Answer:
(22, 9)
Step-by-step explanation:
The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller). I'll call the two integers a and b.
a - b = 13 a + b² = 103
<u> +b +b</u>
a = 13 + b plug this into the second equation
a + b² = 103
(13+b) + b² = 103 subtract 103 from both sides to get one side equal to zero
<u>-103 -103</u>
b² + b - 90 = 0 what factors (two numbers multiply) to -90 that also add up
to 1? The only two that work are -9 and 10.
(b-9)(b+10) = 0 so b-9 = 0 or b+10 = 0
<u>+9 +9</u> or <u>-10 -10</u>
b = 9 or b = -10 but both numbers must be positive
b = 9 and a = 13 + b so a = 13 + 9 = 22
(22, 9)
Answer:
Check step by step explanation
Step-by-step explanation:
a) Let x represent the amount of rides she takes, the 6 and 2.5 represent the amount of money required to enter
A(x) = 1.5x + 6
B(x) = 2x + 2.5
b) You can find this by making the 2 equations equal to each other and solving for x
1.5x + 6 = 2x + 2.5
3.5 = .5x
7 = x
7 rides make them equal cost
c) Plug in 5 for each of the equations and find out which one is cheaper
A(5) = 1.5 * 5 + 6
A(5) = $13.50
B(5) = 2 * 5 + 2.5
B(5) = $12.50
Carnival B is cheaper
Answer:
The simplest radical form of the cubic root is ![3x^2y^4\sqrt[3]{2x}](https://tex.z-dn.net/?f=3x%5E2y%5E4%5Csqrt%5B3%5D%7B2x%7D)
Step-by-step explanation:
Cube root of 54x^8y^12
That is:
![\sqrt[3]{54x^8y^12}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E8y%5E12%7D)
Can be simplified as:
![\sqrt[3]{54x^8y^12} = \sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E8y%5E12%7D%20%3D%20%5Csqrt%5B3%5D%7B54%7D%5Csqrt%5B3%5D%7Bx%5E8%7D%5Csqrt%5B3%5D%7By%5E12%7D)
We find each separate simplification, and multiply them:
Cubic root of 54:
So
![\sqrt[3]{54} = \sqrt[3]{2*3^3} = 3\sqrt[3]{2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54%7D%20%3D%20%5Csqrt%5B3%5D%7B2%2A3%5E3%7D%20%3D%203%5Csqrt%5B3%5D%7B2%7D)
Cubic root of x^8
![\sqrt[3]{x^8} = \sqrt[3]{x^6*x^2} = x^2\sqrt[3]{x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E8%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E6%2Ax%5E2%7D%20%3D%20x%5E2%5Csqrt%5B3%5D%7Bx%5E2%7D)
Cubic root of y^12
![\sqrt[3]{y^{12}} = y^4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7By%5E%7B12%7D%7D%20%3D%20y%5E4)
Multiplying all these terms:
![\sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12} = 3\sqrt[3]{2}(x^2\sqrt[3]{x^2})(y^4) = 3x^2y^4\sqrt[3]{2x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54%7D%5Csqrt%5B3%5D%7Bx%5E8%7D%5Csqrt%5B3%5D%7By%5E12%7D%20%3D%203%5Csqrt%5B3%5D%7B2%7D%28x%5E2%5Csqrt%5B3%5D%7Bx%5E2%7D%29%28y%5E4%29%20%3D%203x%5E2y%5E4%5Csqrt%5B3%5D%7B2x%7D)
The simplest radical form of the cubic root is
Answer:
-2
Step-by-step explanation:
use the slope formula 
, plug in points 
4/-2 and then reduce -2
Answer: XVW=36
Step-by-step explanation:
The external angle of triangle is equal to the sum of the 2 opposite interior angles.
WXY is an external angle to the triangle and
XVW and VWX are the 2 opposite interior angles, thus
6x - 19 = +17+ 3x+2, that is
6x- 19 =4x +19 (Subtract 4x from both sides)
2x - 19 =19 (add 19 to both sides by 2)
x = 19
Hence
XVW = x + 17 = 19 + 17 = 36
