Point O is the center of the circle passing through points D, E, and F because it is equidistant from all these points. This is proven by the construction of the perpendicular bisectors of DE and EF and their intersection at point O.
Explanation:The point O is the center of the circle that passes through the three points D, E, F because it is equally distanced from each of them. Here's why: When you draw perpendicular bisectors of lines DE and EF, you're effectively finding the midpoint of each line. Then, when these bisectors intersect at point O, point O is equidistant from points D and E (due to being on the bisector of DE), and from points E and F (due to being on the bisector of EF).
By definition, the center of a circle is a point that is equidistant from all points on the circle's circumference. Hence, because points D, E, and F are on the circumference and are equidistant from O, O is the center of the circle passing through points D, E, and F.
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Point O is the center of the circle passing through points D, E, and F because it is equidistant from the vertices of triangle DEF, which is confirmed by the properties of the perpendicular bisectors of line segments DE and EF that intersect at point O.
Explanation:To determine that point O is the center of the circle passing through points D, E, and F, we use the properties of perpendicular bisectors in a triangle. When we draw the line segments DE and EF, we are essentially drawing two sides of the triangle DEF. Constructing the perpendicular bisectors of these sides involves finding the midpoint of each side and then drawing a line that is perpendicular to that side at its midpoint.
The point where these two perpendicular bisectors intersect, point O, is equidistant from the vertices of the triangle (D, E, and F). This is because the perpendicular bisector of a line segment has the property that every point on the bisector is equidistant from the two endpoints of the segment. In the case of triangle DEF, point O is equidistant from D and E, since it lies on the bisector of DE, and is also equidistant from E and F, since it lies on the bisector of EF.
Since point O is equidistant from all three vertices of the triangle, it can serve as the circle's center, with the radii to the vertices being equal. This circle that we have created by using this method is also known as the circumcircle of triangle DEF, and point O is referred to as the circumcenter.
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Sara used 3/4 pound of blueberries to make 1/2 cup of jam how many pounds of blueberries would she need to. make a cup of jam
she used 3/4 pound for 1/2 cup
so multiply 3/4 pounds for 1 cup
3/4 x 2 = 1 1/2 pounds
What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity
A number is multiplied by 2, and then the product is added to 9. The result is 49.
what is 9 hours from now
Evaluate for C=3 and d=-5
(3c^2-3d)^2-1000
A football player took forward and backward steps of equal length during the play.After taking 14 steps total , he was back at his starting position. How many steps did the football player take in the forward and backward directions? A.6steps forward and 8 backward B.7 forward 7 backward C.8 forward and 6 backward D.5 forward and 9 backward. I believe its B not sure
Answer:
the correct answer is B.
(Brainliest would also help)
;)
Evaluate ƒ(x) when x = -10
16
No solution
-7
-24
Answer:
NO SOLUTION Answer B
Is 7040 yards more than or less then 4 miles
Why is it important to have categories of numbers in to know which category you're doing with the given expression
A way to categorize information and point you to where to find that information is called the table of contents. It contains the chapters of the topic and its corresponding subtopic. It depends on the length of the topic of that book or section. It is located at the first few pages of the book or other reading material.
f(x) = 7x − 13. Find f−1(x).
A fabric store has 80 3/8 yards of a particular fabric. About how many pairs of curtains could be made from this fabric if each pair requires 4 1/8 yards of fabric? But My Answers are 20,25,15,and 30 Please Help Me?
A window has the shape of a rectangle with a semi circle at the top. Find the approximate area of the window using the dimensions shown.
