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maria [59]
3 years ago
14

A recipe requires ¼ cup of oil for every ⅔ cup of water. How much oil (in cups) is needed per cup of water?

Mathematics
1 answer:
Ulleksa [173]3 years ago
8 0

Answer:

3/8 cups

Step-by-step explanation:

Divide both sides by 2 to get the value for 1/3 cup of water:

1/3 cup water = 1/8 cup of oil

Now, multiply each side of the equation by 3 to get 1 cup of water:

1 cup water = 3/8 cup of oil

hope this helps!

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HELP HELP Point F is the midpoint of segment DE. DF = 2x+6 and DE = 2x+36. Find DE.
Jobisdone [24]

Answer:

since F is midpoint

DF= FE = 2x+6

DF +FE=DE

2x+6 + 2x+6 = 2x+36

4x + 12 = 2x+36

2x = 24

x=12

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Step-by-step explanation:

4 0
3 years ago
The range of y = - 32x ^ 2 + 90x + 3
mariarad [96]

Given:

The given function is:

y=-32x^2+90x+3

To find:

The range of the given function.

Solution:

We have,

y=-32x^2+90x+3

It is a quadratic function because the highest power of the variable x is 2.

Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.

If a quadratic function is f(x)=ax^2+bx+c, then the vertex of the quadratic function is:

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function, a=-32,b=90,c=3.

\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}

\dfrac{-b}{2a}=\dfrac{-90}{-64}

\dfrac{-b}{2a}=\dfrac{45}{32}

The value of the given function at x=\dfrac{45}{32} is:

y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3

y=\dfrac{2121}{32}

The vertex of the given downward parabola is \left(\dfrac{45}{32},\dfrac{2121}{32}\right). It means the maximum value of the function is y=\dfrac{2121}{32}. So,

Range=\left\{y|y\leq \dfrac{2121}{32}\right\}

Range=\left(-\infty, \dfrac{2121}{32}\right ]

Therefore, the range of the given function is \left (-\infty, \dfrac{2121}{32}\right ].

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Answer:

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Step-by-step explanation:

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