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3 years ago

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If A(x¹,y¹), B(x²,y²), C(x³,y³) and D(x⁴,y⁴) form two line sements AB and CD which condition needs to be met to prove AB is perp

endicular to CD

1 answer:

tester [92]3 years ago

6 0

Answer:

A(x1, y1), B(x2, y2), C(x3, y3), D(x4, y4) form line segments AB and CD

For AB to be perpendicular to CD, triangle ABC should be a right angle or AC^2 = AB^2 + BC^2

(x3-x1)+(y3-y1) = (x2-x1)+(y2-y1) + (x3-x2)+(y3-y2)

If this is equal we can say AB is perpendicular to CD

Hope this helps!

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If P = (-2,7), Find:<br> Ry-axis (P)<br> ([?], [])

kumpel [21]

Answer:

(2, 7)

Step-by-step explanation:

$R_{\text{y-axis}}(\text{P})$ represents the reflection of a point P about the y-axis.

If a point (x, y) is reflected across y-axis, rule for the reflection is,

(x, y) → (-x, y)

If a point (-2, 7) follows the same rule, coordinates of the image point will be,

P(-2, 7) → P'(2, 7)

Therefore, answer is (2, 7).

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3 years ago

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belka [17]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

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3 years ago

Tampa Bay Buccaneers Super Bowl Contenders?

mafiozo [28]

Answer:

Australia.

Bangladesh.

England.

India.

New Zealand.

South Africa.

Sri Lanka.

West Indies.

Step-by-step explanation:

none

hope this helps

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3 years ago

A cube has volume 216cm find total surface area of cube

Katena32 [7]

Answer:

Answer: 216 cm2 (square centimetres $cm^{2}$ , in your question you had to put cm3, cubic centimetres, it's IMPORTANT )

Step-by-step explanation:

A perfect cube by definition has 3 equal dimensions, as an immediate rule: volume and total surface are equal, only the unit of measure changes (cubic for the volume, square for surface).

But let's calculate it anyway:

Volume = Edge * Edge * Edge = length * width * depth = $Edge^{3}$ (remember: all edges are equal in this case)

so Edge = $\sqrt[3]{Volume}$

in your example Edge = $\sqrt[3]{216}$ = 6cm

So the surface of one side is 6*6 = 36 $cm^{2}$

There are 6 sides in total, so the total surface is 6*36 = 216 $cm^{2}$

Note: I call them "edges" but in case of a cube most say just "length"

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3 years ago