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3 years ago

Pls help (9th honors geo - circles)

Mathematics

1 answer:

Mariana [72]3 years ago

6 0

• Angles DXC and AXB form a vertical pair, so they are congruent and have the same measure.

• ∆ABD is isosceles, since it's given that AD and BD are congruent. This means the "base angles" BAD and ABD have the same measure; call this measure x.

• The measure of angle ADB can be computed by using the inscribed angle theorem, which says

m∠ADB = 1/2 (100°) = 50°

(that is, it's half the measure of the subtended arc AB whose measure is 100°)

• The interior angle to any triangle sum to 180° in measure. So we have in ∆ABD,

m∠ADB + 2x = 180°

Solve for x :

50° + 2x = 180°

2x = 130°

x = 65°

• Use the inscribed angle theorem again to find the measure of angle BAC. This will be half the measure of the subtended arc BC, so

m∠BAC = 1/2 (50°) = 25°

• Now in ∆ABX, we have

m∠AXB + 25° + 65° = 180°

m∠AXB = 90°

Hence m∠DXC = 90°.

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3 years ago

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oksano4ka [1.4K]

Answer:

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Step-by-step explanation:

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3 years ago

g Given the system of equations: 15 c1 – 5 c2 – c3 = 2400 - 5 c1 + 18 c2 – 6 c3 = 3500 - 4 c1 - c2 + 12 c3 = 4000 (a) Calculate

denpristay [2]

Answer

(a)

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

(b)

$A^{-1} b = \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

Step-by-step explanation:

Remember that when you want to solve a problem like this, you express the equation as following

$Ax = b$

So, if you know the inverse of $A$ then

$x = A^{-1} b$

For this case

$A = \begin{pmatrix} 15 && 5 && -1 \\ -5 && 18 && -6 \\ -4 && -1 && 12 \end{pmatrix}$

Now for this case the inverse of A would be

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

Then when you multiply with the vector solution

$A^{-1} b = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix} * \begin{pmatrix} 2400 \\ 3500 \\ 4000 \end{pmatrix} = \frac{1}{3493} \begin{pmatrix} 249500 \\ 1197600 \\ 1347300 \end{pmatrix}\\\\\\= \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

So from that information you can conclude that the solution to the system of equations is x = 500/7 y = 2400/7 and z = 2700/7

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3 years ago

Simplify by combining like terms -5a-4a+b

Nitella [24]

-5a-4a+bSimplifying -5a + -4a + b Combine like terms: -5a + -4a = -9a -9a + b

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3 years ago

What is the standard deviation of the data set? Round to the nearest tenth if needed. 2, 4, 7, 8, 9

barxatty [35]

Hiiiiiiii, okay here's the full- explanation for you, so here's the final answer. The explanation of how i got the answer is also below! Hope this helped you!!

Answer:

2.9

Step-by-step explanation:

First the mean or average = sum / data points (or N) = (2 + 4 + 7 + 8 + 9) / 5 = 6

Now we take each of the individual values subtract the mean, and then square them, and add it all up.

(2 - 6)^2 + (4 - 6)^2 + (7 - 6)^2 + (8 - 6)^2 + (9 - 6)^2 = 34

Then we divide this by degrees of freedom = N - 1 to find the sample standard deviation. Note that this is different from the population standard deviation, where we would just divide N, but we use this because our data set is small, like less than 30 points.

34 / (N - 1) -----> = 34 / (5 - 1) = 8.5

Now, this is the variance, so we take the square root of the variance to get the sample standard deviation:

√(8.5) = 2.9 (rounded to 1 decimal place)

Note that scientific calculators, even my $20 version can do these kind of statistics calculations. Just enter the data set as a table of values in statistics mode, and press a few buttons, you're done!

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4 years ago