individuals may need to adjust their financial goals.
• A student solved the equation log4(2x – 12) = 3 as follows: Step 1: 2x – 12 = 34 Step 2: 2x – 12 = 81 Step 3: 2x – 12 = 3^4 Step 4: 2x = 93 Step 5: x = 46.5. Can you explain the error in the student’s reasoning and provide the correct solution, ensuring that your explanation is thorough?
• Identify the error in the student‚Äôs solution shown below and provide the correct answer.
• Triangle ABC has a perimeter of 22 cm, with AB = 8 cm and BC = 5 cm. Based on this information, can you determine if triangle ABC is a right-angled triangle?
• Which graph represents a set of ordered pairs that forms a function?
• What are the sampling methods used in Adam’s survey of high school students’ opinions on hot lunches, where he gives a survey postcard to every twentieth student that enters the building and asks them to mail it in if they choose to participate? Select all that apply: cluster, convenience, simple random, stratified, systematic, voluntary.
• What is the shape of the box-and-whisker plot for Fast Pax’s annual salaries, excluding the outlier of $255,000, and what is the most appropriate measure of center for this data? Additionally, what would you share with a friend about Fast Pax based on this analysis?
• The function f(h) = m(1/2)^h represents the mass m of a radioactive substance remaining after h half-lives. Iron has a half-life of 2.7 years. What equation represents the mass of a 200 mg Iron sample remaining after y years, and how many milligrams remain after 12 years? Options: 1. f(x) = 2.7(0.5)200; 1.7 mg 2. f(x) = 200(0.5)12; 30.8 mg 3. f(x) = 200(0.5)12; 30.8 mg 4. f(x) = 200(0.185)12; 3.2 mg 5. f(x) = 200(0.774)12; 9.2 mg
• An object is dropped from a small plane. As it falls, its distance \( d \) above the ground after \( t \) seconds is given by the formula \( d = -16t^2 + 1000 \). Which inequality can be used to find the interval of time it takes for the object to reach a height greater than 300 feet above the ground?
• Find the mean, median, and mode of the weights of the individuals listed: 105 kg, 53 kg, 76 kg, 91 kg, 120 kg, 61 kg, 55 kg, 98 kg, and 61 kg.
• Look at the graph shown: A coordinate plane graph is displayed with a line that intersects the y-axis at 3 and passes through the point (2, 4). Which equation best represents this line? a) y = 3x + 3 b) y = \(\frac{1}{2}\)x – 3 c) y = \(\frac{1}{2}\)x + 3 d) y = 3x + \(\frac{1}{2}\)
• Consider the diagram and the paragraph proof below. Given: Right triangle ABC as shown, where CD is an altitude of the triangle. Prove: \(a^2 + b^2 = c^2\). Since triangles ABC and CBD both have a right angle and share angle B, they are similar by AA. Similarly, triangles ABC and ACD both have a right angle and share angle A, so they are also similar by AA. The proportions are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as \(a^2 = cf\) and \(b^2 = ce\). Adding \(b^2\) to both sides of the first equation \(a^2 = cf\) leads to the equation \(a^2 + b^2 = cf + b^2\). Since \(b^2\) is equal to \(ce\), we can substitute \(ce\) into the right side of the equation for \(b^2\), resulting in \(a^2 + b^2 = cf + ce\). Applying the distributive property gives us \(a^2 + b^2 = c(f + e)\). What is the last sentence of the proof? Is it: Because \(f + e = 1\), \(a^2 + b^2 = c^2\); Because \(f + e = c\), \(a^2 + b^2 = c^2\); Because \(a^2 + b^2 = c^2\), \(f + e = c\); or Because \(a^2 + b^2 = c^2\), \(f + e = 1\)?
• If I work overtime, I will receive time and a half for every hour over 40 hours. I currently earn $12.00 an hour, and I would like to make an extra $300.00 by working overtime. How many extra hours do I need to work?
