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marta [7]
3 years ago
13

Which of the following points is not collinear with (3, 6) and (-2, -9)?

Mathematics
2 answers:
Radda [10]3 years ago
8 0

Answer:

B: (0, -4)

Step-by-step explanation:

Three points are collinear if they lie on a single straight line. As we know two points of the line, there is a <em>unique</em> line that passes through both of them.

Let's find the equation of the line:

The general equation of a line is y = mx + b, where m represents the slope and b is the y-intercept.

In this case, we know that

\left \{ {{6 = m*3 + b} \atop {-9 = m*(-2) + b}} \right. \\

because we want the line to passes through (3, 6) and (-2, -9)

From the first equation, we deduce that b = 6 - m*3

We replace this in the second one and we get

-9 = (-2)*m + 6 - 3*m\\ -15 = (-5)*m

3 = m

With this, b = 6 - 3*m = 6 - 3*3 = -3

b = -3

So, the equation of the line that passes through (3, 6) and (-2, -9) is

\fbox {y = 3x - 3}

Knowing these, let's see which one of A, B, C or D makes the equation false, i.e. doesn't lie on the line and therefore is not collinear with (3, 6) and (-2, -9). For that, in each case, we have to replace the x of the equation with the first number of the pair and see if it equals the second one.

A: 3*(-1) - 3 = -3 -3 = -6. Correct!

B: 3*0 - 3 = 0 - 3 = -3. Wrong!

C: 3*3 - 3 = 9 - 3 = 6. Correct!

D: 3*0 - 3 = 0 - 3 = -3. Correct!

Therefore, B is not collinear with (3, 6) and (-2, -9)

Lilit [14]3 years ago
5 0
Its B, cause it’s collinear
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Answer:

C=69.1^{\circ}

Step-by-step explanation:

The Law of Cosines is given as:

c^2=a^2+b^2-2ab\cos C.

Plugging in given values, we get:

16^2=8^2+17^2-2\cdot 8\cdot 17\cdot \cos C,\\\cos C=\frac{-97}{-272},\\C=\arccos(\frac{97}{272}),\\C=\fbox{$69.1^{\circ}$}.

3 0
3 years ago
The height in feet of a ball dropped from a 150 ft building is given by h(t)=-16 ft^2 +150, where t is the time in seconds after
ipn [44]

Answer:

Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft

Step-by-step explanation:

we have

h(t)=-16t^{2}+150

where

t ----> is the time in seconds after the ball is dropped

h(t) ----> he height in feet of a ball dropped from a 150 ft

Find h(2)

That means ----> Is the height of the ball  2 seconds after the ball is dropped

Substitute the value of t=2 sec in the equation

h(2)=-16(2)^{2}+150=86\ ft

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After 2 seconds, the height of the ball is 86.00 ft.

7 0
3 years ago
I’m confused please help
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2 years ago
Please help me to solve all the questions would appreciate it if its with full working
Degger [83]

∠ KGH is equal to 77°. This is arrived at by using the knowledge of the total angles in Parallel Lines.

<h3>What are the total angles on a straight line?</h3>

According to the laws of lines and angles, the total number of angles that can exist on a straight line is 180°.

If ∠CED = 25° and ∠BFL = 78°, then: ∠KGH = 180-(25+78), which is equals 77°. This is because the total angles on a straight-line total 180°

<h3>What is ∠LKJ?</h3>

Recall that in angles in parallel lines:

  • Corresponding Angles are always congruent,  
  • Alternate Angles are always congruent, and
  • Interior According always sum up to 180°

Hence,

We can derive ∠LKJ because it is congruent with ∠BGJ.

To get ∠BGJ, we must get ∠LFH because both of them are interior angles and sum up to 180°.

To get ∠LFH, we must subtract ∠BFL from 180° because they are both angles on a straight line.

Hence ∠LFH = 180 - 78 = 102°

Recall that ∠LFH and ∠BGJ are interior angels. Hence

∠BGJ = 180 - 102 = 78°.

Since ∠BGJ is a corresponding ∠ with ∠LKJ, therefore

∠LKJ = 78°

<h3>What is ∠ALM?</h3>

∠ALM is ∠BFL because they are both corresponding angles and are therefore congruent.

<h3>What are the solutions to section B?</h3>

  1. Because ∠ACB and ∠BAC are equal, therefore sides AB and BC are equal in length. We can tell that  ∠ACB and ∠BAC are equal because the total angles in the triangle are equal to 180°

     2. The name given to the triangle mentioned above is Obtuse      

          Triangle. This is because one of the angles exceeds 90°.

Learn more about angles in parallel lines at:
brainly.com/question/24607467
#SPJ1

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Write an equation of the line with a slope of į and y-intercept of -8<br> y =
Lemur [1.5K]

Answer:

your answer is y =-8 hopes this help

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