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Katena32 [7]
2 years ago
13

Given: circle k(O), mAB =(6x−50)°, m∠BCA=(2x)° Find: m∠BAC

Mathematics
1 answer:
natulia [17]2 years ago
5 0

Answer:

40°

Step-by-step explanation:

arc AB has twice the measure of the inscribed angle BCA that intercepts it, so we have the relation ...

(6x-50)° = 2(2x)°

2x -50 = 0

2x = 50

So, angle BCA has measure 50°. Since AC is a diameter, angles BCA and BAC are complementary. Thus ...

m∠BAC = 90° - m∠BCA = 90° - 50°

m∠BAC = 40°

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Yuri is thinking of a 4-digit whole number. He rounds his number to the nearest thousand. His answer is 4000, what is the smalle
konstantin123 [22]

Answer:

Smallest number = 3500

Step-by-step explanation:

Rounding of numbers involve replacing numbers with simpler numbers. In order to round a number to the nearest thousand, the last 3 digits of the number should be considered. If the last 3 digits are less than 500, the number is rounded down(the thousand figure is unaffected), but if the last 3 digits are greater or equal to 500, the number is rounded up.

In this case, Yuri is thinking of a 4-digit whole number and he rounds his number to the nearest thousand. Since his answer is 4000, the smallest number yuri could be thinking of would be 3500 and the highest number he could be thinking of is 4499.

Thus, the smallest number Yuri could be thinking of is 3500

6 0
2 years ago
14) Rounded to the nearest whole number, the square
Katen [24]

Answer:

3934

Step-by-step explanation:

Round 15,479,652 and find square root.

4 0
2 years ago
The monthly issues of the Journal of Finance are available on the Internet. The table below shows the number of times an issue w
kolbaska11 [484]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data below :

312 2753 2595 6057 7624 6624 6362 6575 7760 7085 7272 5967 5256 6160 6238 6709 7193 5631 6490 6682 7829 7091 6871 6230 7253 5507 5676 6974 6915 4999 5689 6143 7086

The maximum value = 7829

Minimum value = 312

Range (maximum - minimum) = (7829 - 312) = 7517

Mode(most frequently occurring) = all observations occur once

Median = 1/2 (n+1)th term

= 1/2 (33+1) = 1/2 (34) = 17th term = 6490 (after rearranging in ascending order)

Mean(m) = Σ(X) /number of observations (n) = (201608)/33 = 6109.33

Variance = Σ(x - m)² / n = 78234131 / 33 = 2370731.2

Standard deviation = sqrt(variance) = sqrt(2370731.2) = 1539.7179

5 0
2 years ago
If 3x-y=123x−y=123, x, minus, y, equals, 12, what is the value of \dfrac{8^x}{2^y} 2 y 8 x ​ start fraction, 8, start superscrip
julia-pushkina [17]

Answer:

2^{12}=4,096

Step-by-step explanation:

You know that 3x-y=12 and have to find

\dfrac{8^x}{2^y}

Use the main properties of exponents:

1. (a^m)^n=a^{m\cdot n}

2. \dfrac{a^m}{a^n}=a^{m-n}

Note that

8=2^3,

then

7^x=(2^3)^x=2^{3\cdot x}=2^{3x}

Now

\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}

Since 3x-y=12, then 2^{3x-y}=2^{12}=4,096

3 0
2 years ago
Read 2 more answers
Circle A and circle B are congruent. CD is a chord of both circles. If AB = 8 ft and CD = 6 ft, how long is a radius?
bazaltina [42]

Let us say that the intersection point of lines AB and CD is called point E. The lines AB and CD are perpendicular to each other which also means that the triangle CEB is a right triangle.

Where the line CB is the radius of the circle while the side lengths are half of the whole line segment:

EB = 0.5 AB = 0.5 (8 ft) = 4 ft

CE = 0.5 CD = 0.5 (6 ft) = 3 ft

Now using the hypotenuse formula since the triangle is right triangle, we can find for the radius or line CB:

CB^2 = EB^2 + CE^2

CB^2 = (4 ft)^2 + (3 ft)^2

CB^2 = 16 ft^2 + 9 ft^2

CB^2 = 25 ft^2

<span>CB = 5 ft = radius</span>

7 0
2 years ago
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