• We are asking everyone to focus on reducing their average transaction time by 10%. Given that the average transaction time for this location is 6 minutes and 52 seconds, what should the target average transaction time be?
• You need to purchase supplies for an employee appreciation picnic. Your boss has provided the following shopping list and asks you to get the best deal by buying from one grocer, either Quality Groceries or Fresh Market. After calling both grocers, you compiled their price information into a table. Which grocer will provide all the picnic supplies for the lowest cost, and what is that cost before sales tax?
• Which of the following graphs could represent the function f(x) = x¬≥ + 8?
• To fit between two windows, the width of a bookshelf must be no greater than a certain number of feet. Mrs. Aguilar purchases a bookshelf that is 77 inches wide. Which statement accurately describes the relationship between the width of the bookshelf and the distance between the windows? A: The bookshelf is 12 inches too wide to fit between the windows. B: The bookshelf will fit between the windows with no extra room remaining. C: The bookshelf will fit between the windows with 1 inch remaining. D: The bookshelf is 5 inches too wide to fit between the windows.
• The Rockville Employment Agency has placed Howard Jacobson in a position as a junior pharmacist with an annual salary of $51,200. The agency’s fee is 40% of the first three weeks’ pay. a. What is Howard’s weekly salary, rounded to the nearest cent? b. What will Howard earn during the first three weeks? c. How much will Howard need to pay the employment agency, rounded to the nearest dollar?
• How can an insurance company profit from premiums while making payouts? Is it because the total value of premiums collected is greater than the total value of payouts made, the premiums equal the payouts, the company relies on a pool of funds for payouts instead of individual premiums, or by issuing policies to individuals who are unlikely to need payouts?
• Indicate the method you would use to prove that the two triangles are congruent. If no method applies, please enter “”none.”” Options: SSS, SAS, ASA, AAS, None
• Which region represents the solution to the given system of inequalities?
• Which statement about the following equation is true: 3x¬≤ – 8x + 5 = 5x¬≤? A. The discriminant is less than 0, so there are two real roots. B. The discriminant is greater than 0, so there are two real roots. C. The discriminant is less than 0, so there are two complex roots. D. The discriminant is greater than 0, so there are two complex roots.
• According to the Rational Root Theorem, what are all the potential rational roots of the function f(x) = 5x¬≥ – 7x + 11?
• An exponential function f(x) is reflected across the y-axis to create the function g(x). Which of the following statements is true regarding f(x) and g(x)? A) The two functions have no points in common. B) The two functions have the same initial value. C) The two functions have opposite output values for any given input value. D) The graphs of the two functions look exactly the same.
• Which statement best describes the relationship between the successive terms in the sequence 2.4, -4.8, 9.6, -19.2? A) The common difference is -7.2. B) The common difference is -2.4. C) The common ratio is -2.0. D) The common ratio is -0.5.
• Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? Is it: 1) all real numbers such that y ‚⧠40, 2) all real numbers such that y ‚â• 0, 3) all real numbers such that 0 ‚⧠y ‚⧠40, or 4) all real numbers such that 37.75 ‚⧠y ‚⧠40?
• The truth table represents the statements p, q, and r as follows: p q r A T T T B T T F C T F T D T F F E F T T F F T F G F F T H F F F Which statements are true for rows A and E? Check all that apply: 1. p ‚àß q 2. p ‚àß r 3. q ‚àß p 4. q ‚àß r 5. r ‚àß p 6. r ‚àß q
• Which graph can be used to find the solutions to the equation 8 – 4x = 2x – 4?
• Which scatterplot has a correlation coefficient closest to r = 1?
• Triangle KLM was dilated according to the rule D‚ÇÄ, 0.75 (x, y). What can be said about the image K’L’M’? Check all that apply: 1) D‚ÇÄ, 0.75 (x,y) = (0.75x, 0.75y) 2) LM is parallel to L’M’. 3) KM is shorter than K’M’. 4) The vertices of the image are closer to the origin than those of the pre-image. 5) The distance from M’ to the origin is exactly half the distance from M to the origin.
