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3 years ago

Determine if the two triangles are congruent. If they are, state how you know.

Mathematics

1 answer:

mylen [45]3 years ago

3 0

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

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What is the largset prime number less that 40

Fantom [35]

Answer:

Step-by-step explanation:

37 can only be multiplied by 1 and 37. Because prime numbers cannot be multiplied by any whole number except 1 and itself, the answer must be 37.

7 0

3 years ago

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What is the value of 2x in this equation 5x - 2(2x - 1) = 2(3x - 4)

KiRa [710]

Answer:

Step-by-step explanation:

Step 1: Write equation

5x - 2(2x - 1) = 2(3x - 4)

Step 2: Solve for x

Distribute: 5x - 4x + 2 = 6x - 8
Combine like terms: x + 2 = 6x - 8
Subtract x on both sides: 2 = 5x - 8
Add 8 to both sides: 10 = 5x
Divide both sides by 5: 2 = x
Rewrite x = 2

Step 3: Check

Plug in x to verify it's a solution.

5(2) - 2(2(2) - 1) = 2(3(2) - 4)

10 - 2(4 - 1) = 2(6 - 4)

10 - 2(3) = 2(2)

10 - 6 = 4

4 = 4

Here we see that x = 2 is indeed a solution

Step 4: Find 2x

2(2) = 4

7 0

3 years ago

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1/X+4 = 5 it is solving rational equations

finlep [7]

X=1
Subtract four so you get 1/x=1
Multiply by x
1x=1
Divide by 1

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3 years ago

A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally. How long will each k

Alexandra [31]

Answer:

Step-by-step explanation:

(24 hours)/(5 knights) = 4.8 hours/knight

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3 years ago

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A survey shows that college students spend on average about $20 per month on Yum Good Ramen. a. Assume that the survey was condu

lawyer [7]

Answer:

a) The 95% confidence interval would be given by (19.168;20.832)

b) The 95% confidence interval would be given by (19.182;20.416)

c) The 95% confidence interval would be given by (19.412;20.588)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n represent the sample size

Part a

The confidence interval for the mean is given by the following formula:

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

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$