We have two right triangles and three different rectangles.
The formula of an area of a right triangle:
![A_T=\dfrac{1}{2}l_1l_2](https://tex.z-dn.net/?f=A_T%3D%5Cdfrac%7B1%7D%7B2%7Dl_1l_2)
l₁, l₂ - legs
We have l₁ = 20cm and l₂ = 21cm. Substitute:
![A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2](https://tex.z-dn.net/?f=A_T%3D%5Cdfrac%7B1%7D%7B2%7D%2820%29%2821%29%3D%2810%29%2821%29%3D210%5C%20cm%5E2)
The formula of an area of a rectangle:
![A_R=lw](https://tex.z-dn.net/?f=A_R%3Dlw)
l - length
w - width
We have:
rectangle #1: l = 22cm, w = 29cm
![A_{R1}=(22)(29)=638\ cm^2](https://tex.z-dn.net/?f=A_%7BR1%7D%3D%2822%29%2829%29%3D638%5C%20cm%5E2)
rectangle #2: l = 22cm, w = 21cm
![A_{R2}=(22)(21)=462\ cm^2](https://tex.z-dn.net/?f=A_%7BR2%7D%3D%2822%29%2821%29%3D462%5C%20cm%5E2)
rectangle #3: l = 22cm, w = 20cm
![A_{R3}=(22)(20)=440\ cm^2](https://tex.z-dn.net/?f=A_%7BR3%7D%3D%2822%29%2820%29%3D440%5C%20cm%5E2)
The total Surface Area of the triangular prism:
![S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2](https://tex.z-dn.net/?f=S.A.%3D2A_T%2BA_%7BR1%7D%2BA_%7BR2%7D%2BA_%7BR3%7D%5C%5C%5C%5CS.A.%3D2%5Ccdot210%2B638%2B462%2B440%3D1960%5C%20cm%5E2)
The arrangement should be based on the decreasing degree of the terms which may be determined by the variable x as it should come first in alphabetical order. The polynomial is then,
10x³ + 2x²y + 2xy^4 - 3y²
The degree is equal to the sum of the exponents. Thus, the answer is 5 and it is letter D.
<h2>Problem:</h2>
Ramona went out with her 3 sisters, they spent $58 plus 9% tax on their meal. They also left 15% tip. If they divided up the bill evenly, how much did each of them spend?
<h2>Solution:</h2>
![\frac{58 + 58(9\% + 15\%)}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B58%20%2B%2058%289%5C%25%20%2B%2015%5C%25%29%7D%7B3%7D%20)
![= \frac{58 + 58(0.09 + 0.15)}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B58%20%2B%2058%280.09%20%2B%200.15%29%7D%7B3%7D%20)
![= \frac{58 + 58 \times 0.24}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B58%20%2B%2058%20%5Ctimes%200.24%7D%7B3%7D%20)
![= \frac{58 + 13.92}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B58%20%2B%2013.92%7D%7B3%7D%20)
![= \frac{71.92}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B71.92%7D%7B3%7D%20)
![= 23.97](https://tex.z-dn.net/?f=%20%3D%2023.97)
<h2>Answer:</h2>
<u>E</u><u>a</u><u>c</u><u>h</u><u> </u><u>o</u><u>f</u><u> </u><u>t</u><u>h</u><u>e</u><u>m</u><u> </u><u>d</u><u>i</u><u>d</u><u> </u><u>s</u><u>p</u><u>e</u><u>n</u><u>d</u><u> </u><u>$</u><u>2</u><u>3</u><u>.</u><u>9</u><u>7</u>
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Answer:
4x^2 - 4x - 3
Step-by-step explanation:
f(x) = 2x - 1
g(x) = x^2 - 4
g(f(x)) = ?
[substitute the x of g(x) with f(x)]
g(x) = x^2 - 4
g(f(x)) = (2x - 1)^2 - 4
[solve]
[binomial * binomial = quadratic equation]
[use FOIL method (first, outer, inner, last)]
g(f(x)) = (2x - 1)(2x - 1) - 4
g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4
[combine like terms]
g(f(x)) = 4x^2 - 2x - 2x + 1 - 4
g(f(x)) = 4x^2 - 4x - 3