Answer:
w ≥ 6
l ≥ 11
Step-by-step explanation:
The perimeter of a rectangle is equal to P = 2l+2w where l=length and w=width. Here the length is 5 feet longer than the width or 5+w. This means the width is w. Substitute P = 34, l=5+w and w into the perimeter equation. Then solve for w.
34 ≤ 2*(5+w) + 2w
34 ≤ 10+2w+2w
34 ≤ 10+4w
24 ≤ 4w
6 ≤ w
This means the width must be at least 6 so the solution is w ≥ 6.
To find the length substitute 6 into l ≤ 5+w.
l ≤ 5 + 6
l ≤ 11
The length is l ≥ 11.
A = (1/2) b * h
h = b - 5
42 = (1/2) * b * (b - 5)
42 = (1/2) * b^2 - 5b
multiply both sides by 2 to clear the fraction (1/2)
2(42) = 2(1/2) *b^2 - 5b
84 = b^2 -5b
Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero.
b^2 - 5b - 84 = 0
Now factor.
(b - 12)(b + 5) = 0
b - 12 = 0; b = 12
b + 5 = 0; b = -5
You can't have a negative length so the answer is 12m
To check the answer:
A = (1/2) * 12* 7
A = 42 m^2
Answer:
y = -3x -4
Step-by-step explanation:
A perpendicular line has a slope that is the negative reciprocal of that of the given line. When the equation starts out in standard form, a line with negative reciprocal slope can be written by swapping the x- and y-coefficients and negating one of them.
The given x- and y-coefficients have the ratio 1:-3, so we can use the coefficients 3 and 1 for our purpose.
The usual process of making the line go through a given point can be used. That is, we can translate the line from the origin to the desired point by subtracting the point coordinates from x and y. Then we have ...
3(x+3) +(y-5) = 0
__
This is "an" equation. It is in no particularly recognizable form. It can be rearranged to the form y = mx + b:
3x +9 +y -5 = 0 . . . . . eliminate parentheses
y = -3x -4 . . . . . subtract terms that are not "y"
Answer:
Equations: 
number of chickens = 52
number of goats = 28
Step-by-step explanation:
Given: A small ranch has chickens and goats
Total number of heads = 80
Total number of legs = 216
To find: number of chickens and goats
To draw: the graph
Solution:
Let x denotes number of chickens and y denotes number of goats.
According to the question,

From (i), put
in (ii)

Put
in equation (i)

So,
number of chickens = 52
number of goats = 28
Use multipliers:
The normal price the shop would sell the racquet for is:
1.6 * 200 = 320
'1.6' is the multiplier that I got using the percentage. Multiplying a value by 1.6 is the same as increasing the value by 60%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the question, now we can use the multiplier 0.75 because we are are reducing the price by 25% (0.25 as a decimal), so:
320 * 0.75 = 240
And now we want just the profit so we take off how much it cost the shop to buy ($200): 240 - 200 = 40