The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
Answers
The perimeter of the polygon is 78 cm. (Option D)
The perimeter of a geometric shape refers to the length that encompasses the figure. Hence, the perimeter of any irregular pentagon can be determined by the adding up the lengths of all sides. As the given polygon circumscribes a circle, the sides of the polygon are tangent to the circle. The two tangent theorem states that if two lines are drawn from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same. Hence, if two lines that are tangent to a circle meet at a point, then the distance from that point to the points of intersection between the tangents and the circle are equal. Hence, the perimeter of the pentagon is:
P = 8 + 8 + 16 + 16 + 6 + 6 + 9 + 9 = 78 cm
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Related Questions
Consider points a, b, and c in the graph. Determine which of these points is relative maxima on the interval x = –1 and x = 2 in the graph.
Answers
Given:
The graph of a function is given.
To find:
The point that is the relative maxima on the interval x = –1 and x = 2 in the graph.
Solution:
Relative maxima: It is the maximum point of a function over a short interval.
From the given graph it is clear that the graph of the function over the interval x = –1 and x = 2 has a relative maxima at (0,0).
Clearly, (0,0) is represented by point a.
So, the point a is the relative maxima on the interval x = –1 and x = 2 in the graph.
Therefore, the correct option is A.
20) Write a division number story with an answer of 1/4.
Be sure to ask a question.
Answers
Answer:
Story: Mr. Lanre bought 8 apples for $2. What is the cost of each apple.
Step-by-step explanation:
Given
\(Answer = \frac{1}{4}\)
Required
Write a division story
A division story could be:
Mr. Lanre bought 8 apples for $2. What is the cost of each apple.
Solving the above problem, we have:
\(Apples = 8\)
\(Total\ Cost =\$2\)
The cost of each is:
\(Each = \frac{Total\ Cost}{Apples}\)
\(Each = \frac{2}{8}\)
Simplify fraction
\(Each = \frac{1}{4}\)
-8x + y = -6 =4x – 2y = 12
Answers
Let:
\(\begin{gathered} -8x+y=-6_{\text{ }}(1) \\ -4x-2y=12_{\text{ }}(2) \end{gathered}\)Using elimination method:
\(\begin{gathered} (1)-2(2)\colon \\ -8x-(-8x)+y-(-4y)=-6-24 \\ 5y=-30 \\ y=-\frac{30}{5} \\ y=-6 \end{gathered}\)Replace the value of y into (1):
\(\begin{gathered} -8x-6=-6 \\ -8x=-6+6 \\ -8x=0 \\ x=\frac{0}{-8} \\ x=0 \end{gathered}\)What is the volume of the sphere? Use 3.14 for pi. Round to the nearest whole number.
423 m³
423 m³
2144 m³
2144 m³
1582 m³
1582 m³
985 m³
Answers
I’m trying to solve this problem I need to convert it to base 5
Answers
Answer: The answer is 29,446,941,856
Step-by-step explanation:
Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice. Write and simplify an expression for the total cost of Sal's purchases.
Answers
The expression for the total cost of Sal's purchases is 7x + 5y cents.
We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.
Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.
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Pls help :(??
Answer the 4 questions pls
Answers
2.) y=2/3x
3.) y=-2x+1
4.) y=1x-2
Higher Order Thinking Mrs. Dryson
divided her collection of 52 glass
bears
into equal groups. She had 1 bear
left over. How many groups did
Mrs. Dryson
make? How many bears
are in
each group?
Answers
To ensure that there is an equal number of glass bears in each group, Mrs. Dryson constructed a total of 17 groups, which can be calculated using arithmetic operations.
What is arithmetic operations?
The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.
As given in the question,
Mrs. Dryson divided her collection of 52 glass bears into equal groups and She had one bear left over
The steps listed below can be used to calculate the total amount of Mrs. Dryson's products:
Step 1: Arithmetic operations can be utilized to calculate Mrs. Dryson's overall output.
Step 2: Keep in mind that there are 52 glass bears in all, and after separating them into equal groups, she was left with just one bear.
Step 3 - The total bear population to divide into groups of an equal number is calculated as follows:
= 52 - 1 = 51
Step 4: The number that is divided by 51 such that the result is an integer is 3.
Step 5 - As a result, Mrs. Dryson created a total of the following groups:
= 51/3 = 17.
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Find the area of the polygon with the given vertices.
