Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z
Answers
The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
How to interpret the segments formed from Triangle Centroid?The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
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Related Questions
Which is the graph of the function f(x) = x3 + x2 + x + 1?
Answers
Answer:
Step-by-step explanation:
the answer is on the graph
"What is the y-intercept of the line that has a slope of- 4 and passes through the point (A)- 10 (B)-6 (C) 8 (D) 10
Answers
The y-intercept which is the point at which x = 0 is; A: -10
How to find the y-intercept?The general form of an equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are given the slope;
m = -4
Now, the line passes through the point 0, -10. Thus;
(y - y1)/(x - x1) = -4
(y + 10)/(x - 0) = -4
y + 10 = -4x
y = -4x - 10
Thus, the y-intercept which is the point at which x = 0 is; y = -10
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WILL MAKE BRAINLIEST!!
Complete the congruence statement for the figure below.
Answers
What is the area of a square with a perimeter of 44 mm?
Answers
Answer:
The area of the square is 121mm
Step-by-step explanation:
To solve this we need two basic formulas:
P = 4s
A = [tex]s^{2}[/tex]
P = perimeter
s = the length of the side
Since the shape is a square all the sides are the same length. To get the value of 's' we need to isolate:
P = 4s
44 = 4s
44 / 4 = 4s / 4
11 = s
Now plug in the answer for 's' to get the area:
A = [tex]s^{2}[/tex]
A = [tex]11^{2}[/tex]
A = 121
Hope this helps.
Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?
Answers
The angle of m∠5 is 116 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line m and n are parallel lines cut by the a transversal.
Hence,
m∠2 = 64 degrees
Therefore,
m∠5 = m∠4 (alternate angles)
Therefore,
m∠5 + m∠2 = 180
m∠5 = 180 - 64
m∠5 = 116 degrees.
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The degree measure of the angle labelled 5; m<5 = 116°.
What is the measure of the angle labelled 5 in the task content?The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;
It follows from the complete task content that; that the measure of angle 2 is; 64°.
On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.
Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.
Therefore, m<5 = 116°.
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In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
Answers
Answer:
PRQ = 65 degrees
Step-by-step explanation:
Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).
SPR + QPR = 180
135 + QPR = 180
QPR = 45
TQP + RQP = 180
110 + RQP = 180
RQP = 70
Since interior angles of a triangle add up to 180 ...
QPR + RQP + PRQ = 180
45 + 70 + PRQ = 180
PRQ = 65
How many 4-digit positive integers are there for which there are no repeated digits, or for which there may be repeated digits, but all digits are odd?
Answers
The number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.
In this question,
Positive integers are 0,1,2,3,4,5,6,7,8,9
Total number of integers = 10
This can be solved by permutation concepts.
Case 1: 4-digit positive integers with no repeated digits,
First digit, cannot be zero. So remaining 9 digits.
Second digit, can be any digit other than the first digit. So 9 digits.
Third digit, can be any digits other than first and second. So 8 digits.
Fourth digit, can be any digits other than first, second, third digit. So 7 digits.
Thus, Number of ways of 4-digit positive integers with no repeated digits ⇒ (9)(9)(8)(7)
⇒ 4536 ways.
Case 2: 4-digit positive integers, there may be repeated digits, but all digits are odd
Odd integers are 1,3,5,7,9
Number of digits = 5
In this case, we can repeat the digits. So all places can have 5 possibilities.
Thus number of ways of 4-digit positive integers with repeated digits, but all digits are odd = (5)(5)(5)(5)
⇒ 625 ways.
Hence we can conclude that the number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.
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please im in a rush i need help
Answers
Answer:
28.5 ft²
Step-by-step explanation:
shaded area = area of triangle minus area of rectangle
shaded area = (1/2)bh - LW
base of triangle = 5 ft + 4 ft = 9 ft
height of triangle = 3 ft + 6 ft = 9 ft
shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)
shaded area = 40.5 ft² - 12 ft²
shaded area = 28.5 ft²
1/5n+3/5n=7/9
Can you help?
Answers
The value of n in 1/5n+3/5n=7/9 is 35/36
How to solve the equation?The equation is given as:
1/5n+3/5n=7/9
Multiply through by 5
n + 3n = 35/9
Evaluate the sum
4n = 35/9
Divide both sides by 4
n = 35/36
Hence, the value of n in 1/5n+3/5n=7/9 is 35/36
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Freddie had saved 231 pennies.
Which statement best describes
the number of pennies he had?
Answers
he has 231 pennies..............
Bd=16 and ac is the perpendicular bisector of bd. 2x-14 37-x d 2y-2 3 y=[?] enter
Answers
The value of y from the given expression is 5
Perpendicular Bisector
Given:
BD = 16
BC = 2y - 2
CD = y + 3
Since AC is a perpendicular bisector of BD:
BC = CD
2y - 2 = y + 3
2y - y = 3 + 2
y = 5
Hence, the value of y from the given expression is 5
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Find the seventh term of the sequence which has a first term of 1/2 and has a common ratio of three
Answers
The seventh term of the sequence is 364.5
Geometric progressionFrom the question, we are to determine the seventh term of the sequence
Using the formula,
[tex]a_{n} = ar^{n-1}[/tex]
Where [tex]a_{n}[/tex] is the nth term
a is the first term
and r is the common ratio
From the given information,
a = 1/2
r = 3
Thus,
[tex]a_{7} = (\frac{1}{2}) 3^{7-1}[/tex]
[tex]a_{7} = (\frac{1}{2}) 3^{6}[/tex]
[tex]a_{7} = \frac{1}{2} \times 729[/tex]
[tex]a_{7} = 364\frac{1}{2} \ OR \ 364.5[/tex]
Hence, the seventh term of the sequence is 364.5
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Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = 3/4x
O h(x) = 1/4x
Answers
Answer:
last answer:
h(x) = 1/4 x
Step-by-step explanation:
First, change f(x) to y.
f(x) = 4x
y = 4x
Then switch the x and y.
y = 4x
x = 4y
Last, solve for y.
x = 4y
x/4 = 4y/4
x/4 = y
y = x/4
This is the same as:
y = 1/4 x
h(x) = 1/4 x
Use the distributive property to write an
addition sentence equivalent to:
8(5+2)
Answers
Answer:
8(5) + 8(2)
Step-by-step explanation:
8 (5 + 2) is 8 (7) or 56
If I distribute the 8 through the problem, I will get the same answer
8(5) + 8(2)
40 + 16
56
Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and c?
Answers
The values of b and c are -4 and 4 respectively
How to determine the values of b and c?The function is given as:
f(x) = x^2 + bx + c
Differentiate f(x)
f'(x) = 2x + b
Set to 0
2x + b = 0
Solve for b
b = -2x
The minimum is (2, 0).
So, we have:
b = -2 * 2
b = -4
Substitute b = -4 in f(x) = x^2 + bx + c
f(x) = x^2 - 4x + c
Substitute (2, 0)
0 = (2)^2 - 4(2) + c
This gives
0 = 4 - 8 + c
Evaluate
c = 4
Hence, the values of b and c are -4 and 4 respectively
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If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
(–h, –k)
(h, k)
(–h, k)
(h, –k)
Answers
The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).
What are the transformation rules for horizontal and vertical shifts?The transformation rules are:
Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)
Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)
Calculation:It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]
This parabola has vertex at (h, k).
Since this equation is obtained by shifting h units horizontally and k units vertically.
So, the original vertex is at (h - h, k - k) = (0, 0)
Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]
Therefore, the given transformed equation of parabola has vertex (h, k).
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Answer:
B] (h,k)
The next answer is Vertex (-5, -4)
☆
EDGE2022; Good luck :3!!!!
