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Marta_Voda [28]
3 years ago
5

The location of point D is (7,1) the location of point F is (5,4). Determine the location of point E which is 1/3 of the way fro

m D to F
Mathematics
1 answer:
IceJOKER [234]3 years ago
6 0

Answer:

( 19/3 , 2 )

Step-by-step explanation:

Given in the question,

point D(7,1)

x1 = 7

y1 = 1

point F(5,4)

x2 = 5

y2 = 4

Location of point E which is 1/3 of the way from D to F

which means ratio of point E from D to F is 1 : 2

<h3>a : b</h3>

1 : 2

xk = x1 + \frac{a}{a+b}(x2-x1)

yk = y1 + \frac{a}{a+b}(y2-y1)

Plug values in the equation

xk = 7 + (1)/(1+2) (5-7)

xk = 19/3

yk = 1 + (1)/(1+2)(4-1)

yk = 2

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5!=5*4*3*2*1;6!=6*5*4*3*2*1 What is the value of 4^4/4!
german

Answer:

\frac{32}{3}

Step-by-step explanation:

If 5! is equal to 5 × 4 × 3 × 2 × 1 and 6! is equal to 6 × 5 × 4 × 3 × 2 × 1, then 4! is equal to 4 × 3 × 2 × 1. Thus, 4! = 4 × 3 × 2 × 1, which can simplify to 24. 4! = 24.

4^{4} is basically 4 × 4 × 4 × 4, which can simplify to 256.

So,  \frac{4^{4}}{4!} = \frac{256}{24}.  \frac{256}{24} can simplify to \frac{32}{3}. Therefore,  \frac{4^{4}}{4!} = \frac{32}{3}.

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3 years ago
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Find point G on AB such that the ratio of AG to GB is 3:2.
lora16 [44]

Using proportions, the coordinates of point G are given as follows:

(1.8, 1.6).

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The points A and B are given as follows:

A(-3, 4) and B(5,0).

For this problem, we have that the ratio of AG to GB is 3:2, hence:

AG = 3/5AB

G - A = 3/5(B - A).

The x-coordinate of G is found as follows:

x + 3 = 3/5(5 + 3)

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The y-coordinate of G is found as follows:

y - 4 = 3/5(0 - 4)

y - 4 = -2.4

y = 1.6.

Hence the coordinates of point G are given as follows:

(1.8, 1.6).

More can be learned about proportions at brainly.com/question/24372153

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