Answer:
a) 1/9 quarts
b) 1/3 quarts
Step-by-step explanation:
Gordon pours 4/9 quarts of milk from a pitcher equally into 4 mugs.
a. Find the amount of milk in each mug.
To solve the first part of this question, we can simply use the idea of proportion;
Let x be the amount of milk in 1 mug
4/9 quarts = 4 mugs
x = 1 mugs
We will cross multiply
4x = 4/9
To get the value of x, we will divide both-side of the equation by 4
4x/ 4 = 4/9 ÷ 4
(on the left hand- side of the equation, 4 will divide 4 leaving us with x)
x = 4/9 ÷ 4
( This ÷4 can be change to become × 1/4)
x = 4/9 × 1/4
(The 4 at the numerator will cancel out the 4 at the denominator leaving us with 1/9)
x = 1/9
Therefore the amount of milk in each mug is 1/9 quart
b.Find the amount of milk in 3 mugs
For this second part of the question, we can also use proportion to solve;
Let x be the amount of milk in 3 mugs
4/9 quarts = 4 mugs
x = 3 mugs
Cross multiply
4x = 3 × 4/9
(At the right-hand side of this equation 3 can divide 9 which will give us 3 )
4x = 1 × 4 /3
4x = 4/3
We can now divide both-side of the equation by 4 to get the value of x
4x/4 = 4/3 ÷ 4
(On the left hand side of the equation, 4 will cancel out 4 leaving us with just x and on the right-hand side of the equation ÷ 4 can be changed to ×1/4)
x = 4/3 × 1/4
(4 will cancel 4 leaving us with 1/3)
x = 1/3
Therefore the amount of milk in 3 mugs is 1/3 quarts
1 bushel = 186 heads of lettuces
multiply each side by 6
6 bushels = 1,116 heads of lettuces
The farmer picked 1,116 heads of lettuces
Please help asap.
Answer:
Step-by-step explanation:
The vertical asymptote is the vertical dashed line in each graph. Its equation is x = constant, where the constant can be read from the graph where the line crosses the x-axis.
The horizontal asymptote is the horizontal dashed line in each graph. Its equation is y = constant, where the constant can be read from the graph where the line crosses the y-axis.
f(x)
The vertical asymptote is x = -4. The horizontal asymptote is y = 3.
g(x)
The vertical asymptote is x = 2. The horizontal asymptote is y = -4.
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The vertical asymptote of g(x) is 2-(-4) = 6 units to the right of that of f(x). The horizontal asymptote of g(x) is -4-3 = -7 units up from that of f(x). The graph of g(x) matches that of f(x) shifted right 6 units and down 7 units.
To find the intersection points of two graphs, set f(x) equals to g(x) and solve for 'x'. Substituting the x-value into either function gives the y-coordinate. The intersection point is the (x, y) pair.
In the subject of Mathematics, to find the specific points where function f(x) and function g(x) intersect, we need to set them equal to each other and solve for the variable x.
The formula we use is f(x) = g(x).
If f(x) is a linear equation such as y = 2x + 3 and g(x) is also a linear equation such as y = -3x + 7, setting them equal gives 2x + 3 = -3x + 7.
Solving for x ends up with x = 0.8. This x value is where the two functions intersect on a graph.
Another step can be taken to find the y coordinate by substituting the x value into either function.
So, if we substitute 0.8 into the function f(x), f(0.8) = 2(0.8) + 3 = 4.6. So the intersection point is (0.8, 4.6).
Learn more about Intersection of functions here:
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Answer:
144 dollars
Step-by-step explanation:
Given the conversion rate of 1 gallon = 16 cups and that 1/2 cup of milk makes 12 muffins, you can make 32 batches of 12 muffins using one gallon of milk.
The subject we are dealing with here is Mathematics and it's about a practical application of ratios and conversions. The student wants to know how many batches of 12 muffins can be made using one gallon of milk, given that 1/2 cup of milk makes 12 muffins.
To solve this, we first need to understand the relationship between gallons and cups. Specifically, 1 gallon is equivalent to 16 cups. If 1/2 cup of milk makes 12 muffins, hence 1 gallon, or 16 cups, will make 2 batches/cup x 16 cups/gallon = 32 batches of muffins.
Therefore, one gallon of milk can be used to bake 32 batches of 12 muffins each.
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