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2 years ago

∠1 and ∠2 are complementary. If m∠1 = 4m∠2, find m∠1

Mathematics

1 answer:

77julia77 [94]2 years ago

8 0

Answer:

∠1 = 72°

Step-by-step explanation:

Complementary angles sum to 90°, thus

∠1 + ∠2 = 90, substitute ∠1 = 4∠2 , thus

4∠2 + ∠2 = 90

5∠2 = 90 ( divide both sides by 5 )

∠2 = 18°

Hence ∠1 = 90 - 18 = 72°

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Any time Speedy the Sloth is not sleeping, she drinks chamomile tea at a steady rate of 2/7 of a cup per hour. Yesterday, she dr

Nitella [24]

<u><em>Answer:</em></u>

She stayed awake for 295 minutes today

<u><em>Explanation:</em></u>

<u>We are given that:</u>

Yesterday, she drank one cup

Today, she drank $\frac{17}{42}$ of a cup more than yesterday

<u>This means that:</u>

Number of cups she drank today = $1+\frac{17}{42}=1\frac{17}{42}cups$

Now, we know that she drinks $\frac{2}{7}$ of a cup per hour any time she is not sleeping

We use cross multiplication to get the time she took to drink $1\frac{17}{42}$ cups

1 hour ...........................> $\frac{2}{7}$ of a cup

?? hours ......................> $1\frac{17}{42}$ cups

Time taken = $\frac{1\frac{17}{42}*1 }{\frac{2}{7} } = \frac{59}{12} = 4\frac{11}{12} hours$

This means that she was awake for $4\frac{11}{12}$ hours

<u>Finally, we convert this to minutes:</u>

Knowing that 1 hour has 60 minutes, therefore:

She stayed awake for $4\frac{11}{12} * 60 = 295$ minutes

Hope this helps :)

8 0

3 years ago

Read 2 more answers

OMG please answer this question for me or else parents will kick me out of the house

cricket20 [7]

20

the input value in the x column is multiplied by 5 to get the output value in the y column

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2 years ago

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The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

liubo4ka [24]

Answer:

$(x,y,z)=(1477, 1464, 1437)$

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
Mr.A earns Rs6000

So, the equation would be

$3x + 5y - 4z = 6000$

Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
Mr B neither lose nor gain meaning he has made 0₹

hence,

$2x - 3y + z = 0$

Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
Mr.C earns 13000₹

therefore,

$- x + 4y + 6z = 13000$

Thus our system of equations is

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

Now solve the equation accordingly:

$\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}$

Solving the equation for x and y yields:

$\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}$

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

$\implies z= \dfrac{217000}{151}$

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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MissTica

Answer:

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Step-by-step explanation:

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2 years ago