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Ok, we can go one by one to solve these problems. 

However, let's note that if we have f(x) = x, we set the function's right side to equal x.

Then, we see if the x value satisfies the conditions given. 

First, we have \(f(x)=2x+8\). Setting this to equal x, we find that \(x=2x+8\)

Solving for x, we find that \(x=-8\). This doesn't satisfy the condition \(1 \le x\le 2\), so it is not a valid solution. 

Next, we have \(f(x)=13-5x\). Setting this to equal x, we have \(x=13-5x\)

Finding the value of x, we get \(x=13/6\). This satisfies the interval, so it is a solution. 

Third, we have \(f(x)=20-14x\). Since this equals x, we can write \(x=20-14x\)

Trying to find x, we have that \(x=4/3\). This does NOT satisfy the interval, so it is not a solution. 

Lastly, we have \(f(x)=40+5x\). setting this function to equal x, we have \(x=40+5x\)

Solving for x, we get \(x=-10\), which is invalid. 

Thus, the only value that works is 13/6. 

So our answer is 13/6. 

Thanks! 

Credits to notthatsmart

Two angles are considered complementary if their measures add up to 90 degrees.     

X + (X+ 32^o)  =  90^o     

      2X + 32^o  =  90^o     

                2X  =  90^o – 32^o     

                2X  =  58^o     

                  X  =  29^o    

         angle₁  =  29^o     

         angle2   =  29^o + 32^o     

         angle₂  =  61^o     

_.     

          40 – 22  = 18     

          ¹/₂ of 18 =  9     

          c² = a² + b²     

          leg²  =  9² + 7²     

          leg²  =  81 + 49  =  140     

          leg  =  sqrt(140)     

          leg  =  11.83     

_.     

A soup company needs to make labels for their soup cans. Their cans have a circumference of 25 cm and a height of 10cm. a) To the nearest tenth, what is the radius of the soup can?     

     Circumference  =  π • diameter     

     25 =  3.1416 • d     

     d  =  25 / 3.1416  =  7.96     

     d  =  2 • r     ——>>     r  =  d / 2     

                                         r  =  7.96 / 2     

                                         r  =  3.98     You can round it to the nearest tenth yourself.     

_.     
 

     V_cylinder  =  π r² h     

     V_icecreampail  =  π • (5²)(14)     =  350 π     

     V_sphere  =  (4/3) π r³     

     V_{icecreamscoop}  =  π • (4/3)(1³)  =  (4/3) π     

     You can dip 350 / (4/3)  scoops out of the pail     

                         350 / (4/3)  =  262.5  which rounds to 262 full scoops     

_.     

A thin strip of wood laminate is to be glued to the edges of a table . The length of laminate required is equal to the perimeter of the table , which has dimensions 190 cm by 95 cm . The laminate is sold in 8ft lengths . How much laminate must be purchased?     

so you need (2)(190)cm + (2)(95) cm of laminate  =  570 cm     

conversion factor from feet to cm is  1 ft  =     30.48 cm     

                                                     so  8 ft  =  243.84 cm     

                     570 cm / 243.84 cm/length  =  2.34 lengths     

assuming they won't sell you part of a length, you need  3 lengths     

_.     

     The area is half.     

     The base is the same.     

     So, the height of the parallelogram has to be half the height of the rectangle.     

     Drop a perpendicular from the top left corner to the base.  That's the Height_{parallelogram}.     

     Height_para / Height_rect  =  0.5000     

     H_para / H_rect  =  opposite / hypotenuse  =  sin(Θ)     

     Θ  =  sin^–1 (0.5000)     

     Θ  =  30^o     

_.     

In terms of pi, what is the area of the circle defined by the equation 2x^2+2y^2+10x-6y-48=x^2+y^2-2x+4y-10     

                                        2x² + 2y² + 10x – 6y – 48  =  x² + y² – 2x + 4y – 10     

                                          x² + y² + 12x – 10y – 38  =  0     

complete the squares       (x² + 12x        )  +  (y² – 10y        )  =  38     

                                         (x² + 12x + 36)  +  (y² –10y + 25)   =  38 + 36 + 25     

                                                (x + 6)²       +       (y – 5)²        =  99     

equation for all circles is          (x – h)²       +       (y – k)²        =  r²       <— (r² is the radius squared)     

                                          Area  =  π r²     

                                          Area  =  π • 99     

                                          Area  =  99 π     

_.     

     D _t   =  A • T²     

     D _3t  =  A • (3T)²     

     D _3t  =  9 • D _t     

_.     

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)  =  (15)(x+6)     

                                                                   7x + 21  =  15x + 90     

                                                                         – 8x  =  69     

x will not be an integer, so there is no solution.     

_.     

wall total area:15*60=900\(m^2\)

a foot=0.3048 meters

each gallon of paint => 400 sqft,

let's convert \(900m^2\)to feet first

Since 1 foot=0.3048 meters, 1 sqft =\(0.3048^2 \) square meters

which is about 0.09290304 square meters,

\(900m^2\)is about 9687.52

9687.52/400=24.2188 but we go to the next number since we need the smallest whole number of gallons:

25

A necklace contains twenty-four spherical beads of silver, each having a radius of 0.5cm. The beads are to be coated, and the cost of coating is $10 per cm2. What is the approximate total cost, to the nearest cent, for coating the beads?     

     A_sphere  =  4 π r²     

     A_{one bead}  =  (4)(3.1416)(0.5 cm)²     

                      =  (4)(3.1416)(0.25 sqcm)     

                      =  3.1416 sqcm    

     A_{24 beads}  =  (24 sqcm)(3.1416)     

                      =  75.3984 sqcm    

     Cost  =  (10 $/sqcm)(75.3984 sqcm)     

               =   753.98 $     

_.     

The answer is 18.