P is the point with coordinates (3, 1)

The lines y1 = 2x - 6, y2 = -3x + 4, y3 = -1/2x + 4 are the sides of a right triangle. Find the perimeter and area of the triang

sergiy2304 [10]

The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

<h3>Perimeter and area of the triangle giving the equation of a line</h3>

First we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.

From the given equation of the lines, the points of intersection of the line are (x₁, y₁) = (- 0.4, 5.2), (x₂, y₂) = (-0.8, 4.4) and (x₃, y₃) = (0, 4)

For the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

For the height

h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²

height = 2√5 / 5

For the hypotenuse

r = √2 · b

r = 2√10 / 5

<h3>Determine the Perimeter and area</h3>

Perimeter = s1+s2+s3

Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5

Perimeter = (2√10 + 4√5) / 5 units

area = 1/2* base * height

A = 0.5 · (2√5 / 5) · (2√5 / 5)

A = 2/5 square units

Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Learn more on area and perimeter of triangles here: brainly.com/question/21511715

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8 0

1 year ago

What is described as a line, segment or Ray that bisects a segment at a right angle?

Elena L [17]

Answer:

something perpendicular probably

7 0

2 years ago

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A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes.

nika2105 [10]

Answer:

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

$\bar X=2.55$ represent the sample mean for the late time for a flight

$\mu$ population mean

$\sigma=12$ represent the population deviation

n=76 represent the sample size

Confidence interval

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

The confidence interval for the true mean is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The Confidence level given is 0.95 or 95%, th significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ . If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got $z_{\alpha/2}=1.96$

Replacing we got:

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

7 0

2 years ago

Compute the conditional probabilities from the two-way frequency table.

Natali5045456 [20]

Answer:

The table is show clearly in the figure attached.

P(boy if favourite activity is swimming) = 8/17 = 0.47

P(girl if favourite activity is sport) = 7/27 = 0.26

P(girl if favourite activity is reading) = 4/6 = 0.67

P(boy if favourite activity is sport) = 20/27 = 0.74

P(favourite activity is swimming if a girl) = 9/20 = 0.45

P(favourite activity is reading if a boy) = 2/30 = 0.07

P(favourite activity is swimming if a boy) = 8/30 = 0.27

P(favourite activity is reading if a girl) = 4/20 = 0.2

6 0

2 years ago

A piece of paper is chosen from a bag that contains 10 pieces of paper numbered 1 through 10. Find the probability that the pape

motikmotik

Answer:

1/5

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers