Final answer:
The center of the circumscribed circle about triangle EFG with given vertices is found by calculating the perpendicular bisectors of the triangle's sides and locating their intersection point, which is the center (8,3).
Explanation:
To find the center of the circumscribed circle about triangle EFG with vertices E(6,4), F(6,2), and G(10,2), we need to determine the perpendicular bisectors of at least two sides of the triangle and then find their intersection point, which will be the center of the circumscribed circle.
First, find the midpoint of side EF, which has the same x-coordinate (since E and F have the same x-coordinate), so the midpoint is (6,3).Next, we need the equation of the perpendicular bisector of EF. Since EF is vertical, its perpendicular bisector is a horizontal line that passes through the midpoint, hence the equation is y = 3.Then, find the midpoint of side FG. As the endpoints have the same y-coordinate, the midpoint will have that y-coordinate (2) and the x-coordinate will be the average of the x-coordinates of F and G, which is (6+10)/2 = 8. So, the midpoint of FG is (8,2).The slope of side FG is 0 (since it's horizontal), so the slope of its perpendicular bisector is undefined, meaning it's a vertical line. Consequently, the equation of this perpendicular bisector is x = 8.Last, by solving the system of equations formed by the two perpendicular bisectors x = 8 and y = 3, we find the intersection point, which is the center of the circumscribed circle: (8,3).12 POINTS PLZ HELP ONLY HAVE 3 MINUTES LEFT
Which statement about histograms is true?
Data is organized in categories.
Data appears as bars that are all about the same height.
Data is organized in equal intervals.
Data appears as bars that do not touch.
Answer:
c
Step-by-step explanation:
The correct statement about Histogram is Data is organized in equal intervals.
What is Histogram?A histogram is a graphical representation of discrete or continuous data. The area of a bar in a histogram is equal to the frequency. The y -axis is plotted by frequency density (which is proportional to the frequency) and the x -axis is plotted with the range of values divided into intervals.
Given:
Equal in breadth and corresponding to equal class intervals are the bars. However, they can occasionally be displayed as a wider variety within their groups, such as in size classes.
The width and data being achieved, for instance, forces a true event of varying class sizes in education upon the base of the graph.
and, for the purpose of displaying evenly spaced-out numerical data. The bars should be in close proximity to one another but not overlap. You can view the frequency distribution of the data or the number of pieces of data contained in each interval using these intervals.
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A business’s assets are valued at $600,000, and the value depreciates 20% per year. Using the formula V(t) = V0(b)t, what is V0, what is (b), and what is the value of the assets after 5 (t) years? Show your work.
t = 5
V0 =
(b) =
Value after 5 years:
PLEASE HELP!
Cynthia is constructing a circle inscribed in a triangle.She has partially completed the construction as shown below.What should her next step be in the construction (worth 50 points)
A. Connect vertex B to the arc markings to complete the angle bisector
B.use a straightedge to find the angle bisectors for angles A and B
C. Connect three arc markings together to form the triangle
D.use the arc markings to determine the radius to construct the circle
Please explain!
The correct next step that Cynthia should do is to:
D. use the arc markings to determine the radius to construct the circle
The arc markings are actually used as the baseline in determining the center and the radius of the circle. The arc markings are created with the use of a compass. All other choices are completely irrelevant because what we need is the arc and not the angles. The angles do not create the circle. Letter C is also wrong because what we are trying to form is the circle and not the triangle. The triangle is already created.
Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).
Which number is greatest?
a. 3.4 × 10-2
b. 4.3 × 10-3
c. 5.2 × 10-4
d. 6.1 × 10-4
Answer:
the answer is d 6.1x 10-4
Step-by-step explanation:
is this correct? if not please let me know how to solve it
WILL PICK BEST ANSWER IF ITS CORRECT TO ANSWER THESE FEW PROBLEMS
YOU MUST EXPLAIN WHY YOU KNOW
1)Which system of linear inequalities is represented by the graph?
(goes with pic 1)
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y > -1/3x + 2
y > 2/3x + 3 and y >-1/3 x + 2
2)
Which system of linear inequalities is represented by the graph?
