PLEASE HELP ASAP

The solution of the first image is: b = √48

The solution of the second image is: c = √125

Step-by-step explanation:

Here we have two triangle rectangles, first, we need to remember the Pythagorean theorem.

For a triangle rectangle with cathetus A and B, and a hypotenuse H, we have the relationship:

A^2 + B^2 = H^2

Where H is the side that is opposite to the right angle (the angle of 90°)

In the first image, we can see that the hypotenuse is equal to 8, and one cathetus is equal to 4.

We want to find the value of b, that is the other cathetus.

Then we have:

4^2 + b^2 = 8^2

b^2 = 8^2 - 4^2

b^2 = 48

b = √48

Second image:

in this case, c is the hypotenuse, a and b are the cathetus.

We know that:

a = 5, b = 10

Then we have the equation:

a^2 + b^2 = c^2

Now we can replace the above values:

5^2 + 10^2 = c^2

25 + 100 = c^2

125 = c^2

√125 = c

180 square centimeters

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: