Which of the equations or inequalities below are true?

Line segment AB has endpoints A(1, 2) and B(5, 3). Find the coordinates of the point that divides the line segment directed from

Tanzania [10]

Answer:

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

Step-by-step explanation:

Given:

Let Point P ( x , y ) divides Segment Am in the ratio 1 : 3 = m : n (say)

point A( x₁ , y₁) ≡ ( 1 , 2)

point B( x₂ , y₂) ≡ (5 , 3)

To Find:

point P( x , y) ≡ ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

$x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}\\\\$

Substituting the values we get

$x=\frac{(1\times 5 +3\times 1) }{(1+3)}\\ \\and\\\\y=\frac{(1\times 3 +3\times 2) }{(1+3)}\\\\\therefore x = \frac{8}{4}=2 \\\\and\\\therefore y = \frac{9}{4}=2.25 \\\\\\\therefore P(x,y) = (2 , 2.25)$

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

7 0

4 years ago

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How do you write:<br> 42 decreased by twice a number <br> in algebraic expression

ratelena [41]

Let the number be x

Twice the number = 2x

42 decrease by twice the number:

42 - 2x

4 0

4 years ago

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The point (4, –3) is on the graph of which function?

Allisa [31]

Answer:

B) y = ½x - 5

Step-by-step explanation:

Just simply plug in the coordinates into the function to confirm their authenticities.

I am joyous to assist you anytime.

7 0

3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.7 millimeters and a standard deviati

slava [35]

Answer:

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.7 millimeters and a standard deviation of 0.08 millimeters.

This means that $\mu = 5.7, \sigma = 0.08$