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Lorico [155]
3 years ago
13

Jonathan finds a piece of metal that is 2 1/5 inches thick. He files off 3/10 inch. He adds a protective covering to the metal t

hat is 2/10 inch thick. Then, he polishes the metal and removes an additional 1/10 inch. What is the final thickness of the metal?
Mathematics
1 answer:
Mama L [17]3 years ago
5 0
<h2>Answer:</h2><h2>The final thickness of the metal = 2 inches.</h2>

Step-by-step explanation:

Jonathan finds a piece of metal that is 2\frac{1}{5}  inches thick.

The thickness of the metal = 2\frac{1}{5} = \frac{11}{5}

He files off \frac{3}{10}  inch,

the thickness becomes =  \frac{11}{5} - \frac{3}{10} = \frac{19}{10}

He adds a protective covering to the metal that is  \frac{2}{10}  inch thick.

the thickness becomes,  \frac{19}{10} + \frac{2}{10} = \frac{21}{10}

Then, he polishes the metal and removes an additional \frac{1}{10} inch.

The final thickness becomes, \frac{21}{10} - \frac{1}{10}  = 2 inches

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Write an equation that is perpendicular to and 3x+y=3 whose y-intercept 5. Anyone please help me, no link just explain how to do
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Answer:

y = \frac{1}{3}x + 5

Step-by-step explanation:

By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other:  m = - \frac{1}{m_{2} }, or equivalently, m_{1} * m_{2} = -1.

Given our linear equation  3x + y = 3  (or y = -3x + 3):

We can find the equation of the line (with a y-intercept of 5) that is perpendicular to y = -3x + 3 by determining the negative reciprocal of its slope, -3, which is \frac{1}{3}.

To test whether this is correct, we can take first slope,  m_{1} = -3,  and multiply it with the negative reciprocal slope m_{2} = \frac{1}{3} :

m_{1} * m_{2} = -1

-3 * \frac{1}{3}  = -1

Therefore, we came up with the correct slope for the other line, which is  \frac{1}{3}.

Finally, the y-intercept is given by (0, 5). Therefore, the equation of the line that is perpendicular to 3x + y = 3 is:

y = \frac{1}{3}x + 5

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3 years ago
Complete the following tables by filling in the missing values and determine the rule for each table:
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Answer:

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Triangle ABC has a right angle at C. Select all measurements which would mean it has a hypotenuse with a length of 10 units. a.
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Option d: Angle A is 30 degrees, BC is 5 units

Option e: AC is 8 units, BC is 6 units

Explanation:

The triangle ABC has a right angle at C.

The length of the hypotenuse is 10 units.

The image of the triangle with this measurement is attached below:

Option a: Angle A is 20 degrees, BC is 2 units

\begin{aligned}\sin 20 &=\frac{2}{h y p} \\h y p &=\frac{2}{\sin 20} \\&=5.8476\end{aligned}

Since, hypotenuse is 10 units, Option a is not correct answer.

Option b: AC is 7 units, BC is 3 units

\begin{aligned}A B &=\sqrt{7^{2}+3^{2}} \\&=\sqrt{49+9} \\&=\sqrt{58}\end{aligned}

Since, hypotenuse is 10 units, Option b is not correct answer.

Option c: Angle B is 50 degrees, BC is 4 units

\begin{aligned}\cos 50 &=\frac{4}{h y p} \\h y p &=\frac{4}{\cos 50} \\&=6.222\end{aligned}

Since, hypotenuse is 10 units, Option c is not correct answer.

Option d: Angle A is 30 degrees, BC is 5 units

\begin{aligned}\sin 30 &=\frac{5}{h y p} \\h y p &=\frac{5}{\sin 30} \\&=10\end{aligned}

Since, hypotenuse is 10 units, Option d is the correct answer.

Option e: AC is 8 units, BC is 6 units

\begin{aligned}A B &=\sqrt{8^{2}+6^{2}} \\&=\sqrt{64+36} \\&=\sqrt{100} \\&=10\end{aligned}

Since, hypotenuse is 10 units, Option e is the correct answer.

Thus, Option d and e are the correct answers.

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