The answer
for such a question, it is required to graph each function, the answer is
<span>f(x) =4/5(4/5 )^x
check the attached file for proof</span>
General Idea:
We need to find the volume of the small cube given the side length of the small cube as 1/4 inch.
Also we need to find the volume of the right rectangular prism with the given dimension (the height is 4 1/2, the width is 5, and the length is 3 3/4).
To find the number of small cubes that are needed to completely fill the right rectangular prism, we need to divide volume of right rectangular prism by volume of each small cube.
Formula Used:
![Volume \; of \; Cube = a^3 \; \\\{where \; a \; is \; side \; length \; of \; cube\}\\\\Volume \; of \; Right \; Rectangular \; Prism=L \times W \times H\\\{Where \; L \; is \; Length, \; W \; is \; Width, \;and \; H \; is \; Height\}](https://tex.z-dn.net/?f=%20Volume%20%5C%3B%20of%20%5C%3B%20Cube%20%3D%20a%5E3%20%5C%3B%20%5C%5C%5C%7Bwhere%20%5C%3B%20a%20%5C%3B%20is%20%5C%3B%20side%20%5C%3B%20length%20%5C%3B%20of%20%5C%3B%20cube%5C%7D%5C%5C%5C%5CVolume%20%5C%3B%20of%20%20%5C%3B%20Right%20%5C%3B%20Rectangular%20%20%5C%3B%20Prism%3DL%20%5Ctimes%20W%20%5Ctimes%20H%5C%5C%5C%7BWhere%20%20%5C%3B%20L%20%5C%3B%20is%20%5C%3B%20Length%2C%20%5C%3B%20W%20%5C%3B%20is%20%5C%3B%20Width%2C%20%5C%3Band%20%20%5C%3B%20H%20%5C%3B%20is%20%5C%3B%20Height%5C%7D%20%20)
Applying the concept:
Volume of Small Cube:
![V_{cube}= (\frac{1}{4} )^3= \frac{1}{64} \; in^3\\\\V_{Prism}= 3 \frac{3}{4} \times 5 \times 4 \frac{1}{2} = \frac{15}{4} \times \frac{5}{1} \times \frac{9}{2} = \frac{675}{8} \\\\Number \; of \; small \; cubes= \frac{V_{Prism}}{V_{Cube}} = \frac{675}{8} \div \frac{1}{64} \\\\Flip \; the \; second \; fraction\; and \; multiply \; with \; the \; first \; fraction\\\\Number \; of \; small \; cubes \;= \frac{675}{8} \times \frac{64}{1} = 5400](https://tex.z-dn.net/?f=%20V_%7Bcube%7D%3D%20%28%5Cfrac%7B1%7D%7B4%7D%20%20%29%5E3%3D%20%5Cfrac%7B1%7D%7B64%7D%20%5C%3B%20in%5E3%5C%5C%5C%5CV_%7BPrism%7D%3D%20%203%20%5Cfrac%7B3%7D%7B4%7D%20%20%5Ctimes%205%20%5Ctimes%20%204%20%5Cfrac%7B1%7D%7B2%7D%20%20%3D%20%5Cfrac%7B15%7D%7B4%7D%20%20%5Ctimes%20%5Cfrac%7B5%7D%7B1%7D%20%20%5Ctimes%20%5Cfrac%7B9%7D%7B2%7D%20%20%3D%20%5Cfrac%7B675%7D%7B8%7D%20%20%5C%5C%5C%5CNumber%20%5C%3B%20of%20%5C%3B%20small%20%5C%3B%20cubes%3D%20%5Cfrac%7BV_%7BPrism%7D%7D%7BV_%7BCube%7D%7D%20%20%20%3D%20%5Cfrac%7B675%7D%7B8%7D%20%20%5Cdiv%20%5Cfrac%7B1%7D%7B64%7D%20%20%5C%5C%5C%5CFlip%20%5C%3B%20the%20%5C%3B%20second%20%5C%3B%20fraction%5C%3B%20and%20%5C%3B%20multiply%20%5C%3B%20with%20%5C%3B%20the%20%5C%3B%20first%20%5C%3B%20fraction%5C%5C%5C%5CNumber%20%5C%3B%20of%20%5C%3B%20small%20%5C%3B%20cubes%20%5C%3B%3D%20%5Cfrac%7B675%7D%7B8%7D%20%5Ctimes%20%5Cfrac%7B64%7D%7B1%7D%20%20%20%3D%205400%20)
Conclusion:
The number of small cubes with side length as 1/4 inches that are needed to completely fill the right rectangular prism whose height is 4 1/2 inches, width is 5 inches, and length is 3 3/4 inches is <em><u>5400 </u></em>
-5x - 7 < 28.....add 7 to both sides
-5x < 35....divide both sides by -5, change the inequality sign (u change the inequality sign when dividing/multiplying by a negative number)
x > -7
Answer:
you can use similar triangle to make known degrees in problems to make then easier to solve. With similar triangle, the angles are the same, but the scale is different. So by using this, one can solve both at the same time, and just just scale up the smaller one or scale down the larger, by the given/found scale.
Step-by-step explanation: