<span>The sum of two numbers is 50. The smaller number is 18 less than the larger number. What are the numbers?
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Equations:
x + y = 50
x = y - 18
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Add and solve for "x"::
2x = 32
x = 16
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Solve for "y"::
16 + y = 50
y = 34
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Hope I helped!
~Tomas</span>
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:
The location of the point is between Quadrant II and Quadrant III
Step-by-step explanation:
we know that
The abscissa refers to the x-axis and ordinate refers to the y-axis
so
in this problem we have
the coordinates of the point are 
see the attached figure to better understand the problem
The location of the point is between Quadrant II and Quadrant III
<h3>
Answer: Choice A</h3>
Domain = (a,b]
Range = [mc + n,md + n)
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Explanation:
The domain stays the same because we still have to go through f(x) as our first hurdle in order to get g(x).
Think of it like having 2 doors. The first door is f(x) and the second is g(x). The fact g(x) is dependent on f(x) means that whatever input restrictions are on f, also apply on g as well. So going back to the "2 doors" example, we could have a problem like trying to move a piece of furniture through them and we'd have to be concerned about the f(x) door.
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The range will be different however. The smallest value in the range of f(x) is y = c as it is the left endpoint. So the smallest f(x) can be is c. This means the smallest g(x) can be is...
g(x) = m*f(x) + n
g(x) = m*c + n
All we're doing is replacing f with c.
So that means mc+n is the starting point of the range for g(x).
The ending point of the range is md+n for similar reasons. Instead of 'c', we're dealing with 'd' this time. The curved parenthesis says we don't actually include this value in the range. A square bracket means include that value.
