Answer:
1- a. The lines 2x+1 and 2x-3 do not intersect because even though they start at different y intercepts, the slope of the lines (2) is the same, so they will never intersect each other.
1- b. You must set both of the equations equal to each other
2x - 3 = 2x +1 then solve for x
x=0 then plug it back in to the equation
2(0) -3 = -3
2(0) + 1 = 1
1- c. They relate to each other because since the lines do not intersect each other, then they will not have any values that are equal to each other, as shown in problem 1-b..
Step-by-step explanation:
Answer: s= -8
Step-by-step explanation:
The gradient of the ski slope can ge used as the slope (literally) of a line equation:
y = mx + b,
where m is the slope and b the y-intercept (the value of y when x = 0).
The first slope would be y = -(1/3)x + b.
The slope is (-1/3) since the ski run is headed downhill. The second ski slope is assumed to have the same gradient ("two parallel straight ski slopes").
y' = -(1/3)x' + b
We may assume that b is the same for both slopes - they start and end at the same point.
We can find b by using the given point (2,-3):
y' = -(1/3)x' + b
-3 = -(1/3)(2) + b
-3 = -(2/3) + b [Add -(2/3) to both sides: (-3 + 2/3 = -9/3 + 2/3 = -7/3]
-7/3 = b
b = -(7/3)
The second ski slope, y', thus has the equation
y' = (1/3)x' -(7/3)
We want the value of s in (s, -5).
y' = (1/3)x' -(7/3)
-5 = (1/3)s -(7/3)
(1/3)s = -5 +(7/3) [-15/3 + 7/3 = -8/3]
(1/3)s = -(8/3) [Multiply both dies by 3]
s = -(24/3)
s = -8
<u><em>Part 1:</em></u><u>Before we begin, you need to remember the following rule:</u>
<u>The given expression is:</u>
Since the base is the same in both numerator and denominator, we can apply the above rule. <u>This means that:</u>
= 12¹⁻³ = 12⁻²
<u><em>Part 2:</em></u><u>Before we begin, you need to remember the following rule:</u>
x⁻ᵃ =
Now, <u>from part 1</u>, we simplified the expression into 12⁻²
Since the power is negative, we can apply the above rule.
<u>This means that:</u>
12⁻² =
Hope this helps :)
Answer:
Option c
Step-by-step explanation:
-7 + (19 + 5) = (-7 + 19) + 5
LHS = -7 + (19+5)
= -7 + 24
= 17
RHS = (-7 + 19) + 5
= 12 + 5
= 17
LHS = RHS
associative property of addition: When three or more numbers are added, the result remains same regardless how the numbers are grouped
Very easy!
6 people= 12 servings so 1 person= 2 servings
We have 112 people so we need 112 x 2= 224 servings
So she will make 224 servings with an 8 servings pan, 224/8= 28 pans.
The minimum number of pans she need in order to serve 112 people is 28 pans!