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ladessa [460]
3 years ago
14

Write three equivalent ratios for the given ratio. Circle the simplest form of the ratio. 10/12 14/2 4/7

Mathematics
2 answers:
zheka24 [161]3 years ago
8 0
The simplest form is 4/7
8/14
12/21
16/28
Oksi-84 [34.3K]3 years ago
4 0
The simplest form would be 4/7
10/12 can be simplified further to 5/6 since 10 and 12 both have a gcf of 2, and if you divide 2 from 10 and 12, you get 5/6 which has no common factor other than 1.
14/2 can also be simplified further to 7/1 since 14 and 2 also have a gcf of 2 which simplifies it to 7/1.
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The line l is tangent to the circle with equation x² + y2 = 169 at the point P.
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Slope formula: If a line passes through two points, then the slope of the line is

m=\dfrac{y_2-y_1}{x_2-x_1}

Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is

m_1=\dfrac{5-0}{12-0}

m_1=\dfrac{5}{12}

We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.

Product of slopes of two perpendicular lines is always -1.

Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.

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m\times \dfrac{5}{12}=-1

m=-\dfrac{12}{5}

Therefore, the gradient or slope of the tangent line l is -\dfrac{12}{5} .

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