a) The dimensions of original rectangle are length= 5 and width= 4.
b) The dimensions of new rectangle are length= 15 and width=8.
<u>Step-by-step explanation</u>:
- length of a rectangle = l
- width of a rectangle = w
- Perimeter of a rectangle = 2(l+w)
<u>Original rectangle</u> :
18 = 2(l+w)
18 = 2l + 2w ---------(1)
<u>New rectangle</u> :
46 = 2(3l+2w)
46 = 6l + 4w ---------(2)
<u>Solving the equations</u> :
Multiply (1) by 2 and subtract (2) from (1)
4l + 4w = 36
-(<u>6l + 4w = 46</u>)
<u>-2l = -10</u>
l = 10/2
length = 5 inches.
Substitute l=5 in (1)
18 = 2(5)+2w
18 = 10+2w
2w = 8
w = 8/2
width = 4 inches.
length of new rectangle = 3(l) = 3
5 = 15 inches.
width of new rectangle = 2(w) = 24 = 8 inches.
Answer:
a) 3 b) y = 3x + 11
Step-by-step explanation:
a)
In order to find the gradient (slope), find the change in y or change in x (rise/run).
-2 - 2 / 7 - (-5)
-2 - 2 / 7 + 5
-4/12 = -1/3
Now that we know the gradient of line AB is -1/3, take the opposite reciprocal of that to find the gradient perpendicular to line AB.
-1/3 ⇒ 3
b)
Take point C's values and the perpendicular gradient found earlier and substitute them into the point-slope form equation.
y - 5 = 3(x - (-2))
y - 5 = 3(x + 2)
y - 5 = 3x + 6
y = 3x + 11
Answer:
y-18=-6(x+3)
Step-by-step explanation:
y-y1=m(x-x1)
m=-6
y-18=-6(x-(-3))
y-18=-6(x+3)
Step-by-step explanation:
cost of an egg= 900/100= Rs.9
Total cost = 100×9=Rs.900
when 8 eggs broken, the eggs remained to sell is 92(100-8)
Total sales = 10.50×92=Rs.966
profit = total cost-total sales
profit =966-900= Rs.66
profit percentage =profit/total sales×100%
66/966×100%=6.832%
The brick will fall to the ground after 9 secs.
<h3>What are quadratic equations?</h3>
Given the equation for height as a function of time is h(t) = -16t2 + 1,296
The height of the brick on the ground is h(t) = 0. Substitute h(t) = 0 into the equation as shown:
Subtract 1296 from both sides
-16t² + 1,296 - 1296 = 0 - 1296
16t² = 1296
t² = 1296/16
t² = 81
t = 9secs
Hence the brick will fall to the ground after 9 secs.
Learn more on equations here: brainly.com/question/13763238