(goes with pic 2)
y > 2x – 1 and y < 2x + 2
y > 2x + 2 and y < 2x – 1
y < 2x + 2 and y > 2x – 1
y < 2x + 1 and y > 2x – 2
3)Which linear inequality is represented by the graph?
(goes with pic 3)
y > 2x + 2
y ≥ 1/2x + 1
y > 2x + 1
y ≥ 1/2x + 2
4)
What is the solution to the system of linear equations?
(goes with pic 4)
(–3, 0)
(–3, 3)
(0, 2)
(3, 1)
Part 1)
In this problem we have two lines
The equation of the fist line is
[tex]y=\frac{2}{3}x+3[/tex]
The solution is the shaded area above the dashed line
so
the inequality is
[tex]y>\frac{2}{3}x+3[/tex]
The equation of the second line is
[tex]y=-\frac{1}{3}x+2[/tex]
The solution is the shaded area below the full line
so
the inequality is
[tex]y\leq -\frac{1}{3}x+2[/tex]
therefore
the answer Part 1) is
[tex]y>\frac{2}{3}x+3[/tex] and [tex]y\leq -\frac{1}{3}x+2[/tex]
Part 2)
In this problem we have two lines
The equation of the fist line is
[tex]y=2x+2[/tex]
The solution is the shaded area above the full line
so
the inequality is
[tex]y\geq 2x+2[/tex]
The equation of the second line is
[tex]y=2x-1[/tex]
The solution is the shaded area below the full line
so
the inequality is
[tex]y\leq 2x-1[/tex]
therefore
the answer Part 2) is
[tex]y\geq 2x+2[/tex] and [tex]y\leq 2x-1[/tex]
Part 3)
In this problem we have only one line
The equation of the line is
[tex]y=2x+1[/tex]
The solution is the shaded area above the dashed line
so
the inequality is
[tex]y>2x+1[/tex]
therefore
the answer Part 3) is
[tex]y>2x+1[/tex]
Part 4)
we know that
the solution of the system of linear equations is the intersection both graphs
so
see the graph
the solution point is [tex](0,2)[/tex]
therefore
the answer part 4) is the option
[tex](0,2)[/tex]
A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle ADC is a right angle and that angle BDC is 32° greater than mangle ADB. Solve an equation to find angle BDC and angle ADB.
Answer:
m∠ADB = 29° and m∠BDC = 61°
Step-by-step explanation:
It is given that m∠ADC = 90°
Since m∠ADB + m∠BDC = 90° [∠ADB and ∠BDC are complimentary]
Since ∠BDC = ∠ADB + 32°
So, m∠ADB + m∠ADB + 32° = 90°
2(m∠ADB) + 32° = 90°
2(m∠ADB) = 90 - 32
2(m∠ADB) = 58°
m∠ADB = 29°
Since m∠ADB + m∠BDC = 90°
So, m∠BDC + 29° = 90°
m∠BDC = 90 - 29
= 61°
Therefore, m∠ADB = 29° and m∠BDC = 61°
m∠ADB = 29° and m∠BDC = 61°
Solving this will just be based on some basic angle theorems in a triangle.
We are given; m∠ADB = 29° and m∠BDC = 61° We are told that m∠ADC is a right angle. This means that; m∠ADC = 90°Now, since m∠ADC = 90°, it means that;m∠ADB + m∠BDC = 90° (because m∠ADB and m∠BDC are complimentary angles due to the fact that angle at point D is 90°)
We are also told that;m∠BDC is 32° greater than angle m∠ADB
This means that we can write as;
m∠BDC = m∠ADB + 32°
From earlier, we saw that;m∠ADB + m∠BDC = 90°
Thus, putting m∠ADB + 32° for m∠BDC, we will have;m∠ADB + m∠ADB + 32° = 90°
2(m∠ADB) + 32° = 90°
Subtract 32° from both sides to get;
2(m∠ADB) = 90° - 32°
2(m∠ADB) = 58°
m∠ADB = 58°/2
m∠ADB = 29°
Puttting 29° for m∠ADB into; m∠ADB + m∠BDC = 90° gives us;29° + m∠BDC= 90°
Subtract 29° from both sides to get;
m∠BDC = 90° - 29°
m∠BDC = 61°
In conclusion, m∠ADB = 29° and m∠BDC = 61°Read more at; brainly.com/question/4687866
A puzzle contains a triangular piece with a base of 3 in. and a height of 4 in. A manufacturer wants to make 80 puzzles. Find the amount of wood used if each puzzle contains 20 triangular pieces.
I believe this question asks for the total amount of area of wood that is needed to make 80 puzzles.
The formula for area of triangle is given as:
A = (1 / 2) b h
where,
b = is the base of the triangle = 3 in
h = height of the triangle = 4 in
So calculating for area of 1 on triangle (A1):
A1 = (1 / 2) (3 in) (4 in)
A1 = (1 / 2) 12 in^2
A1 = 6 in^2
We are given that we are to make 80 puzzles and each puzzle has 20 triangles, therefore the total amount of triangles we need to make is:
n = 80 * 20
n = 1600
Therefore the total area needed (A) is:
A = A1 * n
A = 6 in^2 * 1600
A = 9,600 in^2
In a right triangle angle C measures 40 degrees. The hypotenuse of the triangle is 10in long. What is the approximate length of the side adjacent to angle C?
The perimeter of a triangle is 86 inches. The largest side is four inches less than twice the smallest side. The third side is 10 inches longer than the smallest side. What is the length of each side?
Someone please answer this for me
Segment DE is midsegment of triangle ABC. What is the length of segment DE?
A) 5
B) 10
C) 15
D) 20
Answer:
B) 10
Step-by-step explanation:
If DE is midsegment of the triangle, we know that AC measures twice as DE.
In the problem we have that AC = x + 15 and DE = x + 5
Writing this as an equation we have:
[tex]x + 15 = 2(x+5)\\x+15=2x +10\\15-10=2x-x\\5=x[/tex]
Therefore x = 5 and the length of segment DE is:
x + 5 = 5 + 5 = 10
Therefore the correct answer is B) 10
Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.
How many ways can a librarian arrange 15 books on a top shelf if she has 20 books from which to pick?
Answer: 20!/5!
Step-by-step explanation:
In EFG, mE = 30, mF = 60, and mG = 90. Which of the following statements about EFG are true?
Statements B, C, and F are all true based on the given angle measures in triangle EFG.
Let's reevaluate the statements with the given angle measures in triangle EFG:
m∠E = 30°
m∠F = 60°
m∠G = 90°
A. FG = √3/2 EF
FG = (EF * √3) / 2
This statement is true. FG is indeed equal to √3/2 EF.
B. EG = √3/2 EF
EG = (EF * √3) / 2
This statement is true. EG is equal to √3/2 EF.
C. EG = -√3 FG
EG = -√3 * FG
This statement is true. EG is equal to -√3 FG.
D. EF = -√3 FG
EF = -√3 * FG
This statement is true. EF is equal to -√3 FG.
E. EG = 2 FG
EG = 2 * FG
This statement is true. EG is equal to 2 FG.
F. EF = 2 FG
EF = 2 * FG
This statement is true. EF is equal to 2 FG.
Statements B, C, and F are all true based on the given angle measures in triangle EFG.
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Quadrilateral LMNO is transformed according to the rule T(–2, 4). What are the coordinates of L’? (3, –3) (3, 5) (9, –1) (9, 3)
A transformation specified with a rule T (x, y) means that the figure is undergoing a process of translation. Translation means that only the positions of the coordinates are changed with no other change on the angle, lengths or any other characteristic aside from the position alone.
So since the rule is T (-2, 4) then this means that the figure is moved 2 units left and 4 units up.
The initial coordinates of point L is:
point L = (5, 1)
The coordinates of L’ then is:
point L’ = L(5, 1) + T(-2, 4)
point L’ = (5 – 2, 1 + 4)
point L’ = (3, 5)
Answer:
(3, 5)
(3,5) is the answer.
Can anyone PLEASE help geometry is my worst subject!
Meghan works at an ice cream shop and makes $8.25 per hour Lucas works at a landscaper and makes $6.50 per hour how much more does Meghan makes each hour ?
Annie found that 57 students in her school knew French and 23 of those students knew Spanish, as well. There were 11 students who did not know French but knew Spanish. There were 4 students who knew neither French nor Spanish. Which table best summarizes the data collected by Annie?
