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! } .
____________________________________________________
42/12 = 3.5, 63/18 = 3.5, therefore we will be multiplying the last time by 3.5. 40x3.5= 140, and therefore, the number of pencils produced in 40 seconds is 140
Answer: D= 0.72
Step-by-step explanation: Because 0.18 times 4 is 0.72 miles.
Answer: (-0.4, 6.8)
The graph is attached
Step-by-step explanation:
We can find the axis of symmetry using the formula x = -b/2a
x = - -4/2(-5)
x = 4/-10
x = 0.04
Substitute for x and calculate y
y = 
y = 6.8
Answer:
0
Step-by-step explanation:
First, you need to try to get rid of the ().
To do this:
15 * 3 and 15 * x
This makes 45 and 15x after the = , so the formula is now:
15x + 45 = 45 + 15x
Now get the 15x to the left side. When a number switches sides, it becomes negative when positive and positive when negative. So in this case 15x will become -15x and the 45(on the left) becomes - 45
15x - 15x = 45 - 45
Answer: 0
