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3 years ago

assume that lines m and n are parallel. If the measure of angle 6 is 57° what is the measure of angle 1?

Mathematics

1 answer:

Gemiola [76]3 years ago

4 0

If < 6 = 57, then < 4 = 57.....(corresponding angles are equal)

and < 4 + < 1 = 180.....because they form a linear pair

57 + < 1 = 180
< 1 = 180 - 57
< 1 = 123 <===

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The line y =3x-5 meet x-axis at the point M. The line 3y+2x=2 meets y-axis at point N. Find the equation of the line joining M a

Law Incorporation [45]

Answer-

The line equation is,

$\boxed{\boxed{6x+15y-10=0}}$

Solution-

The line $y =3x-5$ meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

$\Rightarrow 0 =3x-5$

$\Rightarrow 3x=5$

$\Rightarrow x=\dfrac{5}{3}$

So, coordinate of M is $(\dfrac{5}{3},\ 0)$

The line $3y+2x=2$ meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

$\Rightarrow 3y+2(0)=2$

$\Rightarrow 3y=2$

$\Rightarrow y=\dfrac{2}{3}$

So, coordinate of N is $(0,\ \dfrac{2}{3})$

The line joining M and N can be found out by applying two point formula of straight line,

$\Rightarrow \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}$

$\Rightarrow \dfrac{y-0}{\frac{2}{3}-0}=\dfrac{x-\frac{5}{3}}{0-\frac{5}{3}}$

$\Rightarrow \dfrac{y}{\frac{2}{3}}=\dfrac{x-\frac{5}{3}}{-\frac{5}{3}}$

$\Rightarrow -\dfrac{5}{3}y=\dfrac{2}{3}(x-\frac{5}{3})$

$\Rightarrow -5y=2(x-\dfrac{5}{3})$

$\Rightarrow -5y=2x-\dfrac{10}{3}$

$\Rightarrow 2x+5y-\dfrac{10}{3}=0$

As it is given that all the coefficients are integers, so multiplying with 3

$\Rightarrow 6x+15y-10=0$

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4x=6
4x/4=6/4
X=1.5

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Which ordered pair minimizes the objective function C = 60x + 85y?. (0, 160). (55, 70). (80, 50). (170, 0)

dangina [55]

Step-by-step explanation:

The given objective function is $C = 60x + 85y$

To check that which ordered pair is minimizing the objective function-we will substitute all the ordered pair one by one in the given function and we will calculate the value of C. The ordered pair which will give the minimum value will be the answer.

For (0, 160)

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