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adoni [48]
3 years ago
6

Find the coordinates of point b on ac such that the ratio of AB to BC is 2:1

Mathematics
1 answer:
AnnyKZ [126]3 years ago
3 0

Answer:

(-2, 3)

Step-by-step explanation:

The point B is:

B(x,y)

x

AB(A to B) is twice BC(B to C)

AB is 2 - x. BC is x - (-4) = x + 4.

So

2 - x = 2(x + 4)

2 - x = 2x + 8

3x = -6

x = -2

y

Same logic as above.

AB is -5 - y. BC is y - 7.

-5 - y = 2(y - 7)

-5 - y = 2y - 14

3y = 9

y = 3

The point is (-2, 3).

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Answer: C

Step-by-step explanation:

We know that \angle AHB=90^{\circ}, and thus by the exterior angle theorem,

90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}

Thus, \angle CAB=2\theta=\boxed{60^{\circ}}

8 0
2 years ago
Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?
Softa [21]

\boxed{ \mathfrak { question↷}}

Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?

\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}

\boxed{ \mathfrak { solution↷}}

Let Pip get be x and fiona get be x+35

Ratio = 6:1

\tt \frac{x + 35}{x }  = 6

\tt \: x + 35 = 6x

\tt \: 5x = 35

\tt \: x = 7

\boxed{ \sf \: Total  \: money = x + x + 35 = 14+ 35 = £49}

3 0
2 years ago
What is the greatest common factor of (8x-6)
bija089 [108]

Answer:

Step-by-step explanation:

(8x-6)

=2(4x-3)

5 0
3 years ago
The numbers 12, 34, 56, 78, 90 are five two-digit numbers that use
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Answer:

90, 81, 72, 63, 54

Step-by-step explanation:

I think that these numbers make up the most possible product. Having the larger numbers on the side as the tens digit would be a better way of making the product bigger so that you can leave the smaller numbers for the smaller ones digit.

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Answer:

b

Step-by-step explanation:

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