• Sanjay begins to correctly graph the function f(x) = (x + 1)¬≤ – 3. Based on the axis of symmetry and the vertex, which graph could represent Sanjay’s? A.
• A cyclist rode 3.75 miles in 0.3 hours. Q1: How fast was she going in miles per hour? Q2: At that rate, how long will it take her to travel 4.5 miles?
• What expression represents the volume of a rectangular prism, given that the volume is calculated using the formula V = lwh, where l is the length, w is the width, and h is the height?
• Consider the following equation: f(x) = \frac{x^2 + 4}{4x^2 – 4x – 8}. What are the vertical asymptote(s)?
• Points S and T are the midpoints of the sides of triangle FGH. What is the length of side GF?
• Which statement best summarizes the information presented in these graphs? Many Bolivians are farmers, but the agriculture sector contributes little to the GDP. In recent years, the industrial sector has become increasingly important to Bolivia’s economy. The country is investing significant amounts of money in education to promote economic growth. For a healthy economic future, Bolivia must rely on agriculture.
• In the diagram below, quadrilateral ABCD has sides AB and DC that are equal and parallel. A student wrote the following sentences to demonstrate that quadrilateral ABCD is a parallelogram: Since side AB is parallel to side DC, the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and side DB is a common side to triangles ABD and BCD. Thus, triangles ABD and BCD are congruent by the SAS postulate. By CPCTC, angles DBC and ADB are congruent, and sides AD and BC are also congruent. Angles DBC and ADB _______________. Therefore, AD is parallel and equal to BC. Hence, quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student’s proof?
• What is Rachel’s speed in meters per second, given that the variable d models her distance from her exit (in meters) as d = -38t + 220, where t represents seconds after the cameras began recording her stunt?
• An airplane is flying from New York City to Los Angeles. The distance it travels in miles, D, is related to the time in seconds, T, by the equation D = 0.15T. A. How fast is it flying? Be sure to include the units. B. How far will it travel in 30 seconds? C. How long will it take to go 12.75 miles?
• Which graph represents the system of inequalities: 3x + 5y ‚⧠10x and y ‚⧠1?
• What conditions promote karst development? Check all that apply: 1) dry climate 2) good groundwater circulation 3) hard rocks near Earth’s surface 4) moderate to heavy rainfall 5) poor groundwater circulation 6) soft rocks near Earth’s surface
• Which statements are true about the graph of the system of linear inequalities? Check all that apply. 1. The graph of y > 3x – 4 has shading above a dashed line. 2. The graph of y < x + 1 has shading below a dashed line. 3. The graphs of the inequalities will intersect. 4. There are no solutions to the system. 5. The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).
• The side length, s, of a cube is given by the expression x – 2y. If V = s¬≥, what is the volume of the cube? Consider the following expressions: x¬≥ – 6x¬≤y + 12xy¬≤ – 8y¬≥, x¬≥ + 6x¬≤y + 12xy¬≤ + 8y¬≥, 3x¬≥ – 6x¬≤y + 12xy¬≤ – 24y¬≥, and 3x¬≥ + 6x¬≤y + 12xy¬≤ + 24y¬≥.
• Which of the following graphs could represent the function f(x) = -0.08x(x^2 – 11x + 18)?
• Which of the following describes the roots of the polynomial function f(x) = (x + 2)^2(x + 4)(x + 1)^3? A) -2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3 B) -2 with multiplicity 3, 4 with multiplicity 2, and -1 with multiplicity 4 C) 2 with multiplicity 2, -4 with multiplicity 1, and 1 with multiplicity 3 D) 2 with multiplicity 3, -4 with multiplicity 2, and 1 with multiplicity 4
• What is the value of x in the equilateral triangle XYZ, where the base XY is slightly inclined vertically, and the vertex Z is to the left of the base? Side XY, YZ, and ZX are marked with a single tick for equal length. Angle XY is labeled as (2x – 4) degrees, and angle YZ is labeled as 5y degrees. Please enter your answer in the box.
