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Anettt [7]
2 years ago
6

I want pictures of how you did it on paper! please please please help me

Mathematics
1 answer:
denis23 [38]2 years ago
3 0

a) The value of k in the first diagram is 10

b) The value of k in the second diagram is 7.5

<h3>Calculating angles </h3>

From the question, we are to determine the value of k in the given diagrams

a) The diagram shows two parallel lines and a transversal.

NOTE: The interior angles on the same side of the transversal are supplementary

Then, we can write that

5k + 20 + 7k + 40 = 180°

Now, solve for k

5k + 20 + 7k + 40 = 180°

12k + 60 = 180

12k = 180 - 60

12k = 120

k = 120/12

k = 10

Hence, the value of k in the first diagram is 10

b) By the exterior angle theorem, we can write that

12k + 10 + 40 = 8k + 80

NOTE: The <em>exterior angle theorem</em> states that the measure of an exterior angle is equal to the sum of the <u>two opposite interior angles</u>

Now, solve for k in

12k + 10 + 40 = 8k + 80

First, collect like terms

12k - 8k = 80 - 10 - 40

4k = 30

k = 30/4

k = 7.5

Hence, the value of k in the second diagram is 7.5

Learn more on Calculating angles here: brainly.com/question/21369105

#SPJ1

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Find the equation of the line that passes through points (3,5) and (-6,2). Write the equation in slope intercept form.
andrezito [222]
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                              = (5 -2) ÷ (3 - (-6))
                              = ¹/₃
   
     using the point-slope form (y-y₁) = m(x-x₁)
     using (3,5)
           (y - 5) = ¹/₃ (x -3)
             y - 5  = ¹/₃x - 1
        ⇒      <span>  y =   ¹/₃ x  + 4  [OPTION D]


</span>2)        y =  2x  +  5  .... (1)
<span>           </span>y = ¹/₂ x  + 6  .... (2)
       
         by substituting y in (1) for y in (2)

           2x  +  5 = ¹/₂ x  + 6 
                 ³/₂ x = 1
                      x = ²/₃

        by substituting found x (2)

            y = ¹/₂ (²/₃)  + 6
            y = ¹⁹/₃

∴ common point is (²/₃ , ¹⁹/₃)  thus answer is FALSE [OPTION B]


3) Yes [OPTION A]
     This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.

4) No [OPTION B]
       Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other.  Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.

6 0
3 years ago
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