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3 years ago

What is the volume of the regular pyramid?

Mathematics

1 answer:

ad-work [718]3 years ago

7 0

Answer:

Step-by-step explanation:

The volume of the regular pyramid is $V=\dfrac{1}{3}A_{base}H.$

The base of given pyramid is regular hexagon with side 12 cm. The are of this hexagon consistsof area of 6 equilateral triangles and is equal to

$A_{base}=6\cdot \dfrac{1}{2}\cdot 12\cdot 10.4=374.4\ cm^2.$

Hence, the volume of the pyramid is

$V=\dfrac{1}{3}\cdot 374.4\cdot 36=4,492.8\ cm^3.$

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Gary wants to buy a video game with a selling price of $48, on sale for 50% off. The sales tax in his state is 4.5%. How much wi

Anna [14]

Answer:

$25.20

Step-by-step explanation:

First, take the 50% off the sales price:

($48)*(-0.50) = -$24.

($48 - $24) = $24 sale price.

Tax on $24 is ($24)*(0.05) = $1.20

Add the price and sales tax:

$24 + $1.20 = $25.20

5 0

2 years ago

A cylindrical jar's lid has a radius of 4 inches. If the volume is 351.68 in , approximately what is the height of the jar?

balu736 [363]

Answer:

7 inches

Step-by-step explanation:

The volume of a cylinder is calculated using

$V = \pi {r}^{2}h$

where r =4 inches is the radius and V=351.68 is the volume.

To find the height of the jar, we substitute these values and solve for h.

$351.68 = 3.14 \times {4}^{2} \times h$

$351.68 = 50.24h$

Divide both sides by 50.24 to get:

$h = \frac{351.68}{50.24}$

h=7 inches

Therefore the height of the jar is 7 inches

7 0

2 years ago

Solve for y 48= 8/3y

blsea [12.9K]

Answer:

y = 18

Step-by-step explanation:

To find the value of y, you must multiply the fraction 8/3 by its reciprocal 3/8 to both sides. That means you do 48 times 3/8 to get your y value. Once you multiply you get 144/8 which simplifies to 18.

6 0

3 years ago

Simplify the expression (2i-5j)×(3i+4j)

Alex_Xolod [135]

Answer:

-6-7ji-20j^(2)

Step-by-step explanation:

3 0

3 years ago

Will Mark Brainiest!!! Simplify the following:

xz_007 [3.2K]

Answer:

1.B

2.A

3. B

Step-by-step explanation:

1. $\frac{x+5}{x^{2} + 6x +5 }$

We have the denominator of the fraction as following:

$x^{2} + 6x + 5 \\= x^{2} + (1 + 5)x + 5\\= x*x + 1x + 5x + 5*1\\= x ( x + 1) + 5(x + 1)\\= (x + 1) (x + 5)$

As the initial one is a fraction, so that its denominator has to be different from 0.

=> ( $x^{2} +6x+5$ ) ≠ 0

⇔ (x +1) (x +5) ≠ 0

⇔ (x + 1) ≠ 0; (x +5) ≠ 0

⇔ x ≠ -1; x ≠ -5

Replace it into the initial equation, we have:

$\frac{x+5}{x^{2} + 6x +5 } = \frac{x+5}{(x+1)(x+5)}$

As (x+5) ≠ 0; we divide both numerator and denominator of the fraction by (x +5)

=> $\frac{x+5}{x^{2} + 6x +5 } = \frac{x+5}{(x+1)(x+5)} = \frac{1}{x+1}$

So that $\frac{x+5}{x^{2} + 6x +5 } = \frac{1}{x+1}$ with x ≠ 1; x ≠ -5

So that the answer is B.

2. $\frac{(\frac{x^{2} -16 }{x-1} )}{x+4}$

As the initial one is a fraction, so that its denominator has to be different from 0

=> x + 4 ≠ 0

=> x ≠ -4

As $\frac{x^{2}-16 }{x-1}$ is also a fraction, so that its denominator (x-1) has to be different from 0

=> x - 1 ≠ 0

=> x ≠ 1

We have an equation: $x^{2} - y^{2} = (x - y ) (x+y)$

=> $x^{2} - 16 = x^{2} - 4^{2} = (x -4) (x +4)$

Replace it into the initial equation, we have:

$\frac{(\frac{x^{2} -16 }{x-1} )}{x+4} \\= \frac{x^{2} -16 }{x-1} . \frac{1}{x + 4}\\= \frac{(x-4)(x+4)}{x-1}. \frac{1}{x + 4}$

As (x + 4) ≠ 0 (proven above), we can divide both numerator and the denominator of the fraction by (x +4)

=> $\frac{(x-4)(x+4)}{x-1} .\frac{1}{x+4} =\frac{x-4}{x-1}$

So that the initial equation is equal to $\frac{x-4}{x-1}$ with x ≠-4; x ≠1

=> So that the correct answer is A

3. $\frac{x}{4x + x^{2} }$

As the initial one is a fraction, so that its denominator (4x + x^2) has to be different from 0

We have:

(4x + x^2) = 4x + x.x = x ( x + 4)

So that: (4x + x^2) ≠ 0 ⇔ x ( x + 4 ) ≠ 0

⇔ $\left \{ {{x\neq 0} \atop {(x+4)\neq0 }} \right.$ ⇔ $\left \{ {{x\neq 0} \atop {x \neq -4 }} \right.$

As (4x + x^2) = x ( x + 4) , we replace this into the initial fraction and have:

$\frac{x}{4x + x^{2} } = \frac{x}{x(x+4)}$

As x ≠ 0, we can divide both numerator and denominator of the fraction by x and have:

$\frac{x}{x(x+4)} =\frac{x/x}{x(x+4)/x} = \frac{1}{x+4}$

So that $\frac{x}{4x+x^{2} } = \frac{1}{x+4}$ with x ≠ 0; x ≠ -4

=> The correct answer is B

3 0

3 years ago