Knew Spanish Did not know Spanish Total
Knew French 57 34 91
Did not know French 11 4 15
Total 68 38 106
Knew Spanish Did not know Spanish Total
Knew French 12 34 46
Did not know French 11 4 15
Total 23 38 61
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 4 11 15
Total 27 45 72
Answer:
Table C is the correct option.
Step-by-step explanation:
We are given,
Number of students which knew French = 57
Number of students which knew both French and Spanish = 23
Number of students which knew Spanish but not French = 11
Number of students which knew neither French nor Spanish = 4
So, we get that,
Number of students not knowing French = 57 - 23 = 34
Hence, the table for the given situation is,
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72
Thus, option C is correct.
option C is correct-
The size of a bicycle is determined by the diameter of the wheel. You want a 24-in bicycle for Christmas. What is the circumference of one of the wheels? A 75.4 in B 75.3 in C 37.7 in D 37.6 in
The circumference of one of the wheels is:
Option: A 75.4 in.
Step-by-step explanation:The 24-in bicycle means that the diameter of the wheel of the bicycle isL 24 in.
We know that the wheel of the bicycle is in the shape of a circle.
This means that the diameter of circle is: 24 in.
Hence, the radius(r) of circle is: 12 in.
( since we know that the radius(r) of the circle is half the diameter(d) of the circle)
Now, we are asked to find the circumference of the circle.
The circumference(C) of the circle is given by:
C=2πr
i.e.
C=2×3.14×12
i.e.
C=75.36 in.
which to the nearest tenth is: C=75.4 in.
Which of the expressions are equivalent to the one below? Check all that apply. (10 + 8) • 2
Which of the following statements is true?
The number 2 /3 is an irrational number.
The number -4 is a whole number.
The number 9 is a rational number.
The number 5/8 is a natural number.
The square root of 12 is between A.) 3 and 4 B.) 4 and 5 C.) 5 and 6 D.) 6 and 7
. In the algebraic expression mc034-1.jpg 7, 17, and –10 are _____ terms. operations. coefficients. variables.
Answer:
Coefficient
Step-by-step explanation:
The correct option is A.
In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are coefficients.
A. Coefficients. The numbers 7, 17, and -10 are coefficients in the expression 7a + 17b - 10c because they are the constants that multiply the variables a, b, and c respectively.
B. Incorrect. Operations are mathematical actions like addition, subtraction, multiplication, or division, not the constants themselves.
C. Incorrect. Variables, denoted by a, b, and c, are letters or symbols representing unknown or changing quantities, not the constants.
D. Incorrect. Terms are the individual parts of an expression separated by addition or subtraction, consisting of a coefficient and possibly a variable or variables multiplied together. The numbers 7, 17, and -10 are coefficients within the terms of the expression but are not terms themselves.
So, the correct option is A. Coefficients.
The complete question is here:
In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are ______
A. coefficients.
B. operations.
C. variables.
D. terms.
Find Y of the polygon
I need to know how to find angle "H"
Point C is the center of the circle. The measure of angle ACB is 12x – 7. Arc AB measures 10x + 7. Find the value of x.
Answer:
x=7
Step-by-step explanation:
Subtract 10x
from both sides of the equation.
12x−7−10x=7
Subtract 10x
from 12x
2x−7=7
Add 7
to both sides of the equation.
2x=7+7
Add 7 and 7
2x=14
Divide each term by 2 and simplify.
x=7
Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?
The volume of a sphere with radius r is 4 3 πr 3 . what is the volume of a sphere with radius 5
Final answer:
To find the volume of a sphere with a radius of 5, plug the value into the formula V = (4/3)πr³. The result is approximately 523.6 cm³.
Explanation:
The question asks for the volume of a sphere with a given radius. The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius of the sphere.
To find the volume of a sphere with radius 5, we substitute r with 5 in the formula:
V = (4/3)π(5)³
V = (4/3)π(125)
V = (4/3)π(125) = 500/3π cm³
The volume of a sphere with radius 5 is therefore 500/3π cubic centimeters, which is approximately 523.6 cm³ when rounded to one decimal place.