All categories

3 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(4,10), B(10, 10) , and C(10, 2) ?

Mathematics

1 answer:

const2013 [10]3 years ago

4 0

Answer:

(7,6)

Step-by-step explanation:

Triangle ABC with vertices at points A(4,10), B(10, 10) , and C(10, 2) is a right triangle with the hypotenuse AC.

The circumcenter of the right triangle is the midpoint of the hypotenuse.

Find the coordinates of the midpoint O of the hypotenuse AC:

$x_O=\dfrac{4+10}{2}=7\\ \\y_O=\dfrac{10+2}{2}=6$

So, O(7,6)

You might be interested in

Ahhhh i need help again.

qwelly [4]

Answer:

Step-by-step explanation:

A. these simply to 21 + 7x and 21 + 3x

this one is incorrect because the 7x and 3x are different

B. these simplify to 10 + x and 10 + x

this is the correct one since they are exactly the same

C. these simplify to 21x and 7x + 21

these two are not the same because one expression has only a number with a variable but the other one has a number with a variable <em>and </em>another number

D. these simplify to $\frac{7}{3-x}$ and $\frac{7}{x-3}$

in subtraction, the order of the 3 and the x matters, so the equations are not the same
example: 6 - 4 = 2 but 4 - 6 = -2

3 0

2 years ago

Simone has 20 bills. One fifth of the bills are hundreds, 1/4 of them are fifties, 1/10 of them are $20s. The rest of the bills

larisa [96]

If Simone has 20 bills, then:

1/5 of 20 = 4 [hundreds]
1/4 of 20 = 5 [fifites]
1/10 of 20 = 2 [$20s]

4 * 100 + 5 * 50 + 2 * 20 = 400 + 250 + 40 = 690 [out of $780]
4 + 5 + 2 = 11 [out of 20 bills]

So now we can easily find out she had 9 bills of tens - because 20 - 11 = 9 or because (780 - 690) ÷ 10 = 90 ÷ 10 = 9.

5 0

3 years ago

Answer for number 19

murzikaleks [220]

I’m in High school I never did that

7 0

3 years ago

Read 2 more answers

Solve for x. -2(16 - 4x) - 8 = 6(x + 2)

Amanda [17]

So...

-2(16-4x)-8=6(x+2)            Multiply
-32+8x-8=6x+12                 Add like terms
-40+8x=6x+12                    Subtract 6x from both sides
-40+2x=12                          Add 40 to both sides
2x=52                                 Divide 2 from both sides
x=26                                   Substitute to check
-2(16-4(26))-8=6((26)+2)   Add and multiply in parenthesis
-2(-88)-8=6(28)                  Multiply
176-8=168                         Subtract
168=168

So x=26

I hope this helps! Have a great day!

6 0

3 years ago

5. True or False. (a) All other factors remaining the same, increasing the sample size, n, will decrease the width of a con denc

Igoryamba

Answer:

a) True

b) True

c) True

d) False

e) False

Step-by-step explanation:

(a) All other factors remaining the same, increasing the sample size, n, will decrease the width of a confidence interval.

True. Confidence intervals are calculated by calculating margin of error (ME) around the mean using the formula

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic (z-score or t-score)
s is the standard deviation of the sample(or of the population if it is known)
N is the sample size

As the formula suggests, all other factors remaining the same, if we increase N, ME decreases.

b) We expect 95% of all 95% confidence intervals for the population mean to contain the sample mean.

True. This is what 95% confidence level assumes.

(c) The t-distribution is symmetric and centered at the population mean

True.

(d) The t-distribution is very similar to the standard normal distribution regardless of its degrees of freedom.

False. As the degrees of freedom increases t-distribution resembles the standard normal distribution. For small sample sizes (<30), this is not true.

(e) All other factors remaining the same, a 90% confidence interval for a population mean is narrower than an 95% confidence interval for the same population

False. 90% confidence interval for a population mean is wider than an 95% confidence interval for the same population

5 0

3 years ago