well, if that function f(x) were to be continuos on all subfunctions, that means that whatever value 7x + k has when x = 2, meets or matches the value that kx² - 6 has when x = 2 as well, so then 7x + k = kx² - 6 when f(2)
![f(x)= \begin{cases} 7x+k,&x\leqslant 2\\ kx^2-6&x > 2 \end{cases}\qquad \qquad f(2)= \begin{cases} 7(2)+k,&x\leqslant 2\\ k(2)^2-6&x > 2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 7(2)+k~~ = ~~k(2)^2-6\implies 14+k~~ = ~~4k-6 \\\\\\ 14~~ = ~~3k-6\implies 20~~ = ~~3k\implies \cfrac{20}{3}=k](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cbegin%7Bcases%7D%207x%2Bk%2C%26x%5Cleqslant%202%5C%5C%20kx%5E2-6%26x%20%3E%202%20%5Cend%7Bcases%7D%5Cqquad%20%5Cqquad%20f%282%29%3D%20%5Cbegin%7Bcases%7D%207%282%29%2Bk%2C%26x%5Cleqslant%202%5C%5C%20k%282%29%5E2-6%26x%20%3E%202%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%207%282%29%2Bk~~%20%3D%20~~k%282%29%5E2-6%5Cimplies%2014%2Bk~~%20%3D%20~~4k-6%20%5C%5C%5C%5C%5C%5C%2014~~%20%3D%20~~3k-6%5Cimplies%2020~~%20%3D%20~~3k%5Cimplies%20%5Ccfrac%7B20%7D%7B3%7D%3Dk)
Answer:
Step-by-step explanation:
<u>Slope intercept form:</u>
<u>Use two points from the graph:</u>
<u>The first point is the y-intercept: </u>
<u>Find the slope using the slope formula:</u>
- m = (y2 - y1)/(x2 - x1)
- m = (-9 - (-8))/3 = -1/3
<u>The equation is:</u>
Answer Interest rate = 12.3%
The compound interest formula is given by:
Where
A = Future amount
P = Present amount (Principal amount)
r = Interest rate in decimal form
n = No. of times compounded per year
t = time in years.
We can say that if:
Present amount = P
Future amount = 3P
r = 12.3/100 = 0.123
n = 1
t = ?
Substitute the values in the formula of compound interest:
Taking log on both sides.
Round off to nearest option
t ≅ 9 years
Simultaneous Equations
2u + b = $110
4u + 3b = $268
(x2) 4u + 2b = $220
(x1) 4u + 3b = $268
<em />If both the matching coefficients are the same, we subtract equation 2 from equation 1
2b - 3b = -b
$220 - $268 = $-48
-b = -$48
b = $48
If you want to find out what a unicycle costs...
Substitute b = $48 into the first equation
2u + $48 = $110
Balance the equation, whatever happens on one side, happens on the other.
2u + $48 (-$48) = $110 (-$48)
2u = $62
2u(/2) = $62(/2)
u = $31
The answer is <span>D.∠3
If you use a proctor you can see they measure the same
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