9514 1404 393
Answer:
see attached
Step-by-step explanation:
Most of this exercise is looking at different ways to identify the slope of the line. The first attachment shows the corresponding "run" (horizontal change) and "rise" (vertical change) between the marked points.
In your diagram, these values (run=1, rise=-3) are filled in 3 places. At the top, the changes are described in words. On the left, they are described as "rise" and "run" with numbers. At the bottom left, these same numbers are described by ∆y and ∆x.
The calculation at the right shows the differences between y (numerator) and x (denominator) coordinates. This is how you compute the slope from the coordinates of two points.
If you draw a line through the two points, you find it intersects the y-axis at y=4. This is the y-intercept that gets filled in at the bottom. (The y-intercept here is 1 left and 3 up from the point (1, 1).)
To solve this problem, let us first assign some
variables. Let us say that:
x = pigs
y = chickens
z = ducks
From the problem statement, we can formulate the
following equations:
1. y + z = 30 --->
only chicken and ducks have feathers
2. 4 x + 2 y + 2 z = 120 --->
pig has 4 feet, while chicken and duck has 2 each
3. 2 x + 2 y + 2 z = 90 --->
each animal has 2 eyes only
Rewriting equation 1 in terms of y:
y = 30 – z
Plugging this in equation 2:
4 x + 2 (30 – z) + 2 z = 120
4 x + 60 – 2z + 2z = 120
4 x = 120 – 60
4 x = 60
x = 15
From the given choices, only one choice has 15 pigs. Therefore
the answers are:
She has 15 pigs, 12 chickens, and 18 ducks.
The width of the pool is 10 feet.
<h3>What is area of rectangle?</h3>
The area of rectangle is product of length and breadth.
Let the width be x.
length = 24 + 2x. and breadth = 12 + 2x
We know, area= 1408 ft².
(12 + 2x)(24 + 2x) = 1408
12*24 + 12*2x + 24*2x + (2x)² = 1408
288 + 72x + 4x² = 1408
4x² + 72x + 288 - 1408 = 0
4x² + 72x - 1120 = 0
x² + 18x - 280 = 0
x² - 10x + 28x - 280 = 0
x(x - 10) + 28(x - 10) = 0
(x - 10)(x + 28) = 0
So, x=10, -28.
Hence, the width be 10 feet.
Learn more about this concept here:
brainly.com/question/26638297
#SPJ1
Answer:
A 5
Step-by-step explanation:
Parts on the left have the same ratio as parts on the right.
... x/(x+5) = (x -2)/(x +1)
Multiplying by (x+5)(x+1), we get
... x(x +1) = (x -2)(x +5)
... x² +x = x² +3x -10 . . . . eliminate parentheses
... 0 = 2x -10 . . . . . . . . . . subtract x²+x
... 0 = x -5 . . . . . . . . . . . . divide by 2
... 5 = x . . . . . . . . . . . . . . . add 5
