Answer:
<h2>x > -5</h2>
Step-by-step explanation:
-5(x + 7) < -10 <em>use the distributive property </em><em>a(b + c) = ab + ac</em>
(-5)(x) + (-5)(7) < -10
-5x - 35 < -10 <em>add 35 to both sides</em>
-5x < 25 <em>change the signs</em>
5x > - 25 <em>divide both sides by 5</em>
x > -5
This chart represents a proportional relationship. The rate of change will be 4.
<h3>What is the constant of proportionality?</h3>
Firstly, there is a proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called the constant of proportionality.
Given;
x y
1 4
2 8
3 12
4 16
Here, x = ky
put the first value
k = 1/4
This chart represents a proportional relationship.
So the rate of change will be

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Answer:
x = 500 yd
y = 250 yd
A(max) = 125000 yd²
Step-by-step explanation:
Let´s call x the side parallel to the stream ( only one side to be fenced )
y the other side of the rectangular area
Then the perimeter of the rectangle is p = 2*x + 2* y ( but only 1 x will be fenced)
p = x + 2*y
1000 = x + 2 * y ⇒ y = (1000 - x )/ 2
And A(r) = x * y
Are as fuction of x
A(x) = x * ( 1000 - x ) / 2
A(x) = 1000*x / 2 - x² / 2
A´(x) = 500 - 2*x/2
A´(x) = 0 500 - x = 0
x = 500 yd
To find out if this value will bring function A to a maximum value we get the second derivative
C´´(x) = -1 C´´(x) < 0 then efectevly we got a maximum at x = 500
The side y = ( 1000 - x ) / 2
y = 500/ 2
y = 250 yd
A(max) = 250 * 500
A(max) = 125000 yd²
Answer:
y = 5x-1
Step-by-step explanation:
parallel lines have the same slope.
y intercept: -1
slope: 5
- 1 is the same as +-1
so, y = 5x-1
Answer:
There are 25 students in the class.
Step-by-step explanation:
Let x be the number of students in the class
12% failed and the number of students is 3
x*12% = 3
x*.12 = 3
Divide each side by .12
x * .12 /.12 = 3/.12
x =25
There are 25 students in the class