Step-by-step explanation:
The length of a rectangle, l = 3 units
The breadth of a rectangle, b = 4 units
Nancy needs to increase both the length and the width of the rectangle by 2 units.
The area of a rectangle is given by
A = length(l) × breadth(b)
Here,
A = 3 × 4
= 12 unit²
If both length and width of the rectangle increase by 2 units,
New length = (4+2) = 6 units
New width = (3+2) = 5 units
New area = 6 × 5 = 30 unit²
Hence, new area becomes 30 unit².
Answer:
D; 5pi/3 units
Step-by-step explanation:
Here, we want to find the period of the function;
y = 3/2 cot (3/5x) + 5
By definition, the period of a function is the interval between two matching points in the function.
Let’s say it is the distance between two peaks, crests, etc on a function.
To find the value of the period. We shall standardize the function.
What this means is that we shall be writing the function in the standard form.
The standard form is as follows;
f(x) = A trig(Bx -C) + D
Where trig refers to the accompanying trigonometric function in question.
Comparing this standard form with our question, we can see that;
A is 3/2
B is 3/5
C is 0
D is 5
Now for cot and tan functions, we shall need to divide pi by the absolute value of B
Thus we have; pi divided by 3/5 which gives 5pi/3 units
Your fraction is:
![13 \frac{12}{11}](https://tex.z-dn.net/?f=%2013%20%5Cfrac%7B12%7D%7B11%7D%20%20)
The whole number is 13. In the fraction, the numerator(top number) is 12 and the denominator(bottom number) is 11. When the numerator is greater than the denominator, it is called an improper fraction.
- To simplify it, subtract the denominator from the numerator and leave the remainder as the numerator and keep the denominator. Then add 1 to the whole number.
First subtract:
![\frac{12}{11} - \frac{11}{0} = \frac{1}{11}](https://tex.z-dn.net/?f=%20%5Cfrac%7B12%7D%7B11%7D%20-%20%5Cfrac%7B11%7D%7B0%7D%20%20%3D%20%5Cfrac%7B1%7D%7B11%7D%20%20)
Your new fraction is ![\frac{1}{11}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B11%7D%20%20)
Now add 1 to the whole number:
![13 + 1 = 14](https://tex.z-dn.net/?f=%2013%20%2B%201%20%3D%2014%20)
Add them together:
![14 + \frac{1}{11} = 14 \frac{1}{11}](https://tex.z-dn.net/?f=%2014%20%2B%20%5Cfrac%7B1%7D%7B11%7D%20%3D%2014%20%5Cfrac%7B1%7D%7B11%7D%20%20)
in simplest form is ![\bf 14 \frac{1}{11}](https://tex.z-dn.net/?f=%20%5Cbf%2014%20%5Cfrac%7B1%7D%7B11%7D%20%20)
Step-by-step explanation:
Given.
![3x+5y=3](https://tex.z-dn.net/?f=3x%2B5y%3D3)
![x+2y=0](https://tex.z-dn.net/?f=x%2B2y%3D0)
Take the second equation and subtract 2y to both sides.
![(x+2y)-2y=0-2y](https://tex.z-dn.net/?f=%28x%2B2y%29-2y%3D0-2y)
![x=-2y](https://tex.z-dn.net/?f=x%3D-2y)
Substitute x into the first equation and simplify.
![3x+5y=3](https://tex.z-dn.net/?f=3x%2B5y%3D3)
![3(-2y)+5y=3](https://tex.z-dn.net/?f=3%28-2y%29%2B5y%3D3)
![-6y+5y=3](https://tex.z-dn.net/?f=-6y%2B5y%3D3)
![-y=3](https://tex.z-dn.net/?f=-y%3D3)
Invert.
![y=-3](https://tex.z-dn.net/?f=y%3D-3)
Substitute Y into your second equation.
![x+2y=0](https://tex.z-dn.net/?f=x%2B2y%3D0)
![x+2(-3)=0](https://tex.z-dn.net/?f=x%2B2%28-3%29%3D0)
![x-6=0](https://tex.z-dn.net/?f=x-6%3D0)
Add -6 to both sides.
![(x-6)+6=0+6](https://tex.z-dn.net/?f=%28x-6%29%2B6%3D0%2B6)
![x=6](https://tex.z-dn.net/?f=x%3D6)
Answer:
(6, -3)
Answer:
p= 76
A=338
Step-by-step explanation:
Perimeter: 15+18+18+8+17=76
Area:
15x18=270+(8x17/2)
270+68=338