Answer:
Part A
The number of cups of blue paint that Lara mixed with each cup of red paint is 3 cups of blue paint
Part B
1/3 cup of red paint is added to 1 cup of blue paint
Part C
The unit price per cup of blue paint is $8 per cup of blue paint
Step-by-step explanation:
The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint is 3: 1
Part A: Write a sentence to describe the number of cups of blue paint that Lara mixed with each cup of red paint (4 points)
The ratio is
Blue paint : Red paint
= 3 : 1
Hence,
The number of cups of blue paint that Lara mixed with each cup of red paint is 3 cups of blue paint
Part B: How many cups of red paint should Lara add to each cup of blue paint to make the shade of purple? Explain your reasoning (4 points)
From Part A , we know that
3 cups of blue paint = 1 cup of red paint
1 cup of blue paint = y
Cross Multiply
3 × y = 1 × 1
y = 1/3
Hence, 1/3 cup of red paint is added to 1 cup of blue paint
Part C: I Lara purchased 6 cups of blue paint for $48, what is the unit price per cup of blue paint? (2 points)
6 cups of blue paint = $48
1 cup of blue paint = x
6 × x = $48 × 1
x = $48/6
x = $8
Answer:
The restriction of the domain of f(g(x)) is that x cannot be 3.
Step-by-step explanation:
The first step to solve this question is finding the function, replacing the values. So
The function is a fraction, which means that the restriction is that the denominator cannot be zero. So
The restriction of the domain of f(g(x)) is that x cannot be 3.
You add the ratio numbers to make 10 then divide 150 by 10. (15)
then you multiply 15 by 1:4:5
to make 15:60:75
-x-y=-5
-x+y=1
adding up the equations gives;
-2x=-4
x=2
replacing in the first equation;
-2-y=-5
-2+5=y
y=3
They would intersect at (2,3)
The answer is the first one, impossible. This is because it shows that there are red and black cards, but never mentions that there are blue cards at all. This also means there are no blue cards. How could you get a blue card when there are none? It's impossible.
