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4 years ago

40 POINTS!!! WILL MARK BRAINLIEST!!! What postulate or theorem are these triangles congruent by?

Mathematics

1 answer:

kondor19780726 [428]4 years ago

7 0

Answer:

It could be AAA

Step-by-step explanation:

there are only angles and no sides that are labled

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The given line segment has a midpoint at (3, 1).

Katena32 [7]

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)

Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ .

Therefore the line passing through (2, 4) and (4, -2) has an equation:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\\frac{y-4}{x-2}=\frac{-2-4}{4-2}\\\frac{y-4}{x-2}=\frac{-6}{2}\\y-4=x-2(-3)\\y-4=-3x+6\\y=-3x+10$

Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10

Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:

$m_1m_2=-1$ .

Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:

$m_1m_2=-1\\-3m_2=-1\\m_2=\frac{1}{3}$

Since it is the perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:

$\frac{y-y_1}{x-x_1}=m\\\frac{y-1}{x-3}=\frac{1}{3}\\ y-1= \frac{1}{3}(x-3)\\ y-1=\frac{1}{3}x-1\\y=\frac{1}{3}x$

the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is $y=\frac{1}{3}x$

7 0

3 years ago

Read 2 more answers

The following information is obtained from two independent samples selected from two normally distributed populations.

AysviL [449]

A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:

μ1 − μ2 = x1 – x2 = 7.82 – 5.99

μ1 − μ2 = 1.83

B. The formula for confidence interval is given as:

Confidence interval = (x1 –x2) ± z σ

where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58

and σ is calculated using the formula:

σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]

σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]

σ = 0.988297

Going back to the confidence interval:

Confidence interval = 1.83 ± (2.58) (0.988297)

Confidence interval = 1.83 ± 2.55

Confidence interval = -0.72, 4.38

3 0

3 years ago

(-8-3i) - (-9-5) the difference is ?

OLEGan [10]

Answer:

The answer is 6-3 i

Step-by-step explanation:

4 0

3 years ago

A pen cost y dollars,how much will 25 such pens cost

kiruha [24]

Answer:

25y

Step-by-step explanation:

y×25=25y

3 0

3 years ago

If y represents a number, write an expression that represents the sum of y and a number one greater than y

Dimas [21]

Answer:

2y+1=0

Step-by-step explanation:

a number one greater than y is y+1

so sum of y and y+1= 2y+1

3 0

4 years ago

Read 2 more answers