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nordsb [41]
2 years ago
7

Point H is the circumcenter of triangle DEF. Which must be true? Check all that apply. Point H is the center of the circle that

passes through points D, E, and F. Point H is the center of the circle that passes through points L, M, and N. MEH NEH DLH FNH
Mathematics
1 answer:
Dmitrij [34]2 years ago
5 0
The circumcenter of a triangle is the intersection of the perpendicular bisectors.It is the center of the triangle's circumcircle. And a circumcircle is the circumscribed circle of the triangle. This unique circle passes through each of the triangle's three vertices. According to these definitions the following statement is true:
Point H is the center of the circle that passes through points D, E, and F. 


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ABCD is a rectangle and A and B are the points (4,2) and (2,8) respectively. Given that the equation of AC is y=x-2, find a) Equ
Rudik [331]

A(4,2), B(2,8)

AC: y=x-2

Point point form for a line through (a,b) and (c,d) is (c-a)(y-b)=(d-b)(x-a)

AB is  (2 - 4)(y - 2) = (8-2)(x-4)

-2(y - 2)=6(x-4)

y - 2 = -3(x-4)

y = -3x + 14

BC is perpendicular through B, so slope 1/3 and we calculate the constant as y-(1/3)x:

y = (1/3) x  + (8 - (1/3)(2) ) = (1/3) x + 22/3

a)Answer:  BC is  y =  (1/3) x + 22/3

C is the meet of AC and BC,

x - 2 = (1/3) x + 22/3

3x - 6 = x + 22

2x = 28

x = 14

y = x-2 = 12

Check: y = (1/3)x + 22/3 = (14+22)/3 = 36/3 = 12  good

C(14,12)

The remaining corner is D.   We have A-B=D-C or

D = A+C-B+C = (4,2)+(14,12)-(2,8) = (16, 6)

b)Answer: B(2,8) [given, but asked for]  C(14,12), D(16,6)

8 0
2 years ago
Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people c
Alex17521 [72]

Answer:

a)X=3300

b)Y=7770

Step-by-step explanation:

From the question we are told that:

Number Teachers T=6

Number Student S=12

Number in committee n=5

a) Generally the equation for exactly 3 students on the committee is mathematically given by

X=^{S}C_3*^{T}C_3

X=^{12}C_3*^{6}C_3

X=3300

b) Generally the equation for at least one teacher and at least one student on the committee is mathematically given by

Total Ways-(no of ways of selection no teacher or student)

Where total Ways

T=^{(6+12)}C_5

T=8568

Therefore

Y=8568-^{6}C_0*^{12}C_5+^{12}C_0*^{6}C_5

Y=8568-798

Y=7770

8 0
2 years ago
Britton rotated trapezoid ABCD 180° on the coordinate plane. If angle B is 20° and angle D is 90°, what is the degree measuremen
olasank [31]

Answer:

The answer is 20 degrees

Step-by-step explanation:

A trapezoid is a quadrilateral with four angles and the sum of the four angles is 360 degrees.

Britton rotated the trapezoid ABCD 180º, but we were not told that he tampered with the angles size or shape, we can now agree that it is still the same trapezoid that was rotated without any alterations in angles, size and shape.

Since we've been given that the angle B is 20º, and the measurement was not altered when rotating the trapezoid. Therefore the angle B' will also be 20º.

I hope this helps.

6 0
2 years ago
Read 2 more answers
A large department store is curious about what sections of the store make the most sales. The manager has data from ten years pr
Snowcat [4.5K]

Answer:

Hypotheses:

H0: There is no difference in the distribution of current sales.

H1: There is a difference in the distribution of current sales.

Enter the test statistic - round to 4 decimal places. 23.0951

Enter the p-value - round to 4 decimal places. 0.0003

Can it be concluded that there is a statistically significant difference in the distribution of sales?

Yes

please mark me brainliest!

7 0
2 years ago
Five hundred sixth-grade students
viktelen [127]
<h3>The ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1</h3>

<em><u>Solution:</u></em>

Given that,

Five hundred sixth-grade students  were surveyed

Which means,

sixth-grade students = 500

125 had traveled on an airplane

<em><u>What is the ratio of total sixth-grade students to the number of students who had  traveled on an airplane?</u></em>

Therefore,

total sixth-grade students : students  traveled on airplane = 500 : 125

<h3>Ratio = 500 : 125</h3>

Reduce to lowest terms,

Divide both sides by 5

<h3>Ratio = 100 : 25</h3>

Further reduce to simplest terms,

Divide both sides by 25

<h3>Ratio = 4 : 1</h3>

Thus the ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1

6 0
2 years ago
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