1 Solving Equations and Inequalities Graphically Solve the given equation or inequality graphically. -23. (а) х — 2 3 4 — х (b) х — 2 > 4 — х 24. (а) - 2х +3%3D Зх — 7 (b) -2x + 3 s 3x – 7
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- Animals are kept as an experiment but are on a strict diet. Each animal receives 45g of protein and 6g of fat. There are two mixes, one with 30% protein and 6% fat (mix 1) while the other has 50% protein and 5% fat (mix 2). How many g of each mix should be used to obtain the appropriate diet for one animal? One animals diet should contain __ g of mix 1 One animals diet should contain __ g of mix 2 Show all your work including equations used and calculations.An economy produces steel and lumber. To produce 1 ton of steel requires the consumption of .5 tons of steel and 2 tons of lumber (that's 2 whole tons, not 0.2 tons). To produce 1 ton of lumber requires the consumption of .2 tons of steel, and 0 tons of lumber. Suppose there is a demand for 3 tons of steel and 1 ton of lumber. If a production schedule is calculated to meet this demand, how many tons of steel are produced?1. The graph of a linear equation in two variables is a _____________________line.2. The general form of linear equation in two variables is _______________________.3. Linear equations in three variables are expressed as _________________________.4. The number of variables in is __________________________.5. The solution of a linear equation always ________________________ the equation.
- A tutoring service provides tutoring for a fee. When the tutoring service charges $11/hour, there is a demand for 28 tutors per week. When the hourly rate rises to $17/hour, the demand drops to 16 tutors per week. On the other hand, at $11/hour, the service is able to support only 28 tutors per week, whereas at the rate of $17/hour, it is able to provide 58 tutors per week. Find the price per hour at which the number of tutors demanded and the number of tutors supplied will be equal.Why are there no extraneous solutions when solving linear equations or quadratic equations? A) Linear equations which represent vertical lines have an infinite number of extraneous solutions B) when a linear equation represents a non-vertical line there is only one solution. A quadratic equation may have 0 roots, two equal roots for one solution, or two unequal roots for two solutions C) linear and quadratic equations have no extraneous solutions because their graphs always intersect the x axis D) linear and quadratic equations have no extraneous solutions because they are easy to solve1.) Write an equation for the total cost y of renting a tube for any number of hours x. 2.) Write an equation for renting a kayak for any number of hours. Then write an equation for renting a bicycle any number of hours. 3. ) Make a table finding the cost to rent each item for 1, 2, 3, 4 and 5 hours. (5pts) 4.) After solving the system y = -2x - 3 and y = 2x +5 graphically. Write your solution below.
- true or false: A system of nonlinear algebraic equations h(x)=0 can always be expressed as a fixed-point equation x=g(x).Twelve gallons of a salt solution consists of 30% salt. It is the result of mixing a 40% solution with a 20% solution. How many gallons of each of the solutions was used? Let x= the number of gallons of the 40% solution and y= the number of gallons of the 20% solution. The corresponding modeling system is {x+y=120.4x+0.2y=0.3(12). Solve the system by using the method of substitution. enter the ordered pair ( , )Formulate equations for these problems to find the solution using Gauss-Jordan Elimination of the augmentedmatrix. A fruit stall sells two varieties of kiwi: standard and deluxe. A box of standard kiwi sells for $7, and a box ofdeluxe kiwi sells for $10. In one day, the stand sells 135 boxes of strawberries for a total of $1110. How manyboxes of each type were sold?
- Formulate but do not solve the problem.A theater has a seating capacity of 600 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $3800. How many children attended the show? (Let x, y, and z denote the number of children, students, and adults, respectively.) = 600 = z = 3800Medication Medication A is given six times per day,and medication B is given twice per day. MedicationC is given once every two days, and its dosage is1/2 the sum of the dosages of the other two medications.For a certain patient, the total intake of the threemedications is limited to 28.7 milligrams on days when all three medications are given. If the ratio ofthe dosage of medication A to the dosage of medicationB is 2 to 3, how many milligrams are in each dosage?2. A. Solve the linear inequality: 2(5 – x) ≤ 3(5 – x) - 7 x B. Hence or otherwise, represent your solution set on a number line. 3. Solve the system of linear inequalities: 4x + 2y ≥ 8 y − 4 > x