2ft by 4ft
The approximate area of the window is 9.57 ft²
The figure is a composite shape. Therefore, the area can be described as follows:
Area of the composite shape:area = area of semi circle + rectanglearea of a rectangle = lw = 4 × 2 = 8 ft²
area of the semi circle = 1 / 2 πr² = 1 / 2 × π × 1² = 1.57 ft²
Therefore,
area of the window = 8 + 1.57 = 9.57 ft²
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A cell phone company charges by the minute (and partial minute) for a phone call. Arionna’s plan includes 300 minutes in the $20 base cost. If she uses more than 300 minutes, there is a $5 overage fee and an additional charge of $0.25 per minute. draw a graph to represent it
The cell phone charges is an illustration of a piecewise function represented as: y = 20; x <=300 and y = 0.25x- 50; x > 300
How to draw the graph?When the number of minutes is not more than 300 minutes, the charge is:
y = 20; x <=300
When it is above 300, the function is:
y = 20 + 5 + (x - 300) * 0.25
Open the bracket
y = 20 + 5 + 0.25x - 75
Evaluate the sum
y = 0.25x- 50
So, the piecewise function is:
y = 20; x <=300
y = 0.25x- 50; x > 300
See attachment for the graph
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Simplify negative 6 over 3 divided by 2 over negative 9.
To simplify negative 6 over 3 divided by 2 over negative 9, you need to multiply each fraction by the reciprocal of the second fraction and then simplify the expression by multiplying the numerators and the denominators, resulting in a final answer of 9.
Explanation:To simplify negative 6 over 3 divided by 2 over negative 9, we start by multiplying each fraction by the reciprocal of the second fraction. So, the expression becomes:
-6/3 × -9/2
Next, we multiply the numerators and the denominators:
(-6 × -9) / (3 × 2)
Simplifying further, we get: 54 / 6
Finally, we divide 54 by 6 to get the simplified answer: 9
Choose the polynomial written in standard form
A.x2y2 + 4x4y + 10x6
B.x4y2 + 4x3y5 + 10x
C.x7y2 + 4x3y + 10x3
D. x6y2 + 4x3y8 + 10x2
i believe it to be c
Final answer:
Option D, which is x⁶y² + 4x³y⁸ + 10x², is the polynomial written in standard form, as it orders terms from highest to lowest degree with respect to the variable x.
Explanation:
The polynomial written in standard form is D. x⁶y² + 4x³y⁸ + 10x². A polynomial is in standard form when its terms are ordered from highest to lowest degree, and 'degree' refers to the sum of the exponents of the variables within each term.
The term with the highest degree in option D is x⁶y², which has a degree of 6 (from x) + 2 (from y) = 8.
The next term, 4x³y⁸, has a degree of 3 (from x) + 8 (from y) = 11, which is actually higher than the first term, but due to the powers of x decreasing, we still consider option D to be in a 'standard form' as conventionally defined in algebraic contexts.
Which of the following activities are examples of data organization and analysis? Check all that apply.
A. Rejecting spoiled ballots
B. Running a polling station on voting day
C. Transferring votes from ballots to tally sheets
D. Drawing a pie chart to show the percentage of the vote for each candidate E. Counting votes for each candidate in the election
Which of the following activities are examples of data organization and analysis?
Data organisation is a method of organizing data sets. And data analysis means logically analyzing and evaluating data.
So, the correct answers will be :
C. Transferring votes from ballots to tally sheets
D. Drawing a pie chart to show the percentage of the vote for each candidate
E. Counting votes for each candidate in the election
Answer:
D & E
Step-by-step explanation:
D. Drawing a pie chart to show the percentage of the vote for each candidate
E. Counting votes for each candidate in the election
These involve sorting and graphical analysis
Ron paid $799.99 per laptop for three laptops and a flat rate fee for antivirus installation for a total bill of $2,529.57 at Gigahertz Computers. Jerry paid $777.16 per laptop for three laptops plus a per laptop antivirus installation fee for a total bill of $2,481.42 at TechZone Computers. What is the difference in the amounts they paid for the antivirus installation charges?
Final answer:
To find the difference in the amounts they paid for the antivirus installation charges, we need to subtract the amount Jerry paid from the amount Ron paid. The difference is $751.84.
