If it is a bunch of dots on a graph, then the answer will be the one that has two sets of dots on the same vertical line (the y axis). so if there are two dots right above and below eachother, that graph is the correct answer.
Answer:Its 8.24
Step-by-step explanation:
4 times 2.06 is 8.24 :}
Answer:
![A = 74.7^\circ](https://tex.z-dn.net/?f=A%20%3D%2074.7%5E%5Ccirc)
![B = 42.5^\circ](https://tex.z-dn.net/?f=B%20%3D%2042.5%5E%5Ccirc)
![C = 62.8^\circ](https://tex.z-dn.net/?f=C%20%3D%2062.8%5E%5Ccirc)
Step-by-step explanation:
Given
![A = (-1,2) \to (x_1,y_1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C2%29%20%5Cto%20%28x_1%2Cy_1%29)
![B = (2,8) \to (x_2,y_2)](https://tex.z-dn.net/?f=B%20%3D%20%282%2C8%29%20%5Cto%20%28x_2%2Cy_2%29)
![C = (4,1) \to (x_3,y_3)](https://tex.z-dn.net/?f=C%20%3D%20%284%2C1%29%20%5Cto%20%28x_3%2Cy_3%29)
Required
The measure of each angle
First, we calculate the length of the three sides of the triangle.
This is calculated using distance formula
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2)
For AB
![A = (-1,2) \to (x_1,y_1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C2%29%20%5Cto%20%28x_1%2Cy_1%29)
![B = (2,8) \to (x_2,y_2)](https://tex.z-dn.net/?f=B%20%3D%20%282%2C8%29%20%5Cto%20%28x_2%2Cy_2%29)
![d = \sqrt{(-1 - 2)^2 + (2 - 8)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28-1%20-%202%29%5E2%20%2B%20%282%20-%208%29%5E2)
![d = \sqrt{(-3)^2 + (-6)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28-3%29%5E2%20%2B%20%28-6%29%5E2)
![d = \sqrt{45](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B45)
So:
![AB = \sqrt{45](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B45)
For BC
![B = (2,8) \to (x_2,y_2)](https://tex.z-dn.net/?f=B%20%3D%20%282%2C8%29%20%5Cto%20%28x_2%2Cy_2%29)
![C = (4,1) \to (x_3,y_3)](https://tex.z-dn.net/?f=C%20%3D%20%284%2C1%29%20%5Cto%20%28x_3%2Cy_3%29)
![BC = \sqrt{(2 - 4)^2 + (8 - 1)^2](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%282%20-%204%29%5E2%20%2B%20%288%20-%201%29%5E2)
![BC = \sqrt{(-2)^2 + (7)^2](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%28-2%29%5E2%20%2B%20%287%29%5E2)
![BC = \sqrt{53](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B53)
For AC
![A = (-1,2) \to (x_1,y_1)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C2%29%20%5Cto%20%28x_1%2Cy_1%29)
![C = (4,1) \to (x_3,y_3)](https://tex.z-dn.net/?f=C%20%3D%20%284%2C1%29%20%5Cto%20%28x_3%2Cy_3%29)
![AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B%28-1%20-%204%29%5E2%20%2B%20%282%20-%201%29%5E2)
![AC = \sqrt{(-5)^2 + (1)^2](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B%28-5%29%5E2%20%2B%20%281%29%5E2)
![AC = \sqrt{26](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B26)
So, we have:
![AB = \sqrt{45](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B45)
![BC = \sqrt{53](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B53)
![AC = \sqrt{26](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B26)
By representation
![AB \to c](https://tex.z-dn.net/?f=AB%20%5Cto%20c)
![BC \to a](https://tex.z-dn.net/?f=BC%20%5Cto%20a)
![AC \to b](https://tex.z-dn.net/?f=AC%20%5Cto%20b)
So, we have:
![a = \sqrt{53](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7B53)
![b = \sqrt{26](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B26)
![c = \sqrt{45](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B45)
By cosine laws, the angles are calculated using:
![a^2 = b^2 + c^2 -2bc \cos A](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2%20-2bc%20%5Ccos%20A)