G(2,2) H(3,-1) J(-2,-1)
Answers
Answer:
8
Step-by-step explanation:
hope this helps you
Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
Answers
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
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Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Answers
= 173.903t
Step-by-step Explanation:
The given equation is: f(t) = 227e^(b*t)
To convert it to the form f(t) = ab, we need to write it in the form of f(t) = a * e^(k*t), where a and k are constants.
Let's start by taking the natural logarithm (ln) of both sides:
ln(f(t)) = ln(227e^(b*t))
Using the properties of logarithms, we can simplify this to:
ln(f(t)) = ln(227) + ln(e^(b*t))
ln(f(t)) = ln(227) + b*t
Now, let's define a new constant, k = b, and rewrite the equation in terms of a and k:
ln(f(t)) = ln(a) + k*t
where a = 227 and k = -0.09
Taking the exponential of both sides, we get:
f(t) = e^(ln(a) + k*t)
f(t) = e^(ln(a)) * e^(k*t)
f(t) = a * e^(k*t)
Substituting the values of a and k, we get:
f(t) = 227 * e^(-0.09*t)
Therefore, the equation f(t) = ab is:
f(t) = 227e^(-0.09t) ≈ 173.903t (rounded to three decimal places)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write with fractional exponents. (Do not use parentheses.)
Answers
Answer:
4\(y^{\frac{3}{2} }\)
Step-by-step explanation:
using the rule of exponents/ radicals
\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)
then
4 \(\sqrt{y^{3} }\)
= 4\(y^{\frac{3}{2} }\)
a case of toothpicks has 5,400 toothpicks, there are 9 boxes of toothpicks in the case.how many toothpicks are in each box?
( awnser this untill tmr and u will get 200 points!)
Answers
Answer:
divide it, 5400 divided by 9 is 600.
A circle has an area of 1075.21 m^2
What is the radius to the nearest 1 decimal x.x
Answers
1075.21 = πr²
1075.21/π = r²
r = √1075.21/π
r = 18.5
The speed of a stream is 2 mph. A boat travels 6 miles upstream in the same time it takes to travel 10 miles downstream. What is the speed of the boat in still water?
Answers
The speed of the boat in still water is 8 mph
Here, we want to get the speed of the boat in still water
Here, we are going to bs using two speeds
The speed in moving water and the speed in still water
Let the speed of the boat in still water be x mph
The speed of the boat downstream is (x + 2) mph
The speed of the boat upstream is (x-2) mph
Mathematically,
\(\text{time = }\frac{dis\tan ce}{\text{speed}}\)From the question, we are told that the time taken to travel both upstream and downstream is the same
The time downstream is;
\(\text{time = }\frac{10}{x\text{ + 2}}\)The time upstream is;
\(\text{time = }\frac{6}{x-2}\)Since the times are equal, we equate the two as follows;
\(\begin{gathered} \frac{10}{x+2}\text{ = }\frac{6}{x-2} \\ 10(x-2)\text{ = 6(x+2)} \\ 10x-20\text{ = 6x+12} \\ 10x-6x\text{ = 12 + 20} \\ 4x\text{ = 32x } \\ x\text{ = }\frac{32}{4} \\ x\text{ = 8 mph} \end{gathered}\)
The vertex of the parabola would be located at which coordinates
-6,3
6,3
3,-6
3,6
Answers
\(y = 4 {(x - 6)}^{2} + 3\)
Vertex Form\(y = a {(x - h)}^{2} + k\)
where a-term determines how wide/narrow/upward or downward of the graph.
h-term determines the changes of graph for x-axis
k-term determines the changes of graph for y-axis.
The vertex of parabola is at (h,k).
\(y = 4 {(x - ( + 6)})^{2} + ( + 3)\)
Therefore, h = 6 and k = 3.
Answer\( \large \boxed{(6,3)}\)
What is the range of the relation?
Answers
Match each sentence to the correct equation.
Three is the product of a number and five.
Four is one less than a number.
The quotient of sixteen and a number is two.
The sum of three and a number is ten.
4=x 1
3=5x
16÷x=2
3+x=10
need help fast pls!!
Answers
Answer:
Step-by-step explanation:
Three is the product of a number and five. 3=5x
Four is one less than a number. 4=x - 1
The quotient of sixteen and a number is two. 16÷x=2
The sum of three and a number is ten. 3+x=10
Answer:
Step-by-step explanation:
Three is the product of a number and five. 3*x = 5
Four is one less than a number. 4 = x - 1
The quotient of sixteen and a number is two. 16/x = 2
The sum of three and a number is ten. x + 3 = 10
i dont understand, help?
Answers
f(-2) = -2^2 - (-2)^3
f(-2) = 4+8
f(-2) = 12
Hope it helped !!
