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Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right.

pH is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. The variable x represents the amount of hydronium ions, and f(x) gives the pH level.

Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.

Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.

Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50.

The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = −log10x as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the graph.

f(x) + 1

f(x + 1)

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21/2 or 5/2

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.