Which of the following is a characteristic of the circumcenter of a triangle? A. It is the center of the circle that can be inscribed in a given triangle. B. It is equidistant from all three sides of the triangle. C. It is equidistant from all the vertices in the triangle. D. It is the intersection of all three angle bisectors of the triangle.
Answers
Explanation
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.
Related Questions
Which of the following formulas, when evaluated using rational values for the variables, will result in an irrational number?
Answers
Can someone help me with this and show work pleaseee!!!
Answers
Answer:
10 units and 157.84 units
Step-by-step explanation:
4
substitute t = 1 into the equation
h = - 16(1)² + 6 = - 16 + 6 = - 10
the value is negative since the ball travels down
the ball has travelled 10 units after 1 second
5
substitute t = 3.2 into the equation
h = - 16(3.2)² + 6 = - 16(10.24) + 6 = - 163.84 + 6 = - 157.84
the well is 157.84 units deep
You are in a hot air balloon looking down at two ponds. Pond A which is in front of your balloon, is at an angle of depression that is your birth month (October), in degrees. (October = 10 degrees). Pond B, which is behind the balloon, is at angle of depression that is your Birth Day in degrees. (October 8 = 8 degrees). The balloon is 875 m in the air.
a. Draw and label a diagram
b. Find the distance from the hot air balloon to both Pond A and B
c. FInd the distance between the two ponds.
Answers
a. See attachment for the labelled diagram
b. Using the sine ratio, distance from the hot air to pond A is 5,038.9 m, while distance from the hot air to pond B is 6,287.1 m.
c. Distance between the two ponds is 1,263.5 m.
What is the Sine and Tangent Ratios?Sine ratio, is: sin ∅ = opposite side/hypotenuse length
Tangent ratio is: tan ∅ = opposite side/adjacent length.
a. The diagram with the appropriate labels is shown in the image attached below.
b. Use the sine ratio to find the distance from the hot air to pond A (CA) and to pond B (CB):
CA = hypotenuse
∅ = 10°
Opposite = 875 m
sin 10 = 875/CA
CA = 875/sin 10
CA ≈ 5,038.9 m (distance from the hot air to pond A)
CB = hypotenuse
∅ = 8°
Opposite = 875 m
sin 8 = 875/CB
CB = 875/sin 8
CB ≈ 6,287.1 m (distance from the hot air to pond B)
c. Distance between the two ponds, BA = BD + DA.
Apply the tangent ratio to find BD and DA
tan 8 = 875/BD
BD = 875/tan 8
BD = 6,225.9 m
tan 10 = 875/DA
DA = 875/tan 10
DA = 4,962.4 m
Distance between the two ponds = 6,225.9 - 4,962.4 = 1,263.5 m.
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Calculate the slope of a line that goes through (3,3) and (8,1).
Answers
Answer:
slope formula= y2-y1/x2-x1
=1-3/8-3
= -2/5
pls mark as brainliest thanks!
Quick algebra 1 question for 25 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answers
Yes
It's inverse variationSee
3 contractors took 8hours
4 contractors took 6hours
We observe
No of contracter increases hence time decreasesSo it's inverse variation
Answer:
[tex]\fbox {Yes}[/tex]
Step-by-step explanation:
An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.
Here, as the number of contractors increase, the time taken to complete the work decreases.
∴ Hence, this represents an inverse variation.
Through how many radians does the minute hand of a clock turn during a 3-minute period?
Answers
pi/5.
Think of a clock as a circle. The minute hand when it moves around the clock will have traveled 360 degrees or 2*pi radians, traveling 2*pi radians in 60 minutes. So3 minutes out of 60 minutes is 1/10. So the minute hand travels 1/10 of 2*pi radians (multiply 1/10 and 2*pi to get your answer).
Therefore your answer is pi/5 which is the letter a.
Well, a Radian, simply put, is a unit of measure for angles that is based on the radius of a circle. What this means is that if we imagine taking the length of the radius and wrapping it around a circle, the angle that is formed at the center of the circle by this arc is equal to 1 Radian.
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A pendulum is swinging next to a wall. the distance d(t) (in cm) between the of the pendulum and the wall as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a * sin (b * t) + d at t = 0, when the endulum is exactly in the middle of its swing, the bob is 5 cm away from the wall. the bob reaches the closest point to the wall, which is 3 cm from the wall, 1 second later. find d(t). (t should be in radians)
Answers
The equation of the function d(t) is d(t) = -2sin(π/2 t) + 5
How to determine the function d(t)?The function is given as:
d(t) = a * sin(b * t) + d
The bob is 5 cm away from the wall implies that the vertical shift is 5.