Put your comments below
i need help with this math please
Answers
Expectation is computed by multiplying each outcome (number of hybrids sold) by the corresponding probability, then adding these products:
0×0.32 + 1×0.28 + 2×0.15 + 3×0.11 + 4×0.08 + 5×0.06
= 1.53
So on average, 1.53 hybrids are sold each week.
Yo plz help me I don’t know this
Which number line shows the solution to -6 - (-4)?
Answers
Answer:
B
Step-by-step explanation:
To solve -6-(-4) you need to break it down.
First, multiply -(-4) which would equal 4 (negative times negative equals positive)
Then add 4 to -6 (-6+4)
This equation is being expressed through option B
Hope this helps! :)
Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to indicate exponents. For example, type a2 as a∧2. (Hint: Let s be a length of each side and x be the angle measure; then use these variables in the law of cosines.)
Answers
The algebraic proof shows that the angles in an equilateral triangle must equal 60° each
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.
Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are
cos A = (b² + c² - a²)/2bc
cos B= (a² + c²- b²)/2ac
cos C = (a²+ b²- c²)/2ab
Now, given that the triangle is equilateral, with each of the side lengths equal to s
That is, a = b = c = s
Then, we can write that
cos A = (s² + s² - s²)/(2s×s)
cos A = (s² )/(2s²)
cos A = 1/2
cos A = 0.5
∴ A = cos⁻¹(0.5)
A = 60°
Also
cos B = (s² + s² - s²)/(2s×s)
cos B = (s²)/(2s²)
cos B = 1/2
cos B = 0.5
∴ B = cos⁻¹(0.5)
B = 60°
and
cos C = (s² + s² - s²)/(2s×s)
cos C = (s² )/(2s²)
cos C = 1/2
cos C = 0.5
∴ C = cos⁻¹(0.5)
C = 60°
Thus,
A = 60°, B = 60° and C = 60°
Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.
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Suppose you just purchased a digital music player and have put 14 tracks on it. After listening to them you decide that you like 4 of the songs. With the random feature on your player, each of the 14 songs is played once in random order. Find the probability that among the first two songs played
Answers
The probability that among the first two songs played, exactly 1 of the 4 songs you like is played is 0.452 or 45.2%.
Define probabilityProbability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
There are 4 songs that you like out of the 14 total songs, so the probability of selecting a song that you like on the first draw is 4/14.
On the second draw, the probability of selecting a song that you like is 3/13, since there are now 3 songs that you like out of the remaining 13 songs.
The probability of selecting exactly 1 of the 4 songs you like in the first two draws is given by:
P(exactly 1 like in first two draws) = (4/14) ×(10/13) + (10/14) × (4/13) = 0.452
Therefore, the probability that among the first two songs played, exactly 1 of the 4 songs you like is played is approximately 0.452 or 45.2%.
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A triangular arch is to be constructed over a busy street in order to place a sky bridge traversing one side of the triangle to the other. The base of the arch spans the width of the street, which is 20 feet. Each side of the triangular arch measures 30 feet in length. If the entrances of the sky bridge lie at the midpoints of each side of the triangular arch, and the bridge is to be parallel to the street below, how long will the sky bridge be?
Answers
Answer:
15
Step-by-step explanation:
Simplfy and solve 13+7x66
Answers
Answer:475
PLEASE HELP SOLVE FOR ‘X’!!!
Answers
Answer:
x= 10
Step-by-step explanation:
1/5 x -2/3 = 4/3
Add 2/3 to each side
1/5x -2/3 +2/3 = 4/3 +2/3
1/5x = 6/3
1/5x = 2
Multiply each side by 5
1/5x * 5 = 2*5
x = 10
Scientists estimate there are 70,000 species insects in each acre of the
Amazon Rainforest. How many species are there in 100 acres? *
Answers
Answer:
there are 700 species in every acre
Step-by-step explanation:
divide the amount of species by the amount of acres.
Answer:
7,000,000
Step-by-step explanation:
If there is 70,000 in each acre, just multiply 70,000 times 100 acres.
how do i convert 134five to base ten
Answers
Answer:
44
Step-by-step explanation:
1×5² + 3×5¹ +4×5⁰
25+15+4
44
The average electric usage for a certain month was 73 kWh per day. Determine what the average kWh per day usage will be if it is increased by 3.1%. (2 points)
70.254 kWh
72.745 kWh
74.976 kWh
75.263 kWh
Answers
73•0.031=2.263
2.263+73=75.263
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answers
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610