Answer:
Step-by-step explanation:
(f ° g)(18) is another way of writing f(g(18)) which is telling you to evaluate function g at an x value of 18, then take that answer and plug it in for x in the function. Like this:
g(18) = 18 - 9 so
g(18) = 9. Now take that 9 and plug it into the f function in place of x:
f(9) = -8(9) + 8 and
f(9) = -72 + 8 so
f(9) = -64
Answer:
Step-by-step explanation:
![y=a(1+r/c)^{ct}\\ \\ y=9000(1+.042/12)^{12t}\\ \\ y=9000(1.0035)^{12t}\\ \\ a)\ y=9000(1.0035)^{12(10)}=\$ 13687.61\\ \\ b)\ 15400=9000(1.0035)^{12t}\\ \\ 1.0035^{12t}=77/45\\ \\ 12t ln(1.0035)=ln(77/45)\\ \\ t=(ln(77/45))/(12ln(1.0035))\\ \\ t\approx 12.8\ years](https://tex.z-dn.net/?f=y%3Da%281%2Br%2Fc%29%5E%7Bct%7D%5C%5C%20%5C%5C%20y%3D9000%281%2B.042%2F12%29%5E%7B12t%7D%5C%5C%20%5C%5C%20y%3D9000%281.0035%29%5E%7B12t%7D%5C%5C%20%5C%5C%20a%29%5C%20y%3D9000%281.0035%29%5E%7B12%2810%29%7D%3D%5C%24%2013687.61%5C%5C%20%5C%5C%20b%29%5C%2015400%3D9000%281.0035%29%5E%7B12t%7D%5C%5C%20%5C%5C%201.0035%5E%7B12t%7D%3D77%2F45%5C%5C%20%5C%5C%2012t%20ln%281.0035%29%3Dln%2877%2F45%29%5C%5C%20%5C%5C%20t%3D%28ln%2877%2F45%29%29%2F%2812ln%281.0035%29%29%5C%5C%20%5C%5C%20t%5Capprox%2012.8%5C%20years)
Area of a circle is pi * radius² so:
1) Area = pi * 5²
= 25pi ≈ 78.54 yd²
2) Area = pi * 7²
= 49pi ≈ 153.94 cm²
Circumference is 2 * pi * radius so:
3) Circumference = 2 * pi * 10
= 20pi ≈ 62.83 mi
4) Circumference = 2 * pi * 3.3
= 6.6pi ≈ 20.73 in
Volume of a rectangular prism is length * width * height
5) Volume = 10 * 3 * 10
= 100 * 3
= 300 yd³
6) Volume = 5 * 7 * 5
= 35 * 5
= 175 in³
Not completely sure on the triangular prisms though. I'm almost certain the formula is 1/2 * height * base 1 * base 2 though
Answer:
To get the new scaled copy length and width just multiply by seven (2x7 & 3x7)
New length would be 14 because it's "seven times" the original size
New width would be 21
Step-by-step explanation:
1.) 14 and 21
2.) 14 divided by 7 will give you 2
and 21 divided by 7 will give you 3
The answer for question 2 would be to divide your new answers (21 and 14) by the scaled factor of 7.
ANSWER
![x + y = 60](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2060)
EXPLANATION
Method 1
Vertically opposite angles are equal, therefore
![3x + 55 = 85](https://tex.z-dn.net/?f=3x%20%2B%2055%20%3D%2085)
This implies that,
![3x = 85 - 55](https://tex.z-dn.net/?f=3x%20%3D%2085%20-%2055)
We simplify to get,
![3x = 30](https://tex.z-dn.net/?f=3x%20%3D%2030)
Dividing through by 3 gives,
![x = 10](https://tex.z-dn.net/?f=x%20%3D%2010)
Also,
![2y - 5 = 95](https://tex.z-dn.net/?f=2y%20-%205%20%3D%2095)
This implies that,
![2x = 95 + 5](https://tex.z-dn.net/?f=2x%20%3D%2095%20%2B%205)
We simplify the right hand side to get,
![2x = 100](https://tex.z-dn.net/?f=2x%20%3D%20100)
We divide both sides both sides by 2 to get,
![x = 50](https://tex.z-dn.net/?f=x%20%3D%2050)
![x + y = 50 + 10](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2050%20%2B%2010)
![x + y = 60](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2060)
Method 2
Angles on straight line sums to 180°.
![2y-5+85=180](https://tex.z-dn.net/?f=2y-5%2B85%3D180)
This implies that,
![2y+80=180](https://tex.z-dn.net/?f=2y%2B80%3D180)
![2y=180-80](https://tex.z-dn.net/?f=2y%3D180-80)
![2y=100](https://tex.z-dn.net/?f=2y%3D100)
![y=50](https://tex.z-dn.net/?f=y%3D50)
Also,
![3x+55+95=180](https://tex.z-dn.net/?f=3x%2B55%2B95%3D180)
![3x+150=180](https://tex.z-dn.net/?f=3x%2B150%3D180)
![3x=180-150](https://tex.z-dn.net/?f=3x%3D180-150)
![3x=30](https://tex.z-dn.net/?f=3x%3D30)
![x=10](https://tex.z-dn.net/?f=x%3D10)
![x+y=50+10](https://tex.z-dn.net/?f=x%2By%3D50%2B10)