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3 years ago

Given a cube with a volume of 36 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?

1 answer:

7 0

A square pyramid, if it fit perfectly in a cube, would be 1/3 of its volume.

V(square pyramid)=1/3(volume of cube)
V(square pyramid)=1/3(36)
V(square pyramid)=12cm³

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Use completing the square to determine which of the following gives the solutions to 3x2 - 24x + 40 = 28.

jeka94

Answer:

$x=4+2\sqrt{3}$

$x=4-2\sqrt{3}$

Step-by-step explanation:

Completing the square

when $ax^2+bx+c=0$

Given equation:

$3x^2-24x+40=28$

Subtract 40 from both sides:

$\implies 3x^2-24x=-12$

Divide both sides by 3:

$\implies x^2-8x=-4$

Add the square of half the coefficient of $x$ to both sides:

$(\frac{b}{2})^2=(\frac{-8}{2})^2=16$

$\implies x^2-8x+16=-4+16$

Factor the left side and simplify the right side:

$\implies (x-4)^2=12$

Square root both sides:

$\implies x-4=\pm\sqrt{12}$

Add 4 to both sides and simplify the radical:

$\implies x=4\pm\sqrt{4 \cdot 3}$

$\implies x=4\pm\sqrt{4}\sqrt{3}$

$\implies x=4\pm2\sqrt{3}$

5 0

2 years ago

Which equation is the equation of the line, in point-slope form, that has a slope of -1.8 and passes through the point (-0.5, 1.

pishuonlain [190]

Slope=-1.8, X=-0.5, y=1.9
Equation is y^2-y^1=m(x^2-x^1).
Y-1.9=-1.8(X-(-0.5))
Y-1.9=-1.8x+0.90
Add 1.9 on both sides.
Y= -1.8x+1.
I hope this helps you.

7 0

3 years ago

Read 2 more answers

102 = 1.2 x w what is w?

Free_Kalibri [48]

Answer:

122.4

Step-by-step explanation:

Just Divide.

8 0

3 years ago

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You work in the state of Nebraska where the sales tax is 5 1 2 %. What would be the tax rate expressed as a decimal?

Igoryamba

512% as a decimal would be 5.12

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3 years ago

The three vertices of a triangle are (2, 1), (6, 1), and (3, 6).

Luba_88 [7]

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. This can help you do it.

3 0

3 years ago