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## Do Now

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**Do Now**Solve the system by SUBSTITUTION y = 2x - 7 2x + y = 1 (2, -3)**Objective**• SWBAT review concepts and questions from Algebra 1 Released EOC.**Problem 1**Based on the given data the y-intercept is 5 and the rate of change (slope) is 2/3, so based on the answer choices choice B would be correct.**Problem 2**Looking at the graph we Can generate the equation Y ≤ -2x + 5; however the Answer choices are written In words where they are in standard form 2x + y ≤ 5 and the only Answer choice that models This equation is Choice C.**Problem 3**Based on the difference of squares rule, factoring the expression you will get: (t+6)(t-6) Which is answer choice B.**Problem 4**Based on the equation we can find the vertex by using the equation x = -b/2a so substituting the values in we get: x = -(-8)/2(4) = 1. We then will substitute x into the equation f(x) = 4x2 – 8x + 7. So f(1) = 4(1)2 – 8(1) + 7 = 3. So our vertex is (1,3).Knowing this we can now eliminate choices B and C. We can now look at our y Intercept which is 7 and we then can eliminate choice A. So our answer is D.**Problem 5**4 + w + 2 w + 2 To find the area of the rectangle we use the Formula L∙W = (4+w+2)(w+2) = (w+6)(w + 2). Factoring this expression we get: N = w2 + 8w+12 So choice D is our answer**Problem 6**Shawn walks at a speed of 5 feet per second BUT he begins walking 20 seconds earlier, so An equation to represent each boys walking speed is: Shawn: d = 5t + 100 (at 20 seconds Shawn walked 100 feet) Curtis: d = 6t So solving the system through substitution we get: 6t = 5t + 100 -5t -5t t = 100 So they were walking for 100 seconds when they met BUT Shawn had a 20 second lead so Shawn was walking for 120 seconds**Problem 7**For this problem we need to set up a system of equations. Let x = candy bars and Let y = drinks. So 60x + 110y = 265 120x + 90y = 270 To solve this system multiply the first equation by 2 and solve by elimination. 120x + 220y = 530 120x + 90y = 270 130y = 260 130 130 y = 2 y is the number of drinks so we need to substitute to find x. 120x + 90(2) =270 120x + 180 = 270 120x = 90 x = 0.75 So the cost of the candy bars was $0.75.**Problem 8**Let n = the first positive integer, so the 3 consecutive numbers are: n, n+1, n+2 Since the product of the two smaller integers is 5 less than the largest integer we will set up our equation: n(n+1) = 5(n+2)-5 To find the smallest integer we need to solve for n. n2 + n = 5n + 10 – 5 n2 -4n -5 = 0 (n – 5)(n + 1) = 0 n = 5 and n = -1, but since n has to be a positive integer n = 5 only makes sense.**Problem 9**To see how long it takes the object to hit the ground we need to set our equation equal to zero. 0 = -5t2 + 20t + 60 -5(t2- 4t - 12) = 0 t2 – 4t – 12 = 0 (t – 6) (t + 2) = 0 t = 6 or t = -2 Time can not be negative so at 6 seconds the object will hit the ground.**Problem 10**Let x = Antonio’s Age Let y = Sarah’s Age 2x + 3y = 34 y = 5x Use Substitution to find Sarah’s age 2x + 3(5x) = 34 2x + 15x = 34 17x = 34 x = 2 y = 5(2) = 10 So Sarah’s age is 10**Problem 11**When finding the value of k we need to find the difference from the graph and f(x) = 2(2)x. The y-intercept of the graph is -3 and the y intercept of f(x) = 2(2)x is 2. So the difference between 2 and -3 is -5. So the value of k is -5.**Problem 12**Vv f(x) = 2x + 12 f(7) = 2(7) + 12 f(7) = 26 So it costs $26 dollars to rent 7 movies. Since Makayla has $10, she now needs $16 to rent 7 movies.**Problem 13**Using the Pythagorean Theorem we get: x2 + (x+3)2 = (x+6)2 x2 + x2+6x+9 = x2+12x+ 36 2x2+6x+9 = x2+12x+36 x2 -6x -27 = 0 (x – 9)(x+3) =0 x = 9 or x = -3 So x must equal 9 because Measurement can be negative. X + 3 X + 6 x**Problem 14**Katie’s Turns Jen’s Turns So at the end of turn 3 is when Katie’s points increase but the question said at the beginning of what turn, so at the beginning of the 4th turn is when Katie will have more points.**Problem 15**Alex: 1 mi Sally: 3520 yd 15 min 24 min A: 1 mi ∙ 60 min 1 mi = 1760 yd 15 min 1 hr 2 mi = 3520 yd A: 4 mi S: 2 mi = 1mi 1 hr 24 min 12 min S: 1 mi ∙ 60 min 12 min 1 hr 5 mi 1 hr So Sally walked 1mi/hr faster than Alex.**Problem 16**• = 81/3 ∙x2/3∙y3/3∙z4/3 2x2/3yz4/3 So answer choice B is the correct answer**Problem 17**School Buys: 50x, where x is the candy bars Cost $30 a box to buy School Sells: 50x, where x is the candy bars Want to make $10 profit so they need to make $40. So to find out ho much each candy bar should cost we set up an equation: 50x = 40 x = 40/50 = 0.80 So each candy bar should cost $0.80 which is choice C.**Problem 18**E = mc2 To solve for m we divide both sides by c2 and get m = _E_ Which is choice D c2**Problem 19**This is a quadratic function and the question is asking for the least which is the minimum value of this function. To find the minimum value we need to find the x value of the vertex, because x equals the number of years since 1964. Vertex formula: x = -b =-(-458.3) = 11.01 2a 2(20.8) So 11 years since 1964 is 1964+11 = 1975 So the year of 1975 is when the car value was at its least. So answer choice C is correct.**Problem 20**Based on Exponents Property, we will multiply our exponents and get x-1 which simplifies further to 1_. So choice B is correct. x**Problem 21**0.07 – 0.04 = 0.03 0.14 – 0.07 = 0.07 0.25 – 0.14 = 0.11 0.49 – 0.25 = 0.24 So the average rate of change is: 0.03+0.07+0.11+0.24 4 = 0.1125 Or you can find the average rate of change (slope) of (8,0.04) and (12, 0.49) 0.49 – 0.04 = 0.45 = 0.1125 12 – 8 4**Problem 22**We know the y intercept of f(x) is 5 so we need to find the y intercept of g(x) and find the difference. The rate of change of g(x) is ½ so to find the y intercept we need to find what g(x) equals when x = 0. So the table at the right shows the extension of the table where x = 0. We now see that the y intercept of g(x) is 5.5. So the difference is 5.5 – 5.0, which is 0.5 and Choice C , is the best answer.**Problem 23**y = .10x + 10 z = 0.20x So y – z is .10x + 10 – 0.20x = -0.10x + 10 Which is choice B.**Problem 24**Method one is neither constant or exponential but Method 2 is exponential because the rate of change is a product.