![b^2 = a^2 + c^2 -2ac \cos B](https://tex.z-dn.net/?f=b%5E2%20%3D%20a%5E2%20%2B%20c%5E2%20-2ac%20%5Ccos%20B)
![c^2 = a^2 + b^2 -2ab\ cos C](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20-2ab%5C%20cos%20C)
![a^2 = b^2 + c^2 -2bc \cos A](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2%20-2bc%20%5Ccos%20A)
![(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A](https://tex.z-dn.net/?f=%28%5Csqrt%7B53%7D%29%5E2%20%3D%20%28%5Csqrt%7B26%7D%29%5E2%20%2B%28%5Csqrt%7B45%7D%29%5E2%20-%202%20%2A%20%28%5Csqrt%7B26%7D%29%20%2B%28%5Csqrt%7B45%7D%29%20%2A%20%5Ccos%20A)
![53 = 26 +45 - 2 * 34.21 * \cos A](https://tex.z-dn.net/?f=53%20%3D%2026%20%2B45%20-%202%20%2A%2034.21%20%2A%20%5Ccos%20A)
![53 = 26 +45 - 68.42 * \cos A](https://tex.z-dn.net/?f=53%20%3D%2026%20%2B45%20-%2068.42%20%2A%20%5Ccos%20A)
Collect like terms
![53 - 26 -45 = - 68.42 * \cos A](https://tex.z-dn.net/?f=53%20-%2026%20-45%20%3D%20-%2068.42%20%2A%20%5Ccos%20A)
![-18 = - 68.42 * \cos A](https://tex.z-dn.net/?f=-18%20%3D%20-%2068.42%20%2A%20%5Ccos%20A)
Solve for ![\cos A](https://tex.z-dn.net/?f=%5Ccos%20A)
![\cos A =\frac{-18}{-68.42}](https://tex.z-dn.net/?f=%5Ccos%20A%20%3D%5Cfrac%7B-18%7D%7B-68.42%7D)
![\cos A =0.2631](https://tex.z-dn.net/?f=%5Ccos%20A%20%3D0.2631)
Take arc cos of both sides
![A =\cos^{-1}(0.2631)](https://tex.z-dn.net/?f=A%20%3D%5Ccos%5E%7B-1%7D%280.2631%29)
![A = 74.7^\circ](https://tex.z-dn.net/?f=A%20%3D%2074.7%5E%5Ccirc)
![b^2 = a^2 + c^2 -2ac \cos B](https://tex.z-dn.net/?f=b%5E2%20%3D%20a%5E2%20%2B%20c%5E2%20-2ac%20%5Ccos%20B)
![(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B](https://tex.z-dn.net/?f=%28%5Csqrt%7B26%7D%29%5E2%20%3D%20%28%5Csqrt%7B53%7D%29%5E2%20%2B%28%5Csqrt%7B45%7D%29%5E2%20-%202%20%2A%20%28%5Csqrt%7B53%7D%29%20%2B%28%5Csqrt%7B45%7D%29%20%2A%20%5Ccos%20B)
![26 = 53 +45 -97.67 * \cos B](https://tex.z-dn.net/?f=26%20%3D%2053%20%2B45%20-97.67%20%2A%20%5Ccos%20B)
Collect like terms
![26 - 53 -45= -97.67 * \cos B](https://tex.z-dn.net/?f=26%20-%2053%20-45%3D%20-97.67%20%2A%20%5Ccos%20B)
![-72= -97.67 * \cos B](https://tex.z-dn.net/?f=-72%3D%20-97.67%20%2A%20%5Ccos%20B)
Solve for ![\cos B](https://tex.z-dn.net/?f=%5Ccos%20B)
![\cos B = \frac{-72}{-97.67}](https://tex.z-dn.net/?f=%5Ccos%20B%20%3D%20%5Cfrac%7B-72%7D%7B-97.67%7D)
![\cos B = 0.7372](https://tex.z-dn.net/?f=%5Ccos%20B%20%3D%200.7372)
Take arc cos of both sides
![B = \cos^{-1}(0.7372)](https://tex.z-dn.net/?f=B%20%3D%20%5Ccos%5E%7B-1%7D%280.7372%29)
![B = 42.5^\circ](https://tex.z-dn.net/?f=B%20%3D%2042.5%5E%5Ccirc)
For the third angle, we use:
--- angles in a triangle
Make C the subject
![C = 180 - A -B](https://tex.z-dn.net/?f=C%20%3D%20180%20-%20A%20-B)
![C = 180 - 74.7 -42.5](https://tex.z-dn.net/?f=C%20%3D%20180%20-%2074.7%20-42.5)
![C = 62.8^\circ](https://tex.z-dn.net/?f=C%20%3D%2062.8%5E%5Ccirc)
.
Step-by-step explanation:The cost of an adult ticket to the show is $5.5
The cost of a student ticket to the show is $4.25
A family is purchasing 2 adult tickets and 3 student tickets. This means that the total cost of 2 adult tickets would be
2 × 5.5 = $11
It also means that the total cost of 3 student tickets would be
3 × 4.25 = $12.75
The total cost of 2 adult tickets and 3 student tickets would be
11 + 12.75 = $23.75
If the family pays $25, the exact amount of change they should receive is
25 - 23.75 = $1.25
Answer:
The last one
Step-by-step explanation:
x can only have one value whereas y can be constants like in last graph