Adding Rational Numbers Using Properties of Operations This activity will help you meet these educational goals:
Mathematical Practices—You will make sense of problems and solve them and use mathematics to model real-world situations.

Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F.

Complete the steps below to learn more about the temperature change of the water.

Part A
Write an expression that represents the temperature (in degrees Fahrenheit) of the water after Raul added the ice cubes. Write the expression as the sum of two numbers.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

29933333.33

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).