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2 years ago

Help please quick will be given enough points

Mathematics

1 answer:

Licemer1 [7]2 years ago

3 0

$\\\\\text{Given that,} ~ g(x) = \dfrac 13 x + 5 \\\\\text{Write g(x) as}~ y = \dfrac 13 x +5 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~x = \dfrac 13y +5 \\\\\implies 3x = y + 15~~~~~~~~~~~~~~~~~~~;[\text{Multiply both sides by 3]}\\\\\implies y = 3x -15\\\\\implies g^{-1} (x) = 3x -15 \\$

$\left(g \circ} g^{-1} \right)(x)\\\\=g\left(g^{-1}(x) \right)\\\\=g(3x-15)\\\\=\dfrac 13\cdot(3x-15)+5\\\\=x -5 +5\\\\=x$

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Questions are in the screenshot.

White raven [17]

For question 4, $x = 18$ units,

For question 5, $x = 8.333$ units.

Step-by-step explanation:

Step 1:

Since the given polygons are similar to each other, all the ratios of one polygon to the other will remain equal for all the values of the two similar polygons.

We take the ratio of the same sides of both polygons i.e. the ratio of the lengths or the ratio of the widths.

Step 2:

For question 4, the first rectangle has a length of 9 units while the width is 3 units.

For the second rectangle, the length is x as x is greater than the width in the first rectangle. The width is 6 units.

The ratio of the first rectangle to the second is;

$\frac{3}{6} : \frac{9}{x} , x = (9)(\frac{6}{3} ) = 18.$ So $x = 18$ units.

Step 3:

The shapes in question 5 are made of a square and a triangle.

For the first shape, the side length is 6 units while the side of the triangle is 10 units.

For the second shape, the side length is 5 units while the side of the triangle is x units.

The ratio of the first shape to the second is;

$\frac{6}{5} : \frac{10}{x} , x = (10)(\frac{5}{6} ) = 8.333.$ So $x = 8.333$ units.

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