Answer:
1. (9,6) 2. Find (15,0) on the x axis and trace up until you meet the line, then find the point on the y axis corresponding to that point
Step-by-step explanation:
1.'s explanation is 2.'s explanation but reversed
Answer:
26.5%
Step-by-step explanation:
All you have to do is subtract 64 - 37.5 which would get you to 26.5%. Hope this helps.
Answer:
a) OA = 1 unit
b) OB = 3 units
c) AB = √10 units
Step-by-step explanation:
<u>Given function</u>:
![g(x)=2^x](https://tex.z-dn.net/?f=g%28x%29%3D2%5Ex)
<h3><u>Part (a)</u></h3>
Point A is the y-intercept of the exponential curve (so when x = 0).
To find the y-value of Point A, substitute x = 0 into the function:
![\implies g(0)=2^0=1](https://tex.z-dn.net/?f=%5Cimplies%20g%280%29%3D2%5E0%3D1)
Therefore, A (0, 1) so OA = 1 unit.
<h3><u>Part (b)</u></h3>
If BC = 8 units then the y-value of Point C is 8.
The find the x-value of Point C, set the function to 8 and solve for x:
![\begin{aligned}f(x) & = 8 \\\implies 2^x & = 8\\2^x & = 2^3\\\implies x &= 3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%28x%29%20%26%20%3D%208%20%5C%5C%5Cimplies%202%5Ex%20%26%20%3D%208%5C%5C2%5Ex%20%26%20%3D%202%5E3%5C%5C%5Cimplies%20x%20%26%3D%203%5Cend%7Baligned%7D)
Therefore, C (3, 8) so Point B is (3, 0). Therefore, OB = 3 units.
<h3><u>Part (c)</u></h3>
From parts (a) and (b):
To find the length of AB, use the distance between two points formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}](https://tex.z-dn.net/?f=%5Ctextsf%7Bwhere%20%7D%28x_1%2Cy_1%29%20%5Ctextsf%7B%20and%20%7D%28x_2%2Cy_2%29%5C%3A%5Ctextsf%7Bare%20the%20two%20points.%7D)
Therefore:
![\implies \sf AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20AB%3D%5Csqrt%7B%28x_B-x_A%29%5E2%2B%28y_B-y_A%29%5E2%7D)
![\implies \sf AB=\sqrt{(3-0)^2+(0-1)^2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20AB%3D%5Csqrt%7B%283-0%29%5E2%2B%280-1%29%5E2%7D)
![\implies \sf AB=\sqrt{(3)^2+(-1)^2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20AB%3D%5Csqrt%7B%283%29%5E2%2B%28-1%29%5E2%7D)
![\implies \sf AB=\sqrt{9+1}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20AB%3D%5Csqrt%7B9%2B1%7D)
![\implies \sf AB=\sqrt{10}\:\:units](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20AB%3D%5Csqrt%7B10%7D%5C%3A%5C%3Aunits)
if we divide 107 by 11, we end up with a quotient of 9 and a remainder of 8.
the new mixed fraction will have the quotient upfront followed by a fraction, and the denominator will still be the same 11, but the numerator will be the remainder, namely
![\bf \cfrac{107}{11}\qquad \begin{cases} 107\div 11\\ \cline{1-1} \stackrel{quotient}{9}\\ \stackrel{remainder}{8} \end{cases}\qquad\implies \qquad 9\frac{8}{11}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B107%7D%7B11%7D%5Cqquad%20%5Cbegin%7Bcases%7D%20107%5Cdiv%2011%5C%5C%20%5Ccline%7B1-1%7D%20%5Cstackrel%7Bquotient%7D%7B9%7D%5C%5C%20%5Cstackrel%7Bremainder%7D%7B8%7D%20%5Cend%7Bcases%7D%5Cqquad%5Cimplies%20%5Cqquad%209%5Cfrac%7B8%7D%7B11%7D)