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3 years ago

Jake is wrapping a gift that is in a box with the following dimensions.

Mathematics

1 answer:

dybincka [34]3 years ago

8 0

Answer:

Because you are looking for square inches of wrapping paper, you are looking for the surface area of the box. A three-dimensional box has a top and bottom that are the same size, a front and back that are the same size, and 2 sides that are the same size...or SA = 2(top/bottom area) + 2(front/back area) + 2(side/side area). Our equation fills in nicely like this:

SA = 2(6 * 14) + 2(6 * 8) + 2(14 * 8)

SA = 2(84) + 2(48) + 2(112)

SA = 168 + 96 + 224

SA = 488 square inches of paper to wrap the box.

Step-by-step explanation:

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How much warmer is 12°C than -20°C?

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3 years ago

Read 2 more answers

XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3

nataly862011 [7]

<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = $\frac{1}{2}$ x b x h -------------(i)

Where;

A = 18 $\sqrt{3}$

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18 $\sqrt{3}$ = $\frac{1}{2}$ x b x 6

18 $\sqrt{3}$ = 3b

<em>Divide through by 3</em>

6 $\sqrt{3}$ = b

Therefore, b = XZ = 6 $\sqrt{3}$

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180° [sum of angles in a triangle]

=> XOZ + 30° + 30° = 180°

=> XOZ + 60° = 180°

=> XOZ = 180° - 60°

=> XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

$\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}$

$\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}$

$\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}$

$\frac{1}{12} = \frac{1}{2|OZ|}$

$\frac{1}{6} = \frac{1}{|OZ|}$

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

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3 years ago

Help me with 2, 8, and 10 plz

OverLord2011 [107]

For #2:

<span><span>You need to combine your like terms:
</span> 3x^2 – 2x^2= x^2</span>

4 + 6 = 10

This will now give you:

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3 years ago