Use the information given to enter an equation in standard form.

Mathematics

1 answer:

wariber [46]2 years ago

8 0

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{4})~\hspace{10em} \stackrel{slope}{m}\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{6}(x-\stackrel{x_1}{3})\implies y-4=6x-18 \\\\\\ y=6x-14\implies -6x+y=-14\implies 6x-y=14$

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In ΔLMN, \overline{LN}

Karolina [17]

Answer:

$\bold{\angle NLM = 10^\circ}$

Step-by-step explanation:

Given a ΔLMN.

Line LN is extended to point O.

such that:

$\text{m}\angle MNO = (5x-13)^{\circ}$

$\text{m}\angle NLM = (x-4)^{\circ}$ and

$\text{m}\angle LMN = (2x+19)^{\circ}$

To find:

$\text{m}\angle NLM=?$

Solution:

Kindly refer to the attached image for the given triangle and dimensions of angles.

Let us recall the external angle property of a triangle:

The external angle of a triangle is equal to the sum of two opposite internal angles.

i.e.

$\angle MNO = \angle NLM + \angle LMN\\\Rightarrow 5x-13 = x-4+2x+19\\\Rightarrow 5x-13 = 3x+15\\\Rightarrow 5x-3x = 13+15\\\Rightarrow 2x=28\\\Rightarrow x =14$