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3 years ago

A recipe for cake needs 3/4 if a cup of milk. you are making 1/2 of the recipe.his much milk do you need

2 answers:

6 0

We need 1/2 of 3/4. So it'll look like this:
(3/4)/2

So! We need to work with this fraction inside a fraction. To do so take the denominator and flip it. Then multiply across.

3/4 * 1/2

3/8

Or you can think of it like this!

3/4 is 0.75.

0.75/2 is 0.375 or in fraction form 3/8.

You can find the fraction form of 0.375 like a so... :
(Each time I divide both the numerator and denominator by 5)

375/1000
75 / 200
15 / 40
3 / 8

r-ruslan [8.4K]3 years ago

4 0

I would say it's 3/8 of a cup because if you multiply 3/4 by 2 it would be 6/8. It's the same amount but just a different measurement. Now just take 3 away from 6/8 and you have 3/8 which is half of 3/4.

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Ivory says that the equation 2x+2=x+1 has no solution because the left-hand side is double the right-hand side. Is Ivory Correct

lorasvet [3.4K]

Answer:

No, Ivory is incorrect. The equation does have a solution, and the solution is x = -1.

Step-by-step explanation:

We try to solve the equation first.

2x + 2 = x + 1

We want all variables on the left side and all numbers on the right side.

Subtract x from both sides.

x + 2 = 1

Subtract 2 from both sides.

x = -1

Check: Plug in -1 for x on both sides and see if it makes a true statement.

2x + 2 = x + 1

2(-1) + 2 = -1 + 1

-2 + 2 = 0

0 = 0

0 = 0 is a true statement, so the solution x = -1 is the correct solution.

Answer: Ivory is incorrect. The equation does have a solution, and the solution is x = -1.

8 0

3 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

4 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B-2%7D%20%7D%7Bb%5E%7B4%7D%20%7D" id="TexFormula1" title="\frac{b^{-2} }{b^{4}

MAXImum [283]

Answer: $\frac{1}{b^6}$ or $b^{-6}$

Step-by-step explanation:

$\frac{b^-2+2}{b^4+2}$ Add the exponent two to both sides. After adding -2 and 2 you get 0 and any number raised to the zero power is one. And 4 plus two is 6