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solmaris [256]
3 years ago
6

Find the value of a if the line joining the points (3a,4) and (a,-3) has a gradient of 1

Mathematics
1 answer:
Otrada [13]3 years ago
6 0

Recall that the slope or gradient of a line segment through two points is the ratio of the change in the <em>y</em> coordinate to the change in the <em>x</em> coordinate.

If the gradient is 1, then

1 = (-3 - 4) / (<em>a</em> - 3<em>a</em>)

Solve for <em>a</em> :

1 = -7 / (-2<em>a</em>)

1 = 7/(2<em>a</em>)

2<em>a</em> = 7

<em>a</em> = 7/2

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Triangle A″B″C″ is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows t
andrew-mc [135]

Answer:

segment AB over segment A double prime B double prime = the square root of 13 over 2 times the square root of 13

Step-by-step explanation:

Triangle ABC has vertices at points A(-3,3), B(1,-3) and C(-3,-3).

1. Reflection over x = 1 maps vertices A, B and C as follows

  • A(-3,3)→A'(5,3);
  • B(1,-3)→B'(1,3);
  • C(-3,-3)→C'(5,-3).

2. Dilation by a scale factor of 2 from the origin has the rule

(x,y)→(2x,2y)

So,

  • A'(5,3)→A''(10,6);
  • B'(1,3)→B''(2,6);
  • C'(5,-3)→C''(10,-6)

See attached diagram for details

Note that

A''B''=2AB\\ \\A''C''=2AC\\ \\B''C''=2BC,\\ \\AB=\sqrt{(-3-1)^2+(3-(-3))^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}

so

\dfrac{AB}{A''B''}=\dfrac{2\sqrt{13}}{2\cdot 2\sqrt{13}}=\dfrac{\sqrt{13}}{2\sqrt{13}}

7 0
3 years ago
Each leg of a 45-45-90 triangle measures 14 cm what is the length of the hypotenuse
PtichkaEL [24]

Answer:

14 square roots of 2 is correct

Step-by-step explanation:

5 0
3 years ago
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Suppose that a butterfly can fly 82 feet in 4 seconds. A dragonfly can fly 50 feet in 2 seconds. Which can fly faster and by how
Lady bird [3.3K]

A butterfly can fly 82 feet in 4 seconds.

Distance traveled by butterfly = 82 feet.

Time taken by butterfly =4 seconds

Speed = distance /time

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A dragonfly can fly 50 feet in 2 seconds.

Distance traveled by dragonfly =50 feet.

Time taken by dragonfly =2 seconds.

Speed of dragonfly = 50/2 = 25 feet/second

So dragonfly can fly faster than the butterfly.

Difference in speed = speed of dragonfly - speed of butterfly = 25-20.5 = 4.5

So The dragonfly is 4.5 feet per second faster than butterfly.

Answer: B) The dragonfly is 4.5 feet per second faster.  


5 0
3 years ago
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What are the partial products of 396 divided by 12?
Alisiya [41]
396  divided by 12 will be 33

8 0
3 years ago
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What’s the answer for b plz help bc I don’t know 18= b - 12
Lilit [14]

Answer: b= 30


Step-by-step explanation:


5 0
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