Answer:
The two points solutions to the system of equations are: (2, 3) and (-1,6)
Step-by-step explanation:
These system of equations consists of a parabola and a line. We need to find the points at which they intersect:
![x^2-2x+3=-x+5\\x^2-2x+x+3-5=0\\x^2-x-2=0\\(x-2)(x+1)=0](https://tex.z-dn.net/?f=x%5E2-2x%2B3%3D-x%2B5%5C%5Cx%5E2-2x%2Bx%2B3-5%3D0%5C%5Cx%5E2-x-2%3D0%5C%5C%28x-2%29%28x%2B1%29%3D0)
Since we were able to factor out the quadratic expression, we can say that the x-values solution of the system are:
x = 2 and x = -1
Now, the associated y values we can get using either of the original equations for the system. We pick to use the linear equation for example:
when x = 2 then ![y=-(2)+5=3](https://tex.z-dn.net/?f=y%3D-%282%29%2B5%3D3)
when x= -1 then ![y=-(-1)+5=6](https://tex.z-dn.net/?f=y%3D-%28-1%29%2B5%3D6)
Then the two points solutions to the system of equations are: (2, 3) and (-1,6)
Refer to the attached image.
Let the height of the Empire State Building = BC = 'x'
John is standing at distance from Empire State Building = AB = 1 mile
The angle of elevation = 11°
In triangle ABC,
Consider ![\tan 11^{\circ}= \frac{Perpendicular}{Base}](https://tex.z-dn.net/?f=%20%5Ctan%2011%5E%7B%5Ccirc%7D%3D%20%5Cfrac%7BPerpendicular%7D%7BBase%7D%20)
![\tan 11^{\circ}= \frac{BC}{AB}](https://tex.z-dn.net/?f=%20%5Ctan%2011%5E%7B%5Ccirc%7D%3D%20%5Cfrac%7BBC%7D%7BAB%7D%20)
![\tan 11^{\circ}= \frac{x}{1}](https://tex.z-dn.net/?f=%20%5Ctan%2011%5E%7B%5Ccirc%7D%3D%20%5Cfrac%7Bx%7D%7B1%7D%20)
![0.194= \frac{x}{1}](https://tex.z-dn.net/?f=%200.194%3D%20%5Cfrac%7Bx%7D%7B1%7D%20)
x = 0.194 mile
Since 1 mile =5280 feet
So, x = ![0.194 \times 5280](https://tex.z-dn.net/?f=%200.194%20%5Ctimes%205280%20)
= 1024.32 feet.
So, the height of the Empire State Building is 1024.32 feet.
The area of the circle is found by multiplying the value of PI by the radius raised to the power of 2
the circumference of a circle can be found in 2 ways. If you know the diameter of the circle multiply that by the value of PI. If the radius of the circle is known multiply that by 2 then multiply that by the value of PI.
The information needed is what value of PI to use and either the radius or diameter of the circle.
The circumference is the distance around the circle , so you would want to know the circumference to determine the number of rotations a tire makes.
4x + 2y = 8
When x = -2: 4x + 2y = 8
4(-2) + 2y = 8
-8 + 2y = 8
+ 8 + 8
2y = 16
2 2
y = 8
(x, y) = (-2, 8)
When x = 1: 4x + 2y = 8
4(1) + 2y = 8
4 + 2y = 8
- 4 - 4
2y = 4
2 2
y = 2
(x, y) = (1, 2)
When x = 3: 4x + 2y = 8
4(3) + 2y = 8
12 + 2y = 8
- 12 - 12
2y = -4
2 2
y = -2
(x, y) = (3, -2)
Answer:
The original bill (without the added charge) is 56.00
Step-by-step explanation:
10% was added to the bill and that made it 61.60
So 61.60 = 110% of the original bill.
If the original amount was x, then
61.60 = 1.10x
x = 61.60/1.10
x = 56.00