Answer:
Paula = 4 hours
Roberto = 12 hours
Step-by-step explanation:
Time taken by Paula = x
Time taken by Roberto = x +. 8
Paula's rate = 1/x
Roberto's rate = 1/(x + 8)
Combined rate = 1/3
Time it takes each if them working alone ;
Paula's rate + Roberto's rate = combined rate
1 /x + 1 / (x +8) = 1/3
Take the L. C. M
((x+8) + x) / x(x+8) = 1/3
(2x + 8) / x(x + 8) = 1/3
3(2x + 8) = x(x + 8)
6x + 24 = x² + 8x
x² + 8x - 6x - 24 = 0
x² + 2x - 24 = 0
Solving the quadratic equation :
x² + 6x - 4x - 24 = 0
x(x + 6) - 4(x + 6) = 0
(x - 4) = 0 or (x + 6) = 0
x = 4 or x = - 6
Time taken cannot be negative
Hence, x = 4
Hence, working alone, it takes ;
Time taken by Paula = 4
Time taken by Roberto = 4 + 8 = 12
Answer:
The answer to your question is the letter D. 19.5 u²
Step-by-step explanation:
Process
1.- Calculate the Area of the rectangle ABCD
Area of a rectangle = base x height
= (4 + 5) x 3
= 9 x 3
= 27 u²
2.- Calculate the area of the large triangle
Area of a triangle = base x height/2
-Substitution
Area of a triangle = (4 + 5) x 3/2
-Simplification
Area of a triangle = 9 x 3/2
-Result
Area of a triangle = 13.5 u²
3.- Calculate the area of the small triangle
Area of the triangle = 4 x 3/2
Area of the triangle = 6 u²
4.- Sum up the area of the triangles
Shaded area = 13.5 + 6 = 19.5 u²
To translate a function up or down you add a constant to the function...2 units downward means you must subtract 2 from the original equation...
g(x)=f(x)-2
g(x)=2x^2-8-2
g(x)=2x^2-10
The answer is d, (-2.5,0.75)
If you're looking for Sam's age, the equation is 2x+5=3x-1. When solved, you get 6. Sam is 6.
