Answer:
Our equation is:
y = f(x) = 2.5*x
The domain is the set of the values of x.
The range is the set of the values of y.
They must sell between 55 and 60 candy grams to meet their goal.
If we assume these as restrictions for the domain, then the minimum value of x is 55, and the maximum value of x is 60.
Then the domain is:
D: 55 ≤ x ≤ 60.
Now that we know the domain, we can find the range.
As our equation is linear with a positive coefficient, the minimum in the range will coincide with the minimum in the domain, then we have:
y = 2.5*55 = 137.5
And the maximum will coincide with the maximum in the domain:
y = 2.5*60 = 150.
Then the range is:
y = 137.5 ≤ y ≤ 150
Answer:
4
Step-by-step explanation:
This situation has two unknowns - the total number of half dollars and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.
- h+q=31 is an equation representing the total number of coins
- 0.50h+0.25q=11 is an equation representing the total value in money based on the number of coin. 0.50 and 0.25 come from the value of a half dollar and quarter individually.
We write the first equation in terms of q by subtracting it across the equal sign to get h=31-q. We now substitute this for h in the second equation.
0.50(31-q)+0.25q=11
15.5-0.50q+0.25q=11
15.5-0.25q=11
After simplifying, we subtract 15.5 across and divide by the coefficient of q.
-0.25q=-4.5
q=4
We now know of the 31 coins that 4 are quarters.
Answer:
For a point defined bt a radius R, and an angle θ measured from the positive x-axis (like the one in the image)
The transformation to rectangular coordinates is written as:
x = R*cos(θ)
y = R*sin(θ)
Here we are in the unit circle, so we have a radius equal to 1, so R = 1.
Then the exact coordinates of the point are:
(cos(θ), sin(θ))
2) We want to mark a point Q in the unit circle sch that the tangent has a value of 0.
Remember that:
tan(x) = sin(x)/cos(x)
So if sin(x) = 0, then:
tan(x) = sin(x)/cos(x) = 0/cos(x) = 0
So tan(x) is 0 in the points such that the sine function is zero.
These values are:
sin(0°) = 0
sin(180°) = 0
Then the two possible points where the tangent is zero are the ones drawn in the image below.
Answer:
The common difference (or common ratio) = 0.75
Step-by-step explanation:
i) let the first term be 
= 80
ii) let the second term be 
= . r = 80 × r = 60 ∴ r = 
= 0.75
iii) let the third term be 
= . r = 60 × r = 45 ∴ r = 
= 0.75
iv) let the fourth term be 
= . r = 45 × r = 33.75 ∴ r = 
= 0.75
Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.
Answer:
5−4+4=16+4
Step-by-step explanation:
