Type the correct answer in each box. Round your answers to the nearest tenth.
Triangle ABC is an equilateral triangle. The angle bisectors and the perpendicular bisectors meet at D in such a way that CD = 2DE.
The radius of the inscribed circle is ____ units, and the radius of the circumscribed circle is____ units.
Answers
Since ABC is equilateral, all its angles are 60 degrees. The angle bisectors of an equilateral triangle are also its medians and altitudes, so they all coincide. Therefore, AD, BD, and CD are all angle bisectors, medians, and altitudes of triangle ABC.
Since triangle ABC is equilateral, the medians, altitudes, and angle bisectors all coincide, and they divide each other into segments with a 2:1 ratio. Therefore, we can say that:
CD = 2DE = s/3
We can also find the height of the equilateral triangle using the Pythagorean theorem:
h = sqrt(s^2 - (s/2)^2) = sqrt(3)/2 * s
The area of the equilateral triangle is:
A = 1/2 * s * h = 1/2 * s * sqrt(3)/2 * s = sqrt(3)/4 * s^2
The radius of the inscribed circle is:
r = A / (s + s + s) = sqrt(3)/4 * s^2 / (3s) = sqrt(3)/12 * s
The radius of the circumscribed circle is:
R = s / sqrt(3)
Substituting s = CD + DE + CE = s/3 + s/3 + R into the expression for R, we get:
s = 3R
Therefore:
R = s / 3 = CD + DE + CE = s/3 + s/3 + R
Simplifying:
2R = 2s/3
R = s/3
Substituting s = sqrt(3) * 2R into the expression for r, we get:
r = sqrt(3)/12 * sqrt(3) * 2R = R/2
Therefore, the radius of the inscribed circle is R/2, and the radius of the circumscribed circle is R.
Since R = s/3, the radius of the inscribed circle is (s/3)/2 = s/6.
Since the problem does not specify a value for s, we cannot calculate the radii of the circles.
Related Questions
Bruce says that if a number is a product of 6, then it is not a product of 3. What would you say to Bruce?
Answers
Bruce can be advised to correct his reasoning as the number divisible by six will also remain divisible to 3.
How to find the factors of a number?The factor of a number is any number that divides it completely.
In order to find the factors of a number keep dividing it with the known factors.
Given that,
A number is product of 6.
Then, 6 is the factor of that number.
But the factors of 6 are 2 and 3 which implies that 3 is also a factor of that number.
It implies that Bruce has not applied the correct reasoning to reach the conclusion.
Hence, a number which is a product of 6 can also be a product of 3.
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Mariah owed her grandfather $2.25 but was recently able to pay him back $1.50 how much does Mariah currently owe her grandfather
Answers
Answer:
$0.75
Step-by-step explanation:
2.25-1.50=0.75
You are using a magnifying glass that shows the image of an object that is six tin image of the termite seen through the magnifying glass. 9.5 mm The image length through the magnifying glass is millimeters.
Answers
When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.
When using a magnifying glass, the image of an object appears larger. In this case, the termite is being viewed through a magnifying glass that magnifies the image by a factor of six. The actual length of the termite is not mentioned in the given information. However, it is stated that the length of the image seen through the magnifying glass is 9.5 mm.To determine the actual length of the termite, we can divide the length of the image by the magnification factor. Therefore, the actual length of the termite would be 9.5 mm divided by 6, which is approximately 1.58 mm.Therefore, when viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.For more questions on magnifying glass
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4x-3y≤27 solve for y
Answers
Answer:
y≥−9+4x/3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Customer pays $0.035 per minute for local calls, if the customer made 60 local calls that all lasted 3 minutes, how much will the customer pay?
Answers
The customer will pay $6.30 for the 60 local calls that all lasted 3 minutes.
To find out how much the customer will pay, we need to calculate the total cost for all the local calls.
Step 1: Calculate the total number of minutes for all the calls
Since the customer made 60 local calls and each call lasted 3 minutes, we can multiply 60 by 3 to get the total number of minutes.
60 calls * 3 minutes/call = 180 minutes
Step 2: Calculate the total cost for all the minutes
The customer pays $0.035 per minute for local calls. To find the total cost, we can multiply the total number of minutes by the cost per minute.
180 minutes * $0.035/minute = $6.30
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Potencia con exponente negativo se queda igual. Cierto o Falso?
Answers
Answer:
Cierto
Step-by-step explanation:
16. A pack of pens costs $3. Lynn spent $12
on pens. Each pack has 5 pens. How
many packs did she buy? How many
pens does she have?
