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3 years ago

If ABC = DEF, then angle A. SAS congruence B. SSS congruence C. CPCTC

Mathematics

1 answer:

saveliy_v [14]3 years ago

8 0

Hey there! :D

If you already know that two triangles are congruent, (which is given)

then any other part of the triangle can be proved congruent by CPCTC.

Congruent Parts of Corresponding Triangles are Congruent.

I hope this helps!
~kaikers

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Which is an x-intercept of the graphed function? (0, 4) (–1, 0) (4, 0) (0, –1)

Alex Ar [27]

Answer:

I would need to see the graph

Step-by-step explanation:

To find the x-intercept you find the point which the line intercepts with the x-axis...... The x-axis is the one that runs side to side.

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2 years ago

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How do I prove this? Help Thanks.

eimsori [14]

Answer:

Step-by-step explanation:

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3 years ago

Can you help me, please ……..

dedylja [7]

Answer: The correct answer is 44.60

Step-by-step explanation:

Let's find the area of the rectangle first, and then add it with the area of the Circle to find the total area of the whole shape.

We know that the area of a Rectangle is L(Length) x W(Width)

So using the given information, 8 x 4 = 32

So the Area of the Rectangle = 32

Now let's find the area of the given circle,

Area of a Circle: πr2 Remember ^ = stands for power

The radius is half of the diameter

The diameter of the circle is 4

4/2 = 2 which is our radius, and now let's replace it in the equation.

= 3.14(r)^2

= 3.14(2)^2

= 3.14(4)

= 12.56 or some may have got 12.57

So now we add all areas together to get the total area,

32+12.57 = 44.57

Now rounding off to the nearest tenths, would give us 44.60

So the area of the figure rounded to the nearest tenth is 44.60

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3 years ago

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Each side of the smaller square in the figure below is n inches long, and each side of the larger square is p inches longer than

lana66690 [7]

Answer:

2np + p²

Step-by-step explanation:

The general formula for the area of a square is A = s², where s = the length of one side of the square. In the case of the smaller square the area would be: n x n = n². Since the side of the larger square is 'p' inches longer, the length of one side is 'n + p'. To find the area of the larger square, we have to take the length x length or (n +p)².

Using FOIL (forward, outside, inside, last):

(n + p)(n+p) = n² + 2np + p²

Since the area of the first triangle is n², we can subtract this amount from the area of the larger square to find out how many square inches greater the larger square area is.

n² + 2np + p² - n² = 2np + p²

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3 years ago

The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by WorldOne Research, included the question, "Ho

vitfil [10]

Answer:

Therefore, the sampling distribution of $\bar{x}$ is normal with a mean equal to 9 hours and a standard deviation of 0.7969 hours.

The 95% interval estimate of the population mean $\mu$ is

LCL = 7.431 hours to UCL = 10.569 hours

Step-by-step explanation:

Let X be the number of hours a legal professional works on a typical workday. Imagine that X is normally distributed with a known standard deviation of 12.6.

The population standard deviation is

$\sigma = 12.6 \: hours$

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

The sample size is

$n = 250$

The sample mean is

$\bar{x} = 9 \: hours$

Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.

The population mean would be the same as the sample mean that is

$\mu = \bar{x} = 9 \: hours$

The sample standard deviation would be

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

Where is the population standard deviation and n is the sample size.

$s = {\frac{12.6}{\sqrt{250} }$

$s = 0.7969 \: hours$

Therefore, the sampling distribution of $\bar{x}$ is normal with a mean equal to 9 hours and a standard deviation of 0.7969 hours.

The population mean confidence interval is given by

$\text {confidence interval} = \mu \pm MoE\\\\$

Where the margin of error is given by

$$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\$

Where n is the sampling size, s is the sample standard deviation and is the t-score corresponding to a 95% confidence level.

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 250 - 1 = 249

From the t-table at α = 0.025 and DoF = 249

t-score = 1.9695

$MoE = t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\\\MoE = 1.9695\cdot \frac{12.6}{\sqrt{250} } \\\\MoE = 1.9695\cdot 0.7969\\\\MoE = 1.569\\\\$

So the required 95% confidence interval is

$\text {confidence interval} = \mu \pm MoE\\\\\text {confidence interval} = 9 \pm 1.569\\\\\text {LCI } = 9 - 1.569 = 7.431\\\\\text {UCI } = 9 + 1.569 = 10.569$

The 95% interval estimate of the population mean $\mu$ is

LCL = 7.431 hours to UCL = 10.569 hours

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3 years ago