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Nikolay [14]
3 years ago
7

In 5 years' time, Kate's father will be 3 times as old as Kate. Four years ago, her father

Mathematics
1 answer:
Brut [27]3 years ago
8 0

Answer: Kate = 40/3  Her father = 50

Step-by-step explanation:

Let Kate's age in the present be K

And Kate's father's age in the present be F

3(K+5) = F+5

6(K-6) = F-6

Rearrange the first equation to get

3K+15 = F+5

3K+10 = F

Substitute that into the second question

6K-36 = 3K+10-6

3K = 40

K = 40/3

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

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Find the distance between the points (4,3) and (2,-1). Express your answer in simplest radical form.
Kamila [148]

Answer : B

the distance between the points (4,3) and (2,-1)

We apply distance formula

d^2= (x_2-x1)^2 + (y_2-y_1)^2

(x1,y1) is (4,3)

(x2,y2) is (2,1)

d^2= (2-4)^2 + (-1-3)^2

d^2= (-2)^2 + (-4)^2

d^2 = 4+16 = 20

Take square root on both sides

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the distance between the points (4,3) and (2,-1) is 2sqrt(5)

3 0
3 years ago
A ship travels due west for 90 miles and turns to travel 80 miles in the northwest direction at a 120 degree angle. How far is t
adoni [48]
We breakdown the components of the distances.
(1) 90 miles west.
                          x - component = -90 miles
                          y - component = 0 miles
(2) 80 miles, northwest (120°)
                          x - component = (80 miles)*(sin 30°) = 40 miles (negative)
                          y - component =(80 miles)*(cos 30°) = 69.282 miles (positive)

Solve for the distance,
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4 years ago
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