A 3 packs; 15 pens
B
4 packs; 20 pens
5 packs; 20 pens
6 packs; 30 pens
Answers
Answer:
it should be B Other than that I'm not sure
complete the table by supplying the measure of inscribed angle and its intercepted arc
Answers
Answer/Step-by-step explanation:
Based on the inscribed angle theorem, any inscribed angle = ½ of its intercepted arc
Thus:
✔️Inscribed angle = 57°
Intercepted arc would be: 2*57 = 114°
✔️Intercepted arc would be: 123°
Inscribed angle = ½(123) = 61.5°
✔️Intercepted arc would be: 46°
Inscribed angle = ½(46) = 23°
✔️Inscribed angle = 69°
Intercepted arc would be: 2*69 = 138°
✔️Intercepted arc would be: 155°
Inscribed angle = ½(155) = 77.5°
2 + 8p - 3(12 - 5p) - (2 - 3p)(4)
Answers
\(2+8p-3(12-5p)-(2-3p)(4)\\\\=2+8p-36+15p-8+12p\\\\=35p-42\)
2 + 8p - 36 + 15p - 8 + 12p
35p - 42
What happens to standard deviation when outliers are removed?; How does outliers affect standard deviation?; When the outliers are removed How does this mean change?; How will a high outlier affect the mean and median?; Which data set has an outlier?
Answers
Answer:
Before we declare what happens, we must have an understanding of outliers and standard deviation. Outliers are certain points that are x deviations away from the mean. Standard deviation is a measurement of dispersion in relations to the mean you are identifying. Given this information, when outliers are removed, the standard deviation becomes a lower amount, because you have to think of standard deviation as a population measurement in a way. So imagine the outliers are a prestigious group of people, and if they leave the community, the population is indeed lower. Outliers affect deviation by a measure of extremity. The more extreme an outlier, the more or less a standard deviation will be affected. When outliers are removed, they will lower the standard deviation, which changes the data in respect to population. A high outlier, however, will increase both mean and median no matter what.
Hope this helps!
what would be your first step in completely factoring 6a^2-15a+6
Answers
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
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i need a A pls helppp
Answers
Answer:
option B is correct.
Option A Option B
6x = 66 5x = 30
x = 66/6 x = 30/5
x = 11 x = 6
Option C Option D
6x = 1 7x + 2 = 15
x = 1/6 7x = 15 - 2
x = \(\sf \sf \frac{1}{6}\) x = \(\sf \frac{13}{7}\)
Show your work and explain how you can determine which is a better deal:
10 ounces of orange juice for $2.40 or 8 ounces for $2.08?
Answers
Answer: 10 ounces for $2.40
Step-by-step explanation: The trick behind these problems, always divide. 2.40/10ounces is $0.24. 2.08/8ounces is $0.26. Better deal, therefore smaller answer of the 2, because it's cheaper.
each ounce of orange juice for 8 ounces is 0.26
each ounce of orange juice for the 10 ounces would only be 0.24
so you are getting 2 more ounces of orange juice for only 0.48
Which is equivalent to (2x^2y)(8x^3y^3)?
Answers
Answer: A
Step-by-step explanation: In order to answer this you need to understand the rules of exponents. Whenever you multiply two terms with the same base or variable you add the powers together. For example, 4x*2x = 8x^2 or x^4*x^2 = x^6. Any term with a negative exponent is equivalent to its reciprocal. For example x^-2 = 1/x^2.
Knowing this we expand this equation by multiplying. (2x^-2y) * (8x^-3y^-3) = 16x^-5y^-2. We now move the variables with negative exponents to the bottom. Giving us 16/(x^5y^2).
Determine what the key terms refer to in the following study. A study was conducted in a local community to analyze which voters would be likely to vote and how on an upcoming bond
Answers
The key term in the given study are local community, analysis of voters and upcoming bond.
What is key term of a study?The key term of a study is defined as the main terminologies that can be separated from the thesis of the study.
The topic of the study that was given is " A study was conducted in a local community to analyze which voters would be likely to vote and how on an upcoming bond.
The terminologies that can be gotten from the above topic include the following:
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\(P(x) = x^4 - x^3 - 11x^2 + 9x + 18\). Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviours of the graph and where the company will break even (where P(x) = 0)
Answers
The graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
How did we arrive at this assertion?The function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 is a polynomial function of degree 4.
To sketch the graph of this function without using technology, we can start by analyzing the end behaviors of the function. As x approaches negative infinity, the leading term of the function, x^4, dominates and the function approaches positive infinity. As x approaches positive infinity, the leading term also dominates and the function again approaches positive infinity. This means that the graph will have a shape that rises on both ends.
