20 POINTS AND A FOLLOW plus BRAINIEST IF RIGHT 1. What is the area of sector GHJ, given that 0=pi/4 radians ? Express your answer in terms of pi and as a decimal rounded to the nearest tenth. Show your work.
2. Construct the circle that circumscribes triangle DEF . Use a straightedge and a compass.
(show work by step)
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where
[tex]A[/tex] is the area of the sector
[tex]r[/tex] is the radius of the circle
[tex] \alpha [/tex] is the angle in radians
We know from our problem that the radius of the circle is 5 cm and the angle of the sector is [tex] \frac{ \pi }{4} [/tex], so [tex]r=[/tex] and [tex] \alpha = \frac{ \pi }{4} [/tex]. Lets replace those values in our formula:
[tex]A= \frac{1}{2} r^2 \alpha [/tex]
[tex]A= \frac{1}{2} (5)^2( \frac{ \pi }{4} )[/tex]
[tex]A= \frac{25 \pi }{8} [/tex]
[tex]A=9.8[/tex]
We can conclude that the area of sector GHJ in terms of pi is [tex] \frac{25 \pi }{8}[/tex] [tex]cm^2[/tex], and as a decimal rounded to the nearest tenth is 9.8 [tex]cm^2[/tex].
2. To construct the circle that circumscribes triangle DEF, we are going to draw the perpendicular bisectors of triangle DEF, and then we are going to draw the circle with radius at the interception point of the bisectors. Remember that the perpendicular bisector are the lines that passes trough the midpoint of the segment and are perpendicular to the segment.
Related Questions
The perimeter of the base of a pentagonal prism is 25 inches and one of its lateral edges is 4 inches. The lateral area of the prism is ________ square inches.
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Answer:
Lateral area=100 square inches
Step-by-step explanation:
It is given that the perimeter of the base of a pentagonal prism is 25 inches, therefore each sides of the pentagon will be of 5 inches.
Also, one of its lateral edge is 4 inches, therefore each lateral face has area which will be equal to=[tex]5{\times}4[/tex]=[tex]20[/tex]square inches.
Since, there are 5 lateral faces of the pentagonal prism, therefore the lateral area of the prism will be: [tex]5{\times}20[/tex]
= [tex]100[/tex]square inches.
The unt informs club has 16 members. they need to elect a president, a vice president, a secretary and a treasurer. how many different ways can this group of 4 officers be formed? (order is important)
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Hope this helped!
Cans of juice cost 25p each to produce
There are 6 cans in a pack.
12 packs are sold at £3.60 each.
What is the profit?
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what is the solution of the equation?
please help!!
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[tex] \sqrt{2x+8}-6=4 \\ \\ \sqrt{2x+8}=10 \\ \\ 2x+8=(10)^{2} \\ \\ 2x+8=100 \\ \\ 2x=92 \\ \\ x= 46 [/tex]
|-x-2y| for x =-3 and y=3
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This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.
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It is NOT true that [tex]\dfrac{d}{dx} \left( f^{-1}(x) \right) \ge 0[/tex]
a triangle with a base of 6cm and a height of 8cm is similar to a triangle with base 21cm. What is the height of the second triangle
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Do base over height; [tex] \frac{base}{height}[/tex].
[tex] \frac{6}{8} = \frac{21}{h} [/tex]
h is the height of the second triangle. Solve for h.
Cross multiply.
[tex] \frac{6}{8} = \frac{21}{h} [/tex]
6h = 168
h = 28
The height of the second triangle is 28 cm.
The line plot represents the heights of students in a second-grade classroom. Which statement is true?
A. The median is less than the mode.
B. The median height is 42 inches, and the mode height is 36 inches.
C. Most of the students in the class are shorter in height.
D. The mode is less than the median.
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Answer:
B. The median is less than the mode
Step-by-step explanation:
what is the sum of the geometric series E (-2)(-3)^n-1
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S=(-2)(-3)^(1-1)+(-2)(-3)^(2-1)+(-2)(-3)^(3-1)+(-2)(-3)^(4-1)
S=(-2)[(-3)^0+(-3)^1+(-3)^2+(-3)^3]
S=(-2)[1+(-3)+9+(-27)]
S=(-2)(1-3+9-27)
S=(-2)(-20)
S=40
Answer: Third option 40
Answer:
The sum is 40.
Step-by-step explanation:
Given,
[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}[/tex]
We know that,
[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1}[/tex]
[tex]=(-2)(-3)^{0}+(-2)(-3)^1+(-2)(-3)^2+(-2)(-3)^3[/tex]
[tex]=-2\times 1 - 2\times - 3 - 2\times 9-2\times -27[/tex]
[tex]=-2+6-18+54[/tex]
[tex]=40[/tex]
Hence,
[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=40[/tex]
During a family vacation, Ms. Walker drove 918 miles on 3 tanks of gasoline. Her daughter, Amani, wants to create an equation in the form em equals square tee, to represent the total number of miles, m, her mom can drive on t tanks of gasoline. What number should Amani put in the square to complete her equation?
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Rate=(miles)/(number of tanks)
thus the rate will be:
miles=918 mile
tanks=3 tanks
thus
rate=918/3=306 miles/tank
what is the value of the expression?
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From our circle we can infer that [tex]sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2} [/tex] and [tex]cos\frac{5 \pi }{3}= \frac{1}{2} [/tex].
Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]
We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].
Vanessa is opening a clothing store. She plans to start by selling gym shorts. If it costs her $4 for each pair of shorts, $3 for the ink per pair of shorts, and $0.20 a bag, what is her unit cost per pair of shorts?
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cost of shorts=$4
Number of pairs=1
thus
unit cost=4/1=4 dollars per pair
Answer: 4 dollars per pair
Answer:
its $7.20 on APEX
Step-by-step explanation:
match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
A.
B.
C.
D.
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The correct linear system for the student's question is D. x + 3y \<= 38, x + y \<= 12, which matches the conditions of Lewis's situation for acquiring baseball cards.
The student is looking to match a situation with a linear system. The situation is that Lewis wants at most 12 packages of baseball cards, some containing 4 rookie cards and others 3 rookie cards, with a total of 38 rookie cards at most.
To match the situation with the correct linear system, we must set up two inequalities: one for the number of packages and another for the number of rookie cards.
Let x represent the number of packages with 4 rookie cards and y represent the number of packages with 3 rookie cards.
The first condition is that Lewis can have at most 12 packages, which gives us the inequality x + y \<= 12. The second condition is that the total number of rookie cards is at most 38, which gives us the inequality 4x + 3y \<= 38.
Considering these conditions, the correct answer is: D. x + 3y \<= 38, x + y \<= 12.
Which expression is equivalent to 4 sqrt 16x^11y^8/81x^7y^6
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The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.
Explanation:The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.
We start by simplifying the square root of each component:
Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.Now, divide and simplify:
(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)
Therefore, we get:
(4/9) * x^2 * y
trignometry help what's the answer?
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See attached picture for solution:
Compute the stock turnover in dollars for a product that has sales of $6,000 and an average value of inventory investment of $1,500.
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Solution:
Inventory turnover = Cost of goods sold/Average inventory
Substituting the values given for cost of goods and average inventory;
Inventory turnover = 6,000/1,500 = 4
Answer: 4
Step-by-step explanation:
Given: Cost of product sold = $6,000
Average value of inventory