• Drag and drop the correct answer into each box to complete the proof. Given: Rectangle ABCD. Prove: AC is congruent to BD.
• I see that your new product is available for $412.50 on the website, which includes a 25% discount. How much will it cost if I buy it in the store?
• If f(x) and g(x) are inverse functions of each other, which of the following graphs represents f(g(x))?
• Complete the steps to factor the polynomial by grouping. Given P(x) = x¬≥ + 5x¬≤ – x – 5, how do you factor it into the form P(x) = (x¬≤ – )(x + 5) and ultimately into P(x) = (x – )(x + 1)(x + )?
• Drag and drop the correct answer into each box to complete the proof for parallelogram KLMN, where KN is parallel to LM and KL is parallel to MN. Given: Parallelogram KLMN. Prove: __N__L and __M__K. Statement Reason: Parallelogram KLMN (Given) KL || NM and KN || LM. m_K + m_N = 180¬∞ (Same-Side Interior Angles Theorem), m_L + m_M = 180¬∞, m_K + m_L = 180¬∞. m_K + m_N = m_K + m_L, m_L + m_M = m_K + m_L, m_N = m_L, m_M = m_K. __N__L and __M__K (Angle Congruence Postulate).
• Look at the figure shown below: A triangle RPQ is depicted. Point S is located on side PQ, and point T is on side PR. Points S and T are connected by a straight line. The lengths are as follows: PS = 3x, SQ = 24, PT = 51, and TR = 34. Dora is writing statements to prove that if segment ST is parallel to segment RQ, then x = 12. The statements are: 1. Segment ST is parallel to segment RQ. (Given) 2. Angle QRT is congruent to angle STP because corresponding angles formed by parallel lines and their transversal are congruent. 3. Angle SPT is congruent to angle QPR due to the reflexive property of angles. 4. Triangle SPT is similar to triangle QPR, from the Angle-Angle Similarity Postulate. 5. ? Corresponding sides of similar triangles are in proportion. Which equation can she use as statement 5? a) (3x + 24):3x = 85:51 b) (3x + 24):85 = 3x:51 c) (3x + 24):51 = 3x:85 d) 34:24 = 3x:51
• Which pairs of polygons are similar? Please select all correct answers.
• In March, Delphine’s house experienced 40% more snowfall than in February, where she had f centimeters of snowfall in February. Which of the following expressions represents the amount of snowfall Delphine had at her house in March?
• In triangle √ÜPQR, with PQ = 39 cm and PN as the altitude, find the length of PR given that QN = 36 cm and RN = 8 cm.
• What function models the average annual cost of owning a small dog over x years, given that the one-time costs are $180 and the continuing costs are $400 per year?
• Which graph represents the solution to the following system of inequalities: x + y < 3 and -5x + 2y < 10?
• Which graph represents the function f(x) = -|x| – 2?
• Using the provided table, calculate the profit at each level of running shoe inserts production for the following pairs: Pair 1: $, Pair 2: $, Pair 3: $, Pair 4: $, Pair 5: $.
• Andre came up with the following puzzle: “”I am three years younger than my brother and two years older than my sister. My mom’s age is one less than three times my brother’s age. When you add all our ages together, the total is 87. What are our ages?””
• What are the domain and range of the logarithmic function f(x) = log7(x)? Use the inverse function to justify your answers.
• Graph the image of this triangle after a dilation with a scale factor of 2, centered at the origin. Use the polygon tool to draw the triangle.
• In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x – 4, and HE = 5y + 1. Find the values of x and y. Note that the diagram is not drawn to scale.
• What is the sequence of transformations that maps triangle ABC to triangle A’B’C’? Select from the drop-down menus to correctly identify each step. Step 1: Step 2: There are two triangles on the coordinate plane. Triangle ABC has vertex A at (7, -1), vertex B at (2, -3), and vertex C at (2, -1). Triangle A’B’C’ has vertex A’ at (-3, 7), vertex B’ at (-1, 2), and vertex C’ at (-3, 2).
