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tester [92]
3 years ago
6

Directed line segment AB has endpoints A(2,3) and B(8,15). Point P has coordinated P(6,11). What ratio does P partition AB into?

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
Refer to the graph shown below. It confirms that points A, B and P are
 collinear.

Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
   = 8.9443

Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
   = 4.4721

Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.

Answer:  2:1 ratio.

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Step-by-step explanation:

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Evaluate the exponent expression 3x–4 ⋅ xy2 for x = –1 and y = 2.
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Step-by-step explanation:

Given,

x = - 1

y = 2

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Substitute the given values of x and y in the expression 3x - 4 ⋅ xy².

3x - 4 ⋅ xy²

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= - 3 - 4 ⋅ - 1 ( 4 )

= - 12 ⋅ - 4

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Note : -

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8 0
2 years ago
Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 washington 5 cars and vacuumi
ANEK [815]

Answer:

They charged <u>$6</u> for washing and <u>$2</u> for vacuuming the car.

Step-by-step explanation:

Let the charge of washing a car be 'x'.

And also let the charge of vacuuming a car be 'y'.

Now according to question, Trisha raised $38 washing 5 cars and vacuuming 4 cars.

So framing the above sentence in equation form, we get;

5x+4y=38\ \ \ \ \ equation\ 1

Again according to question, Byron raises $28 by washing 4 cars and vacuuming 2 cars.

So framing the above sentence in equation form, we get;

4x+2y=28\ \ \ \ \ equation\2

Now multiplying equation 2 by '2', we get;

2(4x+2y)=28\times2\\\\8x+4y=56\ \ \ \ equation\ 3

Now we subtract equation 1 from equation 3 and get;

(8x+4y)-(5x+4y)=56-38\\\\8x+4y-5x-4y=18\\\\3x=18\\\\x=\frac{18}{3}=6

Now substituting the value of 'x' in equation 1, we get;

5x+4y=38\\\\5\times6+4y=38\\\\30+4y=38\\\\4y=38-30=8\\\\y=\frac{8}{4}=2

Hence They charged <u>$6</u> for washing and <u>$2</u> for vacuuming the car.

8 0
3 years ago
In 5 years' time, Kate's father will be 3 times as old as Kate. Four years ago, her father
Brut [27]

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Step-by-step explanation:

Let Kate's age in the present be K

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So F = 3*40/3+10 = 50

8 0
2 years ago
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