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3 years ago

Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)

Mathematics

2 answers:

SashulF [63]3 years ago

5 0

9514 1404 393

Answer:

k = 2.8

Step-by-step explanation:

Segments AB and AC are on the same line, so have the same slope. Using the slope formula, we have ...

m = (y2 -y1)/(x2 -x1)

(3 -7)/(8 -0) = (k -7)/(3k -0)

Multiplying by 6k gives ...

-3k = 2(k -7)

-5k = -14 . . . . . . subtract 2k

k = 14/5 = 2.8 . . . . divide by -5

AfilCa [17]3 years ago

4 0

Answer:

k=14/5

Problem:

Three points have coordinates A (0 , 7) , B (8 , 3) and C (3k , k)

Find the value of the constant k for which C lies on the line that passes through A and B

Step-by-step explanation:

The slope of a line containing points (a,b) and (c,d) is found by computing (b-d)/(a-c). This is just the change in y divided by the change in x.

The slope of a line containing points (0,7) and (8,3) is (7-3)/(0-8)=4/-8=-1/2.

The slope of a line containing points (0,7) and (3k,k) and (8,3) is still -1/2 because it doesn't matter what two points on a line you use to calculate the slope. The slope will remain the same no matter the pair of points on the line you choose for it's calculation.

So lets pretend the question is now find the point (3k,k) such that a line with slope -1/2 goes through (3k,k) and (0,7).

We want to solve the equation:

(k-7)/(3k-0)=-1/2

Simplify denominator

(k-7)/(3k)=-1/2

Cross multiple

(k-7)(2)=(-1)(3k)

Distribute or multiply

2k-14=-3k

Subtract 2k on both sides

-14=-5k

Divide both sufes by -5

-14/-5=k

Simplifying fraction

14/5=k

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Akimi4 [234]

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2 years ago

7x(x+1.8)=0<br> 7x(x+1.8)=0<br> 7x(x+1.8)=0 <br> Answer those 3

ahrayia [7]

Answer:

The answer to all of those questions would be x=-1.8

Step-by-step explanation:

7x(x + 1.8) = 0 - Distribute through the Parenthesis -

7x^2 + 12.6x = 0

x(7x + 12.6) = 0

x = 0

7x + 12.6 = 0

7x = -12.6

x = -12.6/7

x = -1.8

so x = 0 or x = -1.8

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3 years ago

Avery selects chips from a bag without looking at them. The bag has 5 green chips, 3 red chips, and 7 blue chips. What is the pr

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3 years ago

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In □PQRS side PQ∥ side RS. If m∠P = 108degree

natka813 [3]

<h2>Given :-</h2>

In □PQRS side PQ∥ side RS. If m∠P = 108degree

and m∠R = 53degree

m∠Q and m∠S.

<h2>Solution :-</h2>

According to angle sum property

P∠Q=180−∠P

∠Q=180−108

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tatyana61 [14]

The value of the angles should be. (x-40°). , (x-20°), (½x-10°) , not (x-40°) + (x-20°)+(½x-10°)

Sum of all the interior angles of a triangle is 180°.

So a equation can be made by the given data,

(x-40°) + (x-20°) + (½ x-10°) = 180°

x-40°+x-20°+½x-10° = 180°

2x+½x -60°-10° = 180°

5/2 x - 70° = 180°

5/2 x = 180° + 70°

5/2 x = 250°

x = 250° × 2/5

x = 50° × 2

x = 100°

So the angles are

x-40° = 100°-40° = 60°

x-20° = 100°–20° = 80°

½x-10° = ½(100)° - 10° = 50° -10° = 40°

The answer can be checked by putting the values of the angle we got in the second statement i.e. Sum of all the interior angles of a triangle is 180°.

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