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3 years ago

8x - 3(2x - 4) * - 9

Mathematics

2 answers:

Zinaida [17]3 years ago

8 0

Answer:

x = 54/31

Step-by-step explanation:

Solve for x:

8 x + 27 (2 x - 4) = 0

27 (2 x - 4) = 54 x - 108:

54 x - 108 + 8 x = 0

Grouping like terms, 54 x + 8 x - 108 = (8 x + 54 x) - 108:

(8 x + 54 x) - 108 = 0

8 x + 54 x = 62 x:

62 x - 108 = 0

Add 108 to both sides:

62 x + (108 - 108) = 108

108 - 108 = 0:

62 x = 108

Divide both sides of 62 x = 108 by 62:

(62 x)/62 = 108/62

62/62 = 1:

x = 108/62

The gcd of 108 and 62 is 2, so 108/62 = (2×54)/(2×31) = 2/2×54/31 = 54/31:

Answer: x = 54/31

trapecia [35]3 years ago

4 0

Answer:

62x - 108

Step-by-step explanation:

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Step-by-step explanation:

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Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with

yan [13]

Answer:

The volume of pyramid B is 64 times the volume of pyramid A.

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, $s_A =$ 12 inches

Height of A, $h_A =$ 8 inches

Side Length of B, $s_B =$ 48 inches

Height of B, $h_B =$ 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

$V_B$ is how many times bigger than $V_A$ ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

$V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}$

Here, base is square, so:

$V=\dfrac{1}{3} \times s^2 \times h$

Volume of pyramid A:

$V_A=\dfrac{1}{3} \times s_A^2 \times h_A$

$\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3$

Volume of pyramid B:

$V_B=\dfrac{1}{3} \times s_B^2 \times h_B$

$\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3$

The volume of pyramid B is 64 times the volume of pyramid A.

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2 years ago