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3 years ago

Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour.

2 answers:

3 0

If 1 cup of that particular vanilla powder has a mass of 128 grams, then $\dfrac{2}{3}$ of a cup of vanilla powder has a mass of

$\dfrac{2}{3} \cdot 128=\dfrac{256}{3}=85\dfrac{1}{3}$ grams.

Since

$85\dfrac{1}{3}-32=53\dfrac{1}{3}$ grams and $\dfrac{5}{12}$ of a cup of vanilla powder is

$\dfrac{5}{12}\cdot 128=\dfrac{5\cdot 128}{12}=\dfrac{5\cdot 32}{3}=\dfrac{160}{3}=53\dfrac{1}{3},$

then correct answer is that he went over by $\dfrac{5}{12}$ of a cup.

Answer: correct choice is B.

Anuta_ua [19.1K]3 years ago

3 0

The answer is B.)

plz mark me as brainliest, it motivates me to answer more of your questions :)

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lys-0071 [83]

Answer:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

Step-by-step explanation:

The given system of linear equations is:

$(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0$

We have to solve the equations for the values of $x, y$ .

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by $sin\theta$ and second equation by $cos\theta$

Now, the equations become:

$(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)$

Now, let us add (1) and (2):

$(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta$

Using the equation:

$(-sin\theta)x+(cos\theta)y=0$

Putting value of $y$ :

$\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta$

So, the answer to the system of linear equations is:

$\bold{x =cos\theta}\\\bold{y=sin\theta}$

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Answer:

Step-by-step explanation:

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3 years ago

Kate paid $27 for a dress that was on sale for 10% off. What was the original price of this dress?

Luba_88 [7]

The best way to go about this questions is to write out a formula in which x represents the original price of the dress: x*0.90=27. To see where the 0.90 came from, if Kate's dress was 10% off, she must have paid 90% of the original price (100%-10%=90%). Then, to convert a percentage to a decimal, move the decimal point twice to the left so 90% becomes 0.90. Then, our formula essentially means that 90% of some number (x) is equal to 27. To solve for x, divide both sides of the formula by 0.90 to get x=$30 which is the final answer.

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