This means that
d = 5
So, we have
d(t) = a * sin(b * t) + 5
The bob reaches the closest point to the wall, which is 3 cm from the wall.
So, the amplitude is
A = 3 - 5
Evaluate
A= -2
So, we have:
d(t) = -2 * sin(b * t) + 5
The period is calculated as:
B = 2π/t
Where
t = (5 + 3)/2
This gives
t = 4
Substitute t = 4 in B = 2π/t
B = 2π/4
Evaluate
B = π/2
So, we have:
d(t) = -2sin(π/2 t) + 5
Hence, the equation of the function d(t) is d(t) = -2sin(π/2 t) + 5
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The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse
Answers
Answer:
Step-by-step explanation:
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse
Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
Answer:
y=-2x+3
Step-by-step explanation:
Use the slope formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
According to the table, x=1 and y=1. There is another point x=2 and y=-1.
We can say that [tex]x_{1}=1[/tex] and [tex]y_{1} =1[/tex]. We can also say that [tex]x_{2}=2[/tex] and [tex]y_{2}=-1[/tex]. Plugging this into the equation we get:
[tex]m=\frac{-1-1}{2-1}=-2[/tex].
This means that the slope of your equation is -1/2
Point intercept form is y=mx+b
So plugging the slope in we have [tex]y=2x+b[/tex]
We can plug in one of the values from the value table for x and y, but to keep things simple, I’m going to just use x=1, and y=1, the first values on the table. Plugging these into the equation we get:
[tex]1=-2(1)+b\\ 1=-2 +b\\b=1+2 \\b=3[/tex]
So our equation is [tex]y=-2x+3[/tex]
A shopkeeper has $680 in the denominations of $50, $20, $10 and $5 notes. The number of notes of each denomination is equal. What is the total number of notes?
Answers
The total number of notes is 32
The number of notes
Let the number of notes be x
$50 = x
$20 = x
$10 = x
$5 = x
Total number of notes = 4x
Let's find 'x'
50x + 20x + 10x + 5x = 680
85x = 680
x = 680/ 85
x = 8
We know that;
Total number of notes = 4x = 4 × 8 = 32 notes
Thus, the total number of notes is 32
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A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66?
If x represents the number of 13 cent stamps and y the 18 cent stamps, which system represents the problem?
Answers
The system of equation which represent the scenario is;
x + y = 42
x + y = 420.13x + 0.18y = 6.66
Simultaneous equationlet
number of 13 cent stamps = xnumber of 18 cent stamps = yTotal cost of the stamps = $6.66Total number of stamps = 42x + y = 42
x + y = 420.13x + 0.18y = 6.66
Therefore, the equation which represent the problem is;
x + y = 42
0.13x + 0.18y = 6.66
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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3.
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length.
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function?
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
Answers
The given function for the difference in length is presented as follows;
[tex]f( \theta) = 2 \cdot cos( \theta) + \sqrt{3} [/tex]
When the pogo stick will be equal to its non compressed length, the difference is zero, therefore;
[tex]f( \theta) = 2 \cdot cos( \theta) + \sqrt{3} = 0[/tex]
[tex] 2 \cdot cos( \theta) = - \sqrt{3} [/tex]
[tex]\theta= arccos \left( \frac{ - \sqrt{3} }{2} \right) [/tex]
Which gives;
[tex] \theta = \frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{6} [/tex]
[tex] \theta = -\frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{6} [/tex]
Part B; If the angle was doubled, we have;
[tex]f( \theta) = 2 \cdot cos(2 \cdot \theta) + \sqrt{3} = 0[/tex]
Therefore;
[tex] 2 \cdot cos(2 \cdot \theta) = - \sqrt{3} [/tex]
Which gives;
[tex] \theta = \frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{12} [/tex]
[tex] \theta = -\frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{12} [/tex]
Between 0 and 2•π, we have;
[tex] \theta = \frac{5\cdot \pi}{12} [/tex]
[tex] \theta = \frac{ 17\cdot \pi}{12} [/tex]
Part C;
The toddler's pogo stick is presented as follows;
[tex]g( \theta) = 1- son^2( \theta) + \sqrt{3} [/tex]
Integrating the original function between 0 and theta gives;
[tex]2 \cdot sin( \theta) + \sqrt{3}\cdot \theta [/tex]
The original length =
Therefore, when the lengths are equal, we have;
[tex]1- son^2( \theta) + \sqrt{3} = 2 \cdot sin( \theta) + \sqrt{3}\cdot \theta [/tex]
The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
[tex]G(x) = 6-x^{4}[/tex]
Step-by-step explanation:
The red graph is the blue graph translated up 3 units, so the answer is [tex]G(x) = 6-x^{4}[/tex].