• A student concluded that the solution to the equation ‚àö(2x + 1) + 3 = 0 is x = 4. Do you agree? Please explain why or why not.
• A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation, the weight is at its highest point. From its resting position, it takes 12 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and highest points is 10 inches, with the resting position at y = 0. Using a sine function, how can you graph this situation? The first point should represent the midline, and the second point should be either a maximum or minimum value on the graph closest to the first point.
• What is the minimum value of a sinusoidal function? Please enter your answer in the box.
• An isosceles triangle has two sides of equal length, denoted as \( a \), and a base \( b \). The perimeter of the triangle is 15.7 inches, leading to the equation \( 2a + b = 15.7 \). Considering that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths are valid options for \( b \)? Select two options from the following: 2 in., 0 in., 0.5 in., 2 in., 7.9 in.
• At what values of x does the graph of f(x) = sin(x) intersect the x-axis?
• Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. She crochets at a rate of \( \frac{1}{15} \) of a blanket per day and has 60 days until the donation. However, Darcie plans to skip some days to volunteer in other ways. Write an inequality to determine the number of days, \( s \), that Darcie can skip crocheting while still meeting her goal. Additionally, graph the solution set for this inequality.
• Triangle XYZ has vertices X(0, 0), Y(0, -2), and Z(-2, -2). It is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2, -2). Which rules could describe the rotation? Check all that apply: R0, 90¬∞, R0, 180¬∞, R0, 270¬∞, (x, y) ‚Üí (-y, x), (x, y) ‚Üí (y, -x).
• Which composition of similarity transformations maps polygon ABCD to polygon A’B’C’D’? Options include: a dilation with a scale factor less than 1 followed by a reflection, a dilation with a scale factor less than 1 followed by a translation, a dilation with a scale factor greater than 1 followed by a reflection, or a dilation with a scale factor greater than 1 followed by a translation.
• A chemist has 200 mL of a 10% sucrose solution and adds x mL of a 40% sucrose solution. The percent concentration, y, of the final mixture is represented by a rational function. The chemist wants the final concentration to be 30%. How many milliliters of the 40% solution should she add to achieve this concentration?
• Two polygons are similar. The perimeter of the larger polygon is 85 meters, and the ratio of the corresponding side lengths is \( \frac{2}{5} \). What is the perimeter of the smaller polygon in meters?
• Identify the initial amount \( a \) and the growth rate \( r \) (as a percentage) of the exponential function \( y = 350(1 + 0.75)^t \). Evaluate the function when \( t = 5 \) and round your answer to the nearest tenth.
• Given the triangles ABC and F, where FC bisects angle BAC, prove that AB/BD = AC/CD.
• How can the perimeter of a quadrilateral in the coordinate plane be calculated if the vertices are known? Should I use the distance formula to find the length of each side and then add the lengths, use the slope formula to determine if opposite sides are parallel, check if consecutive sides are perpendicular, or apply the distance formula to find the side lengths and then multiply two of the side lengths?
• Which of the following statements about the graph of the function y = 2^x are true? Check all boxes that apply. 1. The domain is all real numbers x because the exponent can be any real number. 2. When the x-values increase by 1 unit, the y-value multiplies by 2. 3. The y-intercept is (0, 1). 4. The graph never goes below the x-axis because powers of 2 are never negative. 5. The range is all real numbers.
• Josiah tracked the number of songs from each genre played in an hour on his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player and predicted the number of rock songs to be 300. Which statements about his solution are true? Check all that apply. Josiah’s Music Sample 1: R & B – 5, Pop – 4, Classical – 3, Jazz – 2, Rock – 6; Sample 2: R & B – 4, Pop – 3, Classical – 5, Jazz – 4, Rock – 4. Josiah’s work: 10/20 = x/1,500. 10×30/20×30=x/1,500. 300=x. He should have found the average number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20×75=1,500.