Solve each system of inequalities by graphing. Please help and show work!! EVENS ONLY!! Answer: 2.) (1.0) ; (0.2) (-1,0) ; (0,1) 4.) (1/2 or 0.5, 0) ; (0,1) (-2,0) ; (0,1) 6.) (6/5 or 1.2, 0) ; (0,-3) (1,0) ; (0,1) Step-by-step explanation: So what you have to do is to find the x-intercept and y-intercept. The goal in finding the x-intercept is to isolate x. To find the x-intercept you must subsitute y with 0. For example, y > -2x + 2 will become 0 > -2x + 2. Then you have to isolate 2 and put it on the other side so the equation will be 0 - 2 > -2x + 2 - 2 which will become -2 > -2x. Since we only want to have x, we should divide both sides with -2 since thats the number with the coefficient of x. So its -2 > -2x all over -2. The final answer will be 1 > x. Then you have to find the y-intercept which is basically the opposite of y-intercept. You subsitute x with 0. So the equation would be y > -2(0) + 2 and the final answer will be 2. N...
A 500 mL container is filled with helium gas to a pressure of 3.0 atm at 250°C.approximately how many toy balloons at STP can be filled by helium from this container,assuming each balloon can contain 1L? recall that STP means standard temperature and pressure (1 atm and 273 k). Plss help me Good Day Problem: A 500 mL container is filled with helium gas to a pressure of 3.0 atm at 25.0°C.approximately how many toy balloons at STP can be filled by helium from this container,assuming each balloon can contain 1L? recall that STP means standard temperature and pressure (1 atm and 273 k). First we have to solve for the amount of gas: 1000 ml = 1L (500 ml × 1L / 1000 ml = .5 L) K = 25.0 + 273.15 = 298.15 K Given Data: V (volume) = 500 mL or .5 L P (pressure) = 3.0 atm T (temperature) = 25.0°C or 298.15 K n (moles) = ? unknown R (universal constant) = 0.0821 L.atm/mol.K Solution: We can use the formula PV = nRT, to solve for n, we use n = PV/RT n = PV/RT = 3.0 atm × .5 L / 0.0821...
Jeffrey is asked to graph f(x)=x^2-6x+5. Below is his graph. Is his graph correct or incorrect? Prove your answer by discussing the key characteristics of a quadratic function. Include the shape of the graph based on its leading coefficient, calculation of its vertex, maximum or minimum value as well as its x -intercepts. Answer with Step-by-step explanation: Quadratic function: f(x) = x² - 6x + 5 a = 1 (the leading coefficient) ⇒ a > 0 graph opens upward b = -6 c = 5 Find the vertex (h, k ) where h=axis of symmetry and k = maximum or minimum value depending on value of a: h = -b/2a h = -(-6)/(2)(1) h = 6/2 h = 2 k = f(h) = (h)²- 6h + 5 k = (2)² - 6(2)+5 k = 4 -12 + 5 k = -3 Vertex (h,k): (2, -3) h = axis of symmetry = 2 Since a > 0 , the parabola (graph) of the function opens upward , and has a minimum value (k) = - 3. Find the x-intercepts or roots/zeros of the function by factoring: x² - 6x + 5 = 0 (x - 5) (x - 1) = 0 x - 5 = 0 x = 5 x - 1 = 0 x = 1...
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