Suppose 60% of the freshmen at msu take a course in outdoor survival skills. the probability that a freshman selected at random who did not get lost during a hike is 90%. the probability that a freshman selected at random who took the course and did not get lost is 50%.
Answers
Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
According to the question,
Probability of freshmen who took course at MSU in outdoor survival skills is 0.6.
Probability that a freshmen selected at random who did not get lost during a hike is 0.9.
Probability that a freshman selected at random who took the course and did not get lost is 0.50
Conditional probability = P(A and B)/ P(A)
P(did not get lost/took the course) = P( freshmen did not get lost who took the course and freshmen took the course)/P(freshmen did not get lost)
= 0.5/0.6
= 0.8333
Hence, Probability that a freshman selected at random who took the course and did not get lost and Probability of freshmen who took course at MSU in outdoor survival skills is 0.8333
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_____ is a quantitative statistical analysis that compares and combines the results of individual but similar studies.
Answers
"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.
What is meta analysis?A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.
Some characteristics of meta analysis are-
The statistical method for merging data from various studies is called meta-analysis. Meta-analysis can be used to pinpoint this common impact when the treatment effect (or effect size) is constant from one trial to the next. Meta-analysis can be performed to determine the cause of variance in the effect when it differs between studies.Regulatory agencies occasionally demand a meta-analysis as part of the approval process, which pharmaceutical companies employ to obtain clearance for new medications. Meta-analysis is used by clinicians and applied researchers in a variety of sectors, including medicine, education, psychology, criminal justice, and many more, to identify which therapies are most effective.To know more about Meta-analysis, here
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In the figure pq is parallel to Ed the length of to is 4 cm the length of pt is 16 the length of qt is 20 what is the length of sq
Answers
By applying the basic proportionality theorem (BPT), the length of side SQ is equal to 5 cm.
How to calculate the length of side SQ?In order to determine the length of side SQ, we would apply basic proportionality theorem (BPT) as follows:
Since PQ ǁ RS, PT = 16
PT/RP = QT/SQ
16/4 = 20/SQ
Cross-multiplying, we have:
16SQ = 20 × 4
SQ = 80/16
SQ = 5 cm.
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Complete Question:
In the figure, PQ is parallel to RS. The length of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?
If there are seven points on a plane and no three points are on the same line, how many lines can the points make?
Answers
The number of lines that the points can make is; 21 lines
How to find Collinear Points?We are given that;
- There are 7 points on a Plane
- No 3 points on the plane are on the same line
Thus;
No 3 points are collinear and as such the number of lines that the points can make is found from the combination formula;
C(7,2);
C(7,2) = 7!/(7 - 2)!*2!
= (7 × 6)/(2 × 1)
= 42/2
=21
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What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66
Answers
The root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
How to determine the roots of the equation?The graph that completes the question is added as an attachment
The polynomial function is given as:
x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
From the attached graph, we have the following highlight:
The curves of both equations intersect at
x = -3, x = -2 and x = 3
This means that the root of the polynomial function is -3, -2 and 3
Hence, the root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3
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Complete question
Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
What are the roots of the polynomial equation?
A) –3, –2, 3
B) –3, 2
C) 18, 32
D) 18, 32, 66
The median for the samples from the school math contest are:
The median of Sample 1 from Grades 9 and 10 is 79.
The median of Sample 2 from Grades 11 and 12 is 86.
What conclusions can you derive from the random samples?
The students performed equally between all the grades.
The students in grades 11 and 12 scored higher than the students in grades 9 and 10.
The students in grades 11 and 12 are likely to do well in college.
The students in grades 9 and 10 were not allowed enough time in the school math contest.
The sample size was too small to derive a valid conclusion
Answers
A conclusion which can be derived from these random samples is that: B. the students in grades 11 and 12 scored higher than the students in grades 9 and 10.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Based on the information provided for these samples, we can logically conclude that the students in grades 11 and 12 scored higher than the students in grades 9 and 10 because a median score of 86 is greater than a median score of 79.
