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Iteru [2.4K]
3 years ago
11

Karen has a cube that has a side length of 6 in. The net of the cube is shown.

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0

<em>Question: What is the surface area of the cube?</em>

<em></em>

Answer:

Area = 216\ in^2

Step-by-step explanation:

Given

L = 6 --- length

Required

Determine the surface area

The surface area of a cube is calculated as follows:

Area = 6L^2

Substitute 6 for L

Area = 6 * 6^2

Area = 6 * 36

Area = 216

<em>Hence, the surface area of the cube is </em>216in^2<em></em>

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Write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation.
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The answer would be B: F(x) = 6x - 12

This line passes through both given points.

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What's the hight of a million pennies
TiliK225 [7]

The thickness of a brand new US penny that hasn't been
worn down is 1.52 millimeters.

If you have a million pennies, there are many ways to arrange them.
You can pile them all in one pile, or shovel them into many piles, or
stack them up in any number of stacks up to a half-million stacks
with two pennies in each stack, or try somehow to stack them all up
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Any stack with 'n' pennies in the stack is  1.52n millimeters high.

If you somehow succeed in stacking all million of them in one stack,
then the height of that stack would be . . .

       (1,000,000) x (1.52 mm) =  1,520,000 millimeters
                                                         152,000 centimeters
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3 0
3 years ago
Question included in the image - geometry problem.
iren [92.7K]

Answer:

y = 116°

Step-by-step explanation:

Given that <em>L₁ </em>|| <em>L</em>₂:

The <u>exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.  

Also, ∠y° and ∠2x° are <u>same-side interior angles</u> formed by the intersection of the <em>hypotenuse</em> of the triangle that acts as a transversal to the parallel lines, <em>L₁ </em>and <em>L</em>₂.  Given that ∠y° and ∠2x° are <u>same-side interior angles</u>, then it means that they are the supplements of each other, such that the sum of their measures is 180°.  

Now that we have established these definitions, we can proceed with the solution.

<u>Equation 1</u>:  ∠y° + ∠2x° = 180° ⇒ Same-side interior angles

<u>Equation 2</u>:  ∠y° =  ∠x° + ∠84°  ⇒ exterior angle theorem

Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:

∠y° + ∠2x° = 180°

∠x° +  ∠84° + 2x° = 180°

Combine like terms:

∠3x° + ∠84° = 180°

Subtract ∠84° from both sides:

∠3x° + ∠84° - ∠84° = 180° -∠84°

∠3x° = 180° - ∠84°

∠3x° = 96°

Divide both sides by 3 to solve for x:

\frac{3x}{3} = \frac{96}{3}

∠x° = 32°

Substitute the value of x into Equation 2 to solve for y:

∠y° =  ∠x° + ∠84°

∠y° =  ∠32° + ∠84°

∠y° =  116°

Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:

<h3>Equation 1:</h3>

∠y° + ∠2x° = 180°

116° + 2(32)° = 180°

116° + 64° = 180°

180° = 180° (True statement).

<h3>Equation 2:</h3>

∠y° =  ∠x° + ∠84°

116° = 32° + 84°

116°  = 116°  (True statement)

Therefore, the correct answer is: y = 116°.

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