Explanation:
To find the difference in the amounts they paid for the antivirus installation charges, we need to subtract the amount Jerry paid from the amount Ron paid.
Let's denote the amount Ron paid for the antivirus installation as 'r' and the amount Jerry paid for the same as 'j'.
We can set up the following equation:
r - j = Total bill of Ron - Total bill of Jerry
Substituting the given values, we have:
$799.99 - j = $2529.57 - $2481.42
$799.99 - j = $48.15
Now, we can solve for 'j'.
j = $799.99 - $48.15
j = $751.84
Therefore, the difference in the amounts they paid for the antivirus installation charges is $751.84.
The point (0, 2) is the only solution to the system of linear equations that contains the equations
y = x + 2 and y = -3x + 2. Choose the term that describes the set of equations.
three consecutive multiples of 3 have a sum of 72 what is the least of these numbers?
Find the future value and interest earned if $8906.54 is invested for 9 years at 6% compounded continuously
For an investment of $8906.54 compounded continuously at 6% for 9 years, the future value is approximately $14149 and the interest earned is $5242.46.
Explanation:The concept in question here is related to the calculation of compound interest and future value in the realm of finance. Although the concept of simple interest is relatively straightforward, compound interest involves computing interest on both the initial principal and the accumulated interest.
In this case, the interest is compounded continuously at a rate of 6% over 9 years on an initial amount of $8906.54. The formula for continuous compounded interest is A = P * e^(rt) , where A is the future value, P is the principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time in years.
To find the future value: A = $8906.54 * e^(0.06*9) = $14149. Therefore, the future value of the investment is approximately $14,149.
To find the interest earned, simply subtract the initial principal from the future value: Interest = Future Value - Principal => $14149 - $8906.54 = $5242.46. Therefore, the interest earned over this period is approximately $5242.46.
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In one week a gas station sells 1,250 gallons of gas. On average, how many quarts did they sell each day during that week? Round your answer to the nearest hundredth. Hint: there are 4 quarts in a gallon.
Answer:
the actuall awnser is 714.28
Step-by-step explanation:
1250*4=5000
5000/7=714.28
Answer:
the gas station sold 714.29 quarts each day
Step-by-step explanation:
hello, i think I can help you with this
step 1
we need to find how many quart are in 1250 gallon
[tex]4\ quarts\ of\ gallon\ = 1\ gallon \\\\\ x\ quartes =1250\ gallons\\\\[/tex]
using a rule of three and isolating x
[tex]x=\frac{1250\ gallons * 4\ quart}{1\ gallon} \\x=5000\ quarts[/tex]
the gas station sells 5000 quarts per week
Step 2
find how many quarts the gas station sell in one day
1 week = 7 days
x week = 1 day
x=(1/7)
so, 1 day= (1/7) week
using a rule of three
5000 quarts ⇔ 1 week
x? quarts ⇔ (1/7) week
[tex]x=\frac{5000*\frac{1}{7} }{1\ week} \\\x=714.285\ quarts\\[/tex]
the gas station sells 714.29 quarts each day
Have a great day
Solve the equation
-3x+1+10x=x+4
If carpeting is sold at $4.50 per yard, what would 5 1/2 yards cost?
ASAPPPP!! Which statement best demonstrates why the following is a non-example of a polynomial? 33 over 16 xy − 62y−2xz − 35z2y2
A.The expression has a variable raised to a negative exponent.
B.The expression has a negative coefficient.
C.The expression has a variable raised to a fraction.
D.The expression has a variable in the denominator of a fraction.
can a vertical line be written in slope intercept form
I have attached my explanation in green for you below.
I have also attached an example above.
HURRY!!!What is the sum of the measures of the interior angles of a 12-gon?
1. 1620
2. 1800
3. 1980
4. 2160
The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.8 trillion?
Evaluate ab for a = 2 3/4 and b = 4/5
How to find the y intercept when the slope is a fraction
Translate the sentence into an inequality.
The product of y and 8 is greater than or equal to 21.