Next, we can find the x-intercepts of the function, which are the values of x where P(x) = 0. We can use synthetic division or factorization to find that the function has three real roots: x = -2, x = -1, and x = 3. These values represent the points where the graph intersects the x-axis.
Finally, we can find the y-intercept of the function, which is the value of P(0). We can plug in x = 0 into the function to find that P(0) = 18. This means that the graph intersects the y-axis at the point (0, 18).
Putting all of this information together, we can sketch a rough graph of the function. The graph rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The function is positive between x = -2 and x = -1, and between x = 3 and positive infinity. The function is negative between x = -1 and x = 3.
To summarize, the graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
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The side length of an equilateral triangle is 5 cm.
Find its perimeter
Answers
Step-by-Step Explanation:
Side Length (a) = 5cm
Perimeter = 3a
Therefore,
= 3a
= 3 * 5
= 15
Perimeter = 15 cm
\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)
The side length of an equilateral triangle is 5 cm. Find its perimeter.
\(\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\)
We are given that the triangle is equilateral.
"equi" means "equal" and "lateral" means "sides"
✯ So an equilateral triangle has 3 equal sides.
We are also given that one side is equal to 5 cm.
If one side is equal to 5 cm, and the triangle's equilateral, then the other two sides are equal to 5 cm.
◈ In order to find the perimeter of a shape, you should add all of its side lengths together.
✯ Now, we need to find the perimeter, which we can find using the following formula:-
\(\bold{Perimeter_{(triangle)}=a+b+c}\)
Where a, b, and c are side lengths of the triangle.Now, we add them:-
\(\hookrightarrow\sf{P=5+5+5}\)
So we conclude that the perimeter is equal to:-
\(\hookrightarrow\sf{P=15\:cm}\)
Good luck with your studies.\(\rule{300}{1}\)
James wants to have earned $6,180 amount of interest in 28 years. Currently he finds
that his annual interest rate is 6.12%. Calculate how much money James needs to invest
as his principal in order to achieve this goal.
Answers
Answer:
$3606.44
Step-by-step explanation:
The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.
To do this, we need to use the formula for simple interest:
\(\boxed{I = \frac{P \times R \times T}{100}}\),
where:
I = interest earned
P = principal invested
R = annual interest rate
T = time
By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:
\(6180 = \frac{P \times 6.12 \times 28}{100}\)
⇒ \(6180 \times 100 = P \times 171.36\) [Multiplying both sides by 100]
⇒ \(P = \frac{6180 \times 100}{171.36}\) [Dividing both sides of the equation by 171.36]
⇒ \(P = \bf 3606.44\)
Therefore, James needs to invest $3606.44.
What force in Newtons will accelerate a 7-kilogram bowling ball at 2.5 m/s2?
Enter your answer as a number, rounded to the nearest tenth, with the appropriate unit, like this: 42.5 N.
Answers
Answer:
F=ma where m=mass and a=acceleration
F=7kgx2.5m/s^2
F=17.5N
Each member of a 5-member cross-country team runs a course. Their individual times are as follows:
2 hours 17 minutes
2 hours 48 minutes
1 hour 53 minutes
2 hours 19 minutes
1 hour 38 minutes
The team’s overall score is the average number of minutes it takes for its members to complete the course. What is this team’s score?
Answers
Step-by-step explanation:
the average is the sum of all data points divided by the number of data points (5).
2 hours 17 minutes
2 hours 48 minutes
1 hour 53 minutes
2 hours 19 minutes
1 hour 38 minutes
------------------------------
8 hours 175 minutes
175 minutes = 2 hours 55 minutes
so, we need to add this to the 8 hours and get
10 hours 55 minutes
this we need to divide by 5 for the average time
(10 hours 55 minutes) / 5 = 2 hours 11 minutes =
= 2×60 + 11 = 120 + 11 = 131 minutes.
so, their score is 131.
HELPPPPPPPPP I WILL GIVE U THE BRAINLEST!!!!!!!!
Answers
Answer:
r = 14
d = 28
r^2=28
Circumference = 87.96
C=2πr=2·π·14≈87.96459
substitution to evaluate the indefinite integral
Answers
Answer:
\(\displaystyle \int {e^{5x}} \, dx = \boxed{ \frac{e^{5x}}{5} + C }\)
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
\(\displaystyle (cu)' = cu'\)
Derivative Rule [Basic Power Rule]:
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Methods: U-Substitution
Step-by-step explanation:
Step 1: Define
Identify given.
\(\displaystyle \int {e^{5x}} \, dx\)
Step 2: Integrate Pt. 1
Identify variables for u-substitution.
