12)
(intro) Slope is change in y divided by change in x (axes). Here, the y axis is depth and the x axis is hours. So, the slope is change in depth between any two points, divided by the change in hours between the same points. The slope of this line is half a foot depth divided by 2 hours.
a) So, the slope is 0.5 / 2 = 0.25, or 1/4.
b) The graph shows a constant rate of change because the line is straight (it increases at the same speed. If the line was curving, it would not be a constant rate of change).
c) Yes, because the line has a constant rate of change now.
<em><u>Step-by-step explanation:</u></em>
FIRST, we want to understand every property:
Associative Property: The associative property states that you can add or multiply regardless of how the numbers are grouped so (5 + 4) + 3 = 5 + (4 + 3)
Commutative Property: Commutative is the one that refers to moving stuff around so 3 + 2 = 2 + 3
Additive Inverse Property: This is the number that when added to the original number, equals 0 or it's the opposite of the number so 5 <- is the original number and -5 <- is the additive inverse.
Simplify: Is just to add like terms, and make the equation the simplest.
1. ORIGINAL EXPRESSION
2. Additive Inverse Property
3. Commutative property
4. Associative Property
5. Simplify
6. Simplify
Step-by-step explanation:
We have
First, 125 is a perfect cube because
and
x^3 is a perfect cube because
so we can use the difference of cubes identity
Let say we have two perfect cubes:
64 because 8×8×8=64
and 27 because 3×3×3=27 and let subtract
we know that
but using the difference of cubes identity we should get the same thing.
Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have
So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.
Back on to the topic,
we know that 5 is cube root of 125 and x is the cube root of x^3 so we have
<span>m = 4a + 2c
a = 25; c = 5
Replace a with 25. Replace c with 5.
Then evaluate the expression.
m = 4 * 25 + 2 * 5
m = 100 + 10
m = 110
Answer: 110 meatballs are needed.</span>
Answer:
4) y = 9
5) x = -1
6) y = -5x − 9
Step-by-step explanation:
4) x = 3 is a vertical line with an x-intercept of (3, 0). It has an undefined slope.
A perpendicular line to that will be y = a, which is a horizontal line with a y-intercept of (0, a) and a slope of 0. Since this line passes through (3, 9), the equation of the line must be y = 9.
5) The y-axis is x = 0. A parallel line that includes the point (-1, -2) is x = -1.
6) Parallel lines have the same slope, so:
y = -5x + b
To find the value of b (the y-intercept), plug in the point (-2, 1):
1 = -5(-2) + b
1 = 10 + b
b = -9
y = -5x − 9
