They are asking us to find another 'family' of linear functions. This time, they are asking that 'f(2) = 1' be true for any f(x) in the family. Because we are now provided with a point and no slope, it would be best to use a point-slope form definition. (If we use slope-intercept, we would end up with an unknown intercept and nothing to do about it!)
So, our point would be (2,1). The slope will remain as a variable.
<span>f(x)−f(<span>x1</span>)=m(x−<span>x1</span>)</span>
<span>f(x)−1=m(x−2)</span>
<span>f(x)=m(x−2)+1</span>
If you check, x=2, f(x) will always equal 1, so we have found the correct function family that satisfies the given information.They want you to define a 'family' of linear functions and they give you only a slope, so we are going to have a set of functions in the form
<span>f(x)=mx+b;m=2</span>
<span>f(x)=2x+b</span><span>
This function, "f(x) = 2x + b," can represent any linear function given some y-intercept 'b', so this will be sufficient for first part of our answer. Then, we are asked to graph a few functions of the family. So, we can choose any values for 'b' that we want and graph these on the xy-plane. I would recommend choosing b values close to 0 for ease of graphing. So, b=1, b=0, and b=-1 should be sufficient (they really are not clear about 'how many'). I assume you know how to graph them, but I would be glad to show you how if you are not certain.
</span> We know that to meet the requirements of BOTH parts, it has to be a function of slope 2 and value of f(2) = 1. Well, we already have a function that defines the f(2)=1 is true part, and if we substitute m=2 into that family, then we will have a function of slope 2.
<span><span>f(x)=(2)(x−2)+1=2x−4+1=2x−3</span></span>
Answer:
10
Step-by-step explanation:
first time they spent 11
2nd time was 1 dollar less
since 1 burrito is 2 dollars 3 is 6
and the 4 tacost were 4 dollars
I might be wrong
Answer:
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
Considering the 16 oz jar,
h = 7 inches
Diameter = 5 inches
Radius = diameter/2 = 5/2
r = 2.5 inches
Volume = 3.14 × 2.5² × 7 = 137.375 inches³
Considering the 29 oz jar,
h = 7.5 inches
Diameter = 5.25 inches
Radius = diameter/2 = 5.25/2
r = 2.625 inches
Volume = 3.14 × 2.625² × 7.5 = 162.27 inches³
1) If the cost is directly proportional to volume, then
If 137.375 inches³ cost $1.6
then 162.27 inches³ should cost
(162.27 × 1.6)/137.375 = $1.89
The price of the larger jar would be $1.89
2) If the cost is directly proportional to weight, then
If 16 oz cost $1.6, then
29 oz would cost
(29 × 1.6)/16 = $2.9
The price of the larger jar would be $2.9
C = 0.3*-2.7 = -0.81
Hope it helps:)