Answer:
700%
Step-by-step explanation:
The price increased from $0.30 to $2.40. What is the rate of increase, in percentage?
We can use the formula shown below:
![\frac{New-Old}{Old}*100](https://tex.z-dn.net/?f=%5Cfrac%7BNew-Old%7D%7BOld%7D%2A100)
Where
New Price is 2.40 and the Old Price is 0.30
We substitute and calculate:
![\frac{New-Old}{Old}*100\\\frac{2.40-0.30}{0.30}*100\\=7*100\\=700](https://tex.z-dn.net/?f=%5Cfrac%7BNew-Old%7D%7BOld%7D%2A100%5C%5C%5Cfrac%7B2.40-0.30%7D%7B0.30%7D%2A100%5C%5C%3D7%2A100%5C%5C%3D700)
Hence,
Price increased 700%
Answer:
x = 159; y = 140
Step-by-step explanation:
a = 40
a + y = 180
y = 180 - 40
y = 140
b = 61
b = (180 - x) + a
61 = 180 - x + 40
x = 159
A= Pi*r(r+(squ root of h^2 + r^2))
Answer:
B) ![y=-(x-3)^{2}+2](https://tex.z-dn.net/?f=y%3D-%28x-3%29%5E%7B2%7D%2B2)
Step-by-step explanation:
We are given,
The graph of the parabola opens downwards.
This means that the leading co-efficient of the function will be negative.
So, options C and D are not possible.
Moreover, it is given that the graph cuts x-axis near
i.e.
= 1.5 and
i.e.
= 4.5.
i.e. At y=0, the value of x is near
and
.
A. So, in
, we put y =0.
i.e. ![(x+2)^{2}=2](https://tex.z-dn.net/?f=%28x%2B2%29%5E%7B2%7D%3D2)
i.e. ![x=-2\pm \sqrt{2}](https://tex.z-dn.net/?f=x%3D-2%5Cpm%20%5Csqrt%7B2%7D)
i.e. x = 0.68 and x = 3.41
We see that this does not crosses the x-axis at the given points.
So, option A is wrong.
B. Also, in
, we put y =0.
i.e. ![(x-3)^{2}=2](https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%3D2)
i.e. ![x=3\pm \sqrt{2}](https://tex.z-dn.net/?f=x%3D3%5Cpm%20%5Csqrt%7B2%7D)
i.e. x = 1.68 and x = 4.41.
Thus, this equation cuts the x-axis near the given points i.e. 1.5 and 4.5.
Hence, the equation of the given graph is
.
The formulas:
![\log_a (xy)=\log_a x + \log_a y \\ \log_a (\frac{x}{y})=\log_a x - \log_a y \\ \log_a (x^n)n \log_a x](https://tex.z-dn.net/?f=%5Clog_a%20%28xy%29%3D%5Clog_a%20x%20%2B%20%5Clog_a%20y%20%5C%5C%0A%5Clog_a%20%28%5Cfrac%7Bx%7D%7By%7D%29%3D%5Clog_a%20x%20-%20%5Clog_a%20y%20%5C%5C%0A%5Clog_a%20%28x%5En%29n%20%5Clog_a%20x)
Expand the expression:
![\log_b (\frac{m^2n}{p})=\log_b m^2 + \log_b n - \log_b p= 2 \log_b m+\log_b n - \log_b p](https://tex.z-dn.net/?f=%5Clog_b%20%28%5Cfrac%7Bm%5E2n%7D%7Bp%7D%29%3D%5Clog_b%20m%5E2%20%2B%20%5Clog_b%20n%20-%20%5Clog_b%20p%3D%202%20%5Clog_b%20m%2B%5Clog_b%20n%20-%20%5Clog_b%20p)
Plug the values into the expression: