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3 years ago

Ons: Practice

Mathematics

1 answer:

Sedaia [141]3 years ago

7 0

Answer:

$x = 18$

Step-by-step explanation:

Given

$\frac{x}{6} - 7 = -4$

Required

Solve for x

$\frac{x}{6} - 7 = -4$

Add 7 to both sides

$\frac{x}{6} - 7+7 = -4+7$

$\frac{x}{6} = -4+7$

$\frac{x}{6} = 3$

Multiply through by 6

$6 * \frac{x}{6} = 3 * 6$

$x = 3 * 6$

$x = 18$

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A triangle has a base of (3x + 7) and a height of (5x - 1). A second

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Answer:

The difference between the area of the original triangle and the area of the new triangle is $\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)$ .

Step-by-step explanation:

The equation for the area of a triangle ( $A_{\bigtriangleup}$ ) is:

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Where:

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$h$ - Height, dimensionless.

The expression for each triangle are described below:

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Second Triangle ( $b = 3\cdot (3\cdot x+7)$ , $h = 2\cdot (5\cdot x -1)$ )

$A_{\bigtriangleup,2} = 3\cdot (3\cdot x+7)\cdot (5\cdot x -1)$

The difference between the area of the original triangle and the area of the new triangle is:

$\Delta A_{\bigtriangleup} = A_{\bigtriangleup,2}-A_{\bigtriangleup,1}$

$\Delta A_{\bigtriangleup} = 3\cdot (3\cdot x+7)\cdot (5\cdot x-1)-\frac{1}{2} \cdot (3\cdot x+7)\cdot (5\cdot x-1)$

$\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)$

The difference between the area of the original triangle and the area of the new triangle is $\Delta A_{\bigtriangleup} = \frac{5}{2}\cdot (3\cdot x +7)\cdot (5\cdot x -1)$ .

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