Please help me! due today:(
Answers
Step-by-step explanation:
(π * r²) will give you are of entire circle
the multiply by 60/360 , to give the shaded part
Answer:
A ≈ 25.7 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{60}{360}[/tex]
= π × 7² × [tex]\frac{1}{6}[/tex]
= [tex]\frac{49\pi }{6}[/tex]
≈ 25.7 cm² ( to the nearest tenth )
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answers
Answer:
Question 6) Neither (Not an inverse variation)
Question 7) Inverse variation
Question 8) Inverse variation
Step-by-step explanation:
These are the two formulas we need to know prior to solving the question.
Direct variation: c times x
Inverse variation: c times 1/x --> c/x
- Here, c is the constant
6. y = x + 7
This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.
7. 14 = xy
This equation is an inverse variation.
xy = 14
y = 14/x
14 is the constant, and the format is the same as for an inverse variation.
8. x = -8/y
This equation is an inverse variation.
yx = -8
y = -8/x
-8 is the constant, and the format is the same as for an inverse variation.
So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.
General forms
Direct
y=KxInverse
y=k/xso
#6
y=x+7Not inverse and direct also as 7 is present
#7
14=XYy=14/xYes
#8
x=-8/yy=-8/xYes
Find the area of this circle
Answers
Answer:
[tex] {75ft}^{2} [/tex]
Step-by-step explanation:
[tex]a = \pi{r}^{2} = 3 {r}^{2} \\ a =3 ({ \frac{10}{2} })^{2} = 3 \times {5}^{2} \\ a = 3 \times 25 = 75[/tex]
First, we replace π with 3, since we were told to.We know 10 is the diameter and the radius is half of the diameter, so we divide 10 by 2.We get 5. 5 squared is the same as (5×5). Finally, we multiply 3 by 25.To start solving this exercise, we obtain as data:
π = 3r = 10 ft²a = ?To find the area of the circle. We apply the following formula: A =π r², where
a = areaπ = pir = radiusWe substitute our data in the formula and solve:
Substituting values into the equation:
[tex]\boldsymbol{\sf{A=3*(10 \ ft)^{2} }}[/tex]Taking the square root:
[tex]\boldsymbol{\sf{A=3*100 \ ft^{2} }}[/tex]Multiplying
[tex]\boxed{\boldsymbol{\sf{A=300 \ ft^{2} }}}[/tex]Therefore, the area of the circle is 300 ft².
Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
Answers
The solutions to the given system of equations are x = 6 and y = -5
Simultaneous linear equationsFrom the question, we are to solve the given system of equations
The given system of equation is
4x+5y=-1
-5x-8y=10
Multiply the first equation by 5 and the second equation by 4
5× (4x+5y=-1)
4× (-5x-8y=10)
20x + 25y = -5
-20x - 32y = 40
------------------------
0x + (-7y) = 35
-7y = 35
y = 35/-7
y = -5
Substitute the value of y into the first equation to find x
4x + 5y = -1
4x + 5(-5) = -1
4x -25 = -1
4x = -1 +25
4x = 24
x = 24/4
x = 6
Hence, the solutions to the given system of equations are x = 6 and y = -5
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Which pair of complex numbers has a real-number product? (1 2i)(8i) (1 2i)(2 – 5i) (1 2i)(1 – 2i) (1 2i)(4i)
Answers
The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
According to the statement
we have given Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
So, For this purpose
we have to multiply these pairs with each other.
So,
(1+2i)(8i) = 8i +16(i)^2
And
(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2
And
(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5
And
(1+2i)(4i) = 4i + 6(i)^2
From these multiplication we found that the third pair have a real number product.
So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
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8 more than 3 times a number is the same as -5 times the number.
a. x = -1
b. x = 1
c. x = -2
Answers
Answer:
3x +8 = -5x
3x + 5x = -8
8x = -8x
x = -8 /8
x = -1
Hope it helps...
