When constructing a circle inscribed in a triangle, what is the purpose of constructing a perpendicular segment from the incenter to a side of the triangle?
To determine the center of the circle
To determine the radius of the circle
To connect the midpoints of each side of the triangle
To connect the arc markings from the angle bisectors
Answers
When a circle is inscribed in a triangle, it means that the circle is drawn inside a triangle such that the midpoints of each side of the triangle are tangent to the circle. By doing this, you draw the biggest circle that could fit inside a triangle.
Now, the circle and the triangle have the same center illustrated here by the red dot. When you connect all sides of the triangle to the center (yellow lines), you create three equal angles. This is equal to 360 (one revolution) divided by 3, equals 120°. But when you create a perpendicular bisector from the center (black line), the angle is halved. It will now be 120/2 = 60°. Usually you are given the sides of the triangle. By using pythagorean theorems, you can find, therefore, the radius of the circle. To illustrate, the radius is equal to (s/2)/tan60.
Thus, the answer is: To determine the radius of the circle.
Related Questions
What is the correct way to write 6.3 × 10^8 in standard notation? (25 Points)
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hope this helps:)
(7 zeros behind the decimal.)
Hope this helps!!!
Explain why two similar right triangles will have the same cosine ratios.
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LET θ’s (opp,adj,hypo)=(AB,BC,AC) and (PQ,QR,PR)
Then by similarity,
sinθ=AB/AC=PQ/PR ,cosθ=BC/AC=QR/PR ,tanθ=AB/BC=PQ/QR
the corresponding ratio of (adjacent side/hypotenuse),and hence
the cosine ratio must be the same
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i think it help
which of the following could be the equation of the graph shown below
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2y = 4x - 6
y = 2x - 3....y int = -3 , x int = (3/2,0)
I believe it is going to be : -4x + 2y = -6
Answer:
-4x+2y+-6 and y=3x-2
Find the area of a regular hexagon with a 48-inch perimeter.
48√3 in2
96√3 in2
192√3 in2
in2 means inches squared
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The demand function for an auto parts manufacturing company is given by f(x) = 100000 - 2500x , where x represents price and f(x) represents quantity. f^-1 (x) = _______. In the inverse function, the variable X represents _____
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Answer:
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
The variable X represents the quantity.
Step-by-step explanation:
We are given that
The demand function for an auto parts manufacturing company is fiven by
f(x)=100000-25 x
Where x=Represents price
f(x)= Represents quantity
We have to find inverse function [tex]f^{-1}(X)[/tex]
Let f(x)=X
[tex]X=100000-2500 x[/tex]
[tex]2500x=100000-X[/tex]
[tex]x=\frac{100000-X}{2500}[/tex]
Substituting the value of x then we get
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Therefore, the inverse function
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Where X= Represents the quantity
[tex]f^{-1}(X)[/tex]=Represents price
Find the sum of the first 15 terms of the series 4+16+64+256+...
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I need help with this problem and a few others
Answers
Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
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The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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A delivery truck uses $375 in gasoline during a 3 week period. if the truck is driven 5 days per week, how much is spent on gas each day?
Answers
Final answer:
Approximately $17.86 is spent on gas each day.
Explanation:
To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.
First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.
Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86
Therefore, approximately $17.86 is spent on gas each day.
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
Answers
In the 30°-60°-90° triangle, the side lying opposite to the angle 30° is half the hypotenuse, so:
[tex]a= \frac{x}{2} [/tex]
By the Pythagorean theorem:
[tex]b^2 = c^2-a^2\\ \\b^2=x^2-( \frac{x}{2} )^2 = x^2- \frac{x^2}{4} = \frac{4x^2-x^2}{4}= \frac{3x^2}{4} \\ \\ b= \sqrt{ \frac{3x^2}{4} } = \frac{ \sqrt{3x^2} }{ \sqrt{4} } = \frac{x \sqrt{3} }{2} [/tex]
[tex]\text{Perimeter }=x+ \frac{x}{2} + \frac{x \sqrt{3} }{2}= \frac{2x+x+x \sqrt{3}}{2}= \frac{3x+x \sqrt{3} }{2}[/tex]
For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.
Explanation:In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the
perimeter
of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.
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which angles are corresponding angles? check all that aply
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<1 and <3
Factor the polynomial below.
30x^2 + 15x^2 +10x
Answers
hope this helps
hope this helps!
The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.What is the value of x?
Answers
To answer this question you need to know how to count formula of a rectangle. Area of a rectangle is count by length x width formula. Then if you put the number into the formula it would be:
area = length x width
0.8 square unit= 3.2 unit * x
3.2 x unit = 0.8 square unit
x= 0.8 square unit / 3.2 unit= 0.25 unit
NEED HELP ASAP PLEASE!!!
Answers
help factoring trinomial
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need 2 numbers when added = 5 and when multiplied = -24
answer is D
-3+8 = 5
-3*8 = -24
-24 = (+8) * (-3)
8 - 3 = 5
so
x^2 + 5x - 24 = (x + 8)(x - 3)
answer is
D.(x - 3)(x + 8)
What are the solutions of the equation z2-12z+36=0
Answers
(z - 6)(z - 6) = 0
z - 6 = 0
z = 6
solution is : 6,6
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
Answers
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
You invest $3,756.00 and buy 100 shares of a company's stock. Their value increases by 12%. How much is each share worth?
Answers
$37.56(1.12)
$42.0672
$42.07 (to nearest cent)
Answer:
Each share worth is $42.0672 .
Step-by-step explanation:
As given
You invest $3,756.00 and buy 100 shares of a company's stock.
Their value increases by 12%.
12% is written in the decimal form
[tex]= \frac{12}{100}[/tex]
= 0.12
Share value increase = 0.12 × Investment cost
= 0.12 × 3756
= $450.72
Total value of shares becomes after increases of 12% = Share value increase + Investment cost .
Total value of shares becomes after increases of 12% = $3756+ $450.72
= $4206.72
[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]
[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]
Each shares worth = $42.0672
Therefore the each share worth is $42.0672 .
SOMEONE PLEASE HELP!!!!
Which area formula or formulas show(s) a joint variation?
I A=s^2
II A=pir^2
III A=l*w
Select one:
a. III only
b. II and III
c. II only
d. I, II, and III
Answers
Equation 1
A = s²
Here we have only one variable, 's', and the value of Area will only vary when s varies.
Equation 2
A = πr²
Here the only variable is 'r', which is the radius of a circle. The value of Area, A, varies as radius varies. π is a constant.
Equation 3
A = l×w
Here we have to variables, the 'l' and the 'w'.
We can say that the value of Area, A, will vary jointly as l and w vary
The correct answer is option a)
Answer:
Step-by-step explanation:
Relations and functions need help please.
Answers
So, [tex]f(x) = -x^2 + 1[/tex] becomes [tex]f(-3) = -(-3)^2 + 1[/tex]
[tex]f(-3) = 3^2 + 1 \\ \\ f(-3) = 9 + 1 \\ \\ f(-3) = 10[/tex]
So, f(-3) is equal to 10.
Women athletes at the university of colorado, boulder, have a long-term graduation rate of 67% (source: the chronicle of higher education). over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university of colorado, boulder, is not less than 67%? use a 5% level of significance. find the p-value of the test statistic (round to the nearest ten thousandths).
Answers
The solution would be like this for this specific problem:
H0: p = p0, or
H0: p ≥ p0, or
H0: p ≤ p0
find the test statistic z = (pHat - p0) / sqrt(p0 * (1-p0) / n)
where pHat = X / n
The p-value of the test is
the area under the normal curve that is in agreement with the alternate
hypothesis.
H1: p ≠ p0; p-value is the area in the tails greater than |z|
H1: p < p0; p-value is the area to the left of z
H1: p > p0; p-value is the area to the right of z
Hypothesis equation:
H0: p ≥ 0.67 vs. H1: p < 0.67
The test statistic is:
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 )
z = -1.538681
The p-value = P( Z < z
)
= P( Z < -1.538681 )
= 0.0619
The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.
Answers
The angle EAB is 90+60 = 150.
The law of the cosines helps:
BE^2 = AE^2 + AB^2 - 2*AB*AE*cos(150) = 4^2 + 4^2 - 2*4*4*(-sqrt(3)/2)
BE^2 = 16+16+16*sqrt(3) = 16(2+sqrt(3)),
BE = 4*sqrt( 2 + sqrt(3 ) ) Nice number
BE ~ 7.7274 ... ~ 7.73
In fact, if you take a ruler, one can see that the ratio between AB and BE is ~ 1.95 which s the same number.
Answer: BE = 4*sqrt( 2 + sqrt(3 ) ) ~ 7.73
BE is [tex]7.73[/tex]
What is Square?
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
What is equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.
We have to find BE.
Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]
The angle EAB is [tex]90+60 = 150[/tex]°
Using the law of the cosines, we get
[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]
[tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]
⇒[tex]BE=7.73[/tex]
Hence, we can conclude that BE is [tex]7.73[/tex]
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What is 8q+3(10q^2+2)+8
Answers
= 8q + 30q^2 + 6 + 8
= 30q^2 + 8q + 14
Hope it helped!
if f(x) = (x+1)^-1 and g(x) = x-2, what is the domain of f(x) divided by g(x)
Answers
f(x)=1/(x+1) so
f(x)/g(x) is
1/[(x+1)(x-2)]
Since division by zero approaches infinity, it is not a real value, and is said to be undefined. Division by zero is "not allowed", which just really means that it does not have a real value. So in this case x cannot equal -1 or 2 so the domain is:
All real numbers except -1 or 2...which can be expressed as:
(-oo,-1),(-1,2),(2,+oo)
The circle shown below has ab and bc as its tangents: ab and bc are two tangents to a circle which intersect outside the circle at a point
b. if the measure of arc ac is 160°, what is the measure of angle abc? 80° 40° 60° 20°
Answers
One of the theorems of circle is that the measure of the intercepted arc is twice as that of its opposite angle. In this case, since the intercepted arc measures 160°, then the measure of angle abc is 160/2 = 80°.
Therefore, the answer is 80°.
Answer:
Answer: 20°
Step-by-step explanation:
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18.
Answers: symmetrical, uniform, skewed to the left, skewed to the right.
Answers
x Count
---- ---------
16 2
17 2
18 2
19 2
20 2
21 2
Graph the data set to show the histogram shown below.
It is clear that the data s uniformly distributed.
Answer: uniform
A movie theater sold 422 tickets on Friday. On Saturday, they sold 518 tickets. What was the approximate percentage that ticket sales increased on Saturday?
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Hope that helps!
a rectangle has sides 2x + 3 and x - 4. what is the perimeter of the rectangle
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Evaluate p(7,5) can someone help
Answers
----------------------------------------------
Work Shown:
P(n,r) = (n!)/((n-r)!)
P(7,5) = (7!)/((7-5)!)
P(7,5) = (7!)/(2!)
P(7,5) = (7*6*5*4*3*2*1)/(2*1)
P(7,5) = (5040)/(2)
P(7,5) = 2520
The triangle JKL shown on the coordinate grid below is reflected once to map onto triangle J'K'L': Triangle JKL is drawn on a 4 quadrant coordinate grid with vertices J is at 8, 1. K is at 5, 7. L is at 3, 4. If vertex L' is at (−3, 4), what are the coordinates of vertex J'?
Answers
(1, −8)
(−8, 1)
(−1, 8)
(8, −1)
Answer:
The vertex J' is at (-8,1).
Step-by-step explanation:
If is given that the triangle JKL reflected once to map onto triangle J'K'L'.
The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).
[tex]L(3,4)\rightarrow L'(-3,4)[/tex]
It is in the form of
[tex](x,y)\rightarrow (-x,y)[/tex]
Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.
The vertices of image are,
[tex]K(5,7)\rightarrow K'(-5,7)[/tex]
[tex]J(8,1)\rightarrow J'(-8,1)[/tex]
Therefore the vertex J' is at (-8,1).