Answer: The length of the rectangle is 35 in.
The width of the rectangle is 28 in.
_________________________________________________________
Explanation:
_________________________________________________________
The formula for the area, "A", of a rectangle:
Area (A) = length (L) * width (w) ;
that is: " A = L * w " ;
A = 980 in² (given);
ratio of the length to the width is: " 5 : 4 " (given);
→ Find the length (L) and the width (w).
_________________________________________________________
→ 980 in² = (5x) * (4x) ;
in which: " 980 in² " is the area of the triangle;
" 5x" = the length (L) of the rectangle, for which we shall solve;
" 4x" = the width (w) of the rectangle, for which we shall solve.
_______________________________________________________
If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ;
_______________________________________________________
→ 980 in² = (5x) * (4x) ;
↔ (5x) * (4x) = 980 in² ;
→ (5x) * (4x) = (5) * (4) * (x) * (x) = 20 * x² = 20x² ;
→ 20x² = 980 ;
Divide each side by "10" ; by canceling out a "0" on each side of the equation:
→ 2x² = 98 ;
Now, divide each side of the equation by "2" ;
→ 2x² / 2 = 98 / 2 ;
to get:
→ x² = 49 ;
Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ ⁺√(x²) = √49 ;
to get:
→ x = 7 ;
______________________________________________________
Now, we can solve for the "length" and the "width" ;
→ The length is: "5x" ;
5x = 5(7) = " 35 in " ;
______________________________________________________
→ The width is: "4x" ;
4x = 4(7) = "28 in."
______________________________________________________
Let us check our answer:
→ A = L * w ;
→ 980 in² = ? 35 in. * 28 in. ?? ;
Using a calculator: "35 * 28 = 980" . Yes! ;
____________________________________________________
{ Also note: " in * in = in² " ? Yes! } .
____________________________________________________
Answer:
THE FUNCTION IS ALWAYS INCREASING.
Complete question: The graph of f(x)= power of 3√x + 8 is shown.
Step-by-step explanation:
See attachment for the missing graph.
when x = -16 ; y = -2
when x = -12 ; y = -1.5
when x = -8 ; y = 0
when x = -6 ; y = 1.25
when x = 0 ; y = 2
when x = 6 ; y = 2.5
As the value of x increases, so does the value of y. Thus, the function is always increasing.
Answer:
A
Step-by-step explanation:
Steps to take to determine the answer
- Because the length is in yards, it has to be converted to foot
- Find the area of the patio using the length and width measured in foot
- Determine the area of the square brick
- Multiply the cost of the brick by the area
1 yards = 3 foot
5 x 3 = 15 foot
Area of a rectangle = length x breadth
15 x 10 = 150 ft^2
Cost = 150 x 4 = $600