Please contact me for further explanation....
A company designs microphones for use in conference rooms. a new microphone needs to focus on the person speaking and not the voices of other people in the room. which polar equation would best match the desired audible range of the microphone?
Answers
r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.
How do you know if an equation is polar?Determine the kind of polar equation. The polar equation has the shape of a limaçon, and is written as r = a - b cos. We just need to assess the equation throughout the range [0, 1] and then reflect the graph about the polar axis because the equation passes the condition for symmetry to the polar axis.What is a polar in math?The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.What is the meaning of polar form?In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.Learn more about polar form here:
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Answer:
D
Step-by-step explanation:
2. Which of the following expressions is equivalent to 322?
01
08.1/1
032.2
08-2
Answers
Answer:
C. (32/4)*2
Step-by-step explanation:
C is the correct answer because when we divide 4/2 it equals 2.
Hope this helps!
Answer:
D
Step-by-step explanation:
Given expression:
[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]
Evaluation of the given expression:
[tex] = 8 \times 2 \times 2 [/tex]
[tex] = 32 [/tex]
A. [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]
B. [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]
C. [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]
D. [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]
Only expression D evaluates to the same value as the given expression.
Answer: D
A teacher has 14 senior students, 7 junior students, 4 sophmore, 5 freshmen, what is the proabability that she chooses a senior?
Answers
Answer:
7/15
Step-by-step explanation:
To find the probability the student is a senior
P( senior) = number of seniors / total students
= 14 / ( 14+7+4+5)
= 14/30
= 7/15
Answer:
14/30 or 7/15
Step-by-step explanation:
probability = no. of senior students / total no. of students
probability = 14 / (14+7+4+5)
probability = 14/30
This can be simplified to 7/15.
Hope this helps!
What is the y-intercept of the function f(x)=-2/9x + 1/3?
Answers
Answer:
y-intercept = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the coefficient is the slope (slope = -2/9x)
the constant is the y-intercept (y-intercept=1/3)
this is true for all functions like this
Answer:
The y-intercept is
c) 1/3
Step-by-step explanation:
What is the slope of a line passing through (-4,-5)
and (-2,-9)?
Answers
= (y2-y1)/(x2-x1)
= (-9-(-5))(-2-(-4))
= (-4)(2)
= -8
Answer:
slope = - 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )
m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
Find the area of the polygon formed whe these points are connected a(3,7)b(3,3)c(7,3)d(7,7)
Answers
Here, given
sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)
Let, 3 = x1 & 7= y1 , 3= x2 & 7= y2 , 7= x3 & 3= y3 , 7= x4 & 7= y4
[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}
[tex]\frac{1}{2}[/tex] (32)
16cm^2
Hence, the area of the polygon is 16cm2.
The formula for calculating the area of a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].
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10. A drawer contains only green marbles. After
5 red marbles are added to the drawer, the
probability of picking a red marble is
How many marbles were there in the drawer
originally?
(A) 5
(B) 7
(C) 12
(D) 30
(8)
Answers
Answer:
(D) 30
Step-by-step explanation:
number of green marbles = x
number of red marbles = 5
total number of marbles = x + 5
p(red) = (number of red marbles)/(total number of marbles)
p(red) = 5/(x + 5)
p(red) = 1/7
5/(x + 5) = 1/7
(x + 5) × 1 = 5 × 7
x + 5 = 35
x = 30
Answer: (D) 30
Can someone help me please
Answers
Answer: B. [tex]12log(x)-4log(y)[/tex]
Step-by-step explanation:
Properties of logs:
[tex]log_{a} (\frac{B}{C} )=log_{A}B-log_{A} C[/tex]
[tex]logA^B = BlogA[/tex]
So, [tex]log\frac{x^{12} }{y^4} =logx^{12} -logy^4 =12log(x)-4log(y)[/tex]
It would be 12 log x - 4 log y (B)