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The acting club two-act plays begins at 3:20 P.M. The first act is twice as long as the second act, and there is a 15-minute break between the two acts. The play ends at 4:50 P.M. How long is Act 1?
Answers
Answer:
50 minutes
Step-by-step explanation:
3:20 pm - 4:50 = 90 minutes
90 = 2a + 15 + a
90-15= 75
75= 2a + a
75 = 3a
75/3 = 25
25 x 2 = 50 minutes
Owen has enough materials to build up to 10 birdhouses in shop class. each birdhouse needs 12 square feet of wood. the function w(b) = 12b represents the total amount of wood that owen would need to build b birdhouses. what domain and range are reasonable for the function?
Answers
Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].
What is domain and range of a function?The range of values that we are permitted to enter into our function is known as the domain of a function.
A function's range is the collection of values it can take as input.
Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.
The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.
Therefore, the domain of the function is [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].
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Three consecutive positive prime numbers have a sum that is a multiple of . What is the least possible sum
Answers
Answer:
3, 7, 14
Step-by-step explanation:
small brain
In the diagram below, ABC ~ DEC. What is the value of x?
A. 2
B. 3.5
C. 2.5
D. 3
Answers
5x=18-x
6x=18
x=3
Answer is (D).
Answer:
x = 3
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.
[tex] \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3[/tex]
Answer 1/4 + 3/5-3/10 =
Answers
Answer:
11/20
Step-by-step explanation:
1/4= 10/40
3/5=24/40
3/10=12/40
10/40+24/40= 34/40
34/40 - 12/40= 22/40
simplifies to 11/20
please help asap i am so confused
Answers
The table so fined below based on the information given about the function.
How to illustrate the information?The table based on the function given will be:
Plan A. Plan B
Monday. 10. 30
Tuesday. 20. 40
Wednesday. 40. 50
Thursday. 80. 60
Friday. 160. 70
A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.
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Gerri purchases a coupon book with discounts for her favorite coffee shop. every coupon for the coffee shop offers the same discount. the table shows her total savings, y, based on the number of coupons, x, used from the book. a table showing coffee shop coupon savings with 2 columns and 6 rows. the first column, x, has the entries, 0, 5, 10, 15, 20. the second column, y, has the entries. negative 20, negative 10, 0, 10, 20.
Answers
Slope 2 and y intercept is 10
The question seems to be incomplete and complete and the complete question is shown in the image
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases.
When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.
Y-intercept is the point at which the line intersects the y axis- meaning x = 0
From the table y = -20 when x= 0
y-intercept: -20
To find the slope
m = ΔY/ΔX
m = -20+10/0-5 = 2
Hence the slope is 2 and y intercept is 10
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Help please!!!!
Will give brainliest
Answers
The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.
How to interpret features of trigonometric Graphs?
3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.
c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.
4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.
c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.
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please help me im stuck on this
Answers
Answer:
Step-by-step explanation:
dddfykb
Consider the sequence Three-fourths, four-fifths, StartFraction 5 Over 6 EndFraction, StartFraction 6 Over 7 EndFraction, ellipsis
Which statement describes the sequence? 3/4, 4/5, 5/6, 6/7,...
The sequence diverges.
The sequence converges to 1.
The sequence converges to ∞.
The sequence converges to –∞.
Answers
Using limits, it is found that the correct statement defining the sequence is:
The sequence converges to 1.
What is the rule that defines this sequence?The numerator starts at 3 and increases by 1, while the denominator starts at 4 and increases by 1, hence the rule is:
[tex]\sum_{n = 0}^{\infty} \frac{3 + n}{4 + n}[/tex]
To verify if it converges, we find the limit as n goes to infinity, hence:
[tex]\lim_{n \rightarrow \infty} \frac{3 + n}{4 + n} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]
Hence the sequence converges to 1.
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Answer:
B i took quiz
Step-by-step explanation:
To solve this system of equations using substitution, what could be substituted in place of y in the first equation? 4x = 5 − 2y y − 2x = 7
Answers
Answer:
y = [tex]-\frac{4x-5}{2}[/tex]
Step-by-step explanation:
Step 1: Switch sides
5 - 2y = 4x
Step 2: Subtract 5 from both sides
5 - 2y - 5 = 4x - 5
Step 3: Simplify
-2y = 4x - 5
Step 4: Divide both sides by -2
[tex]\frac{-2y}{-2} = \frac{4x}{-2} - \frac{5}{-2}[/tex]
Step 5: Simplify
y = [tex]-\frac{4x-5}{2}[/tex]