Set u:\(\displaystyle u = 5x\)[u] Differentiate [Derivative Rules and Properties]:
\(\displaystyle du = 5 \ dx\)
Step 3: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]:\(\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\\end{aligned}\)[Integral] Apply Integration Method [U-Substitution]:
\(\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\\end{aligned}\)[Integral] Apply Exponential Integration:
\(\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\\end{aligned}\)[u] Back-substitute:
\(\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\& = \boxed{ \frac{e^{5x}}{5} + C } \\\end{aligned}\)
∴ we have used substitution to evaluate the indefinite integral.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Which expression is equivalent to 25x4 - 10x²y² + y4 - 100?
20 POINTS!
Answers
Answer:
100 is the Answer if I not rong
Question 6
A square is placed within a rectangle. Find the area of the shaded region.
Select one:
O
✪
✪
O
559 ft²
640 ft²
721 ft²
604 ft²
32 ft
19A
9 ft
20 ft
Answers
The area of the shaded region is 559 ft².
How to find the area of the shaded region?In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:
area of the shaded region = area of rectangle - area of square
area of the shaded region = (32 * 20) - (9 * 9)
area of the shaded region = 640 - 81
area of the shaded region = 559 ft²
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Complete Question
See attached image
Estimate the slope of the tangent line (rate of change) to f(x) = ² at x = -1 by finding the slopes of
the secant lines through the points:
a. (-2,4) and (0,0)
secant slope, msec=
b. (-1.5, 2.25) and (-0.5, 0.25)
secant slope, msec=
Answers
a. The secant slope through (-2,4) and (0,0) is -2.
b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.
The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.
To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.
a. (-2,4) and (0,0):
The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:
msec = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
msec = (0 - 4) / (0 - (-2))
= -4 / 2
= -2
So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.
b. (-1.5, 2.25) and (-0.5, 0.25):
The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:
msec = (0.25 - 2.25) / (-0.5 - (-1.5))
= (-2) / (1)
= -2
So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.
By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.
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12. Monica is an unmarried college student with no dependents. Last year, she
made $14,000 working part time as a medical assistant. Each year she files taxes
as Single, takes a standard deduction of $5700 and claims herself as only
exemption for $3650. Based on this information, what tax bracket does Monica
fall into?
Answers
The tax bracket that Monica falls partly into is the $0 - $9,950 bracket. This is because her taxable annual earnings after is less than $9,950. hence she will be paying 10% of what's taxable.
What is a Tax Bracket?A tax bracket is a tax group into which a person falls into depending on their annual income, number of dependents, and marital status.
It is important to know that tax brackets are reviewed from time to time.
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Mia had $22 . Then she started to receive $4 a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her total amount of money. Which of the following ordered pairs is on Mia's graph? ANSWER CHOICES: (2,44) (5,42) (6,24) (1,22)
Answers
Answer: (5, 42)
Step-by-step explanation:
22 + 4x= 42
if we test the options we will see this is the only one that works
42 - 22 = 20
4x = 20
x= 5
which is equal to X the number of weeks they have gotten the allowance.
Juan sold a bicycle at a discount of 15%. If the selling price was $340, find the usual price of the bicycle.
Answers
Answer: $400
Step-by-step explanation:
Discount = 15%
The original price/value of an item is always 100%
So selling price (%) = original price - discount = 100%-15% = 85%
We got selling price as 85%
This implies that 85% = 340
Let's find 1% first, then 100%
1% = 340÷85 = 4
100% = 4 × 100 = $400
The usual (normal/original) price is $400
Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let's represent the usual price of the bicycle by P.
Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).
We can express this relationship as an equation:
S = 0.85P
We also know that the selling price of the bicycle was $340.
Substituting S = $340 into the equation above, we get:
$340 = 0.85P
To find P, we can solve for it:
P = $340 / 0.85
P = $400
Therefore, the usual price of the bicycle was $400.
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PLEASE SOMEBODY HELP Let x and Y be two positive integers such that x-y =75 and the least common multiple of x and y is 360. Find the value of x+y.
Answers
Step-by-step explanation:
xy=360
x-y=75
(x-y)^2+2xy=(x+y)^2-2xy hence we have for x+y= ((x-y)^2+4xy)^0.5 which somehow equals 84.1
How do you use distributive property to solve 3,649 x 6
Answers
Answer:
21894
Step-by-step explanation:
So, since we want to use the distrubutive property, we ant to simplify 3,649
3000+600+40+9
now, multiply 6 to each one of those numbers:
18000+3600+240+54
add them together to get one number
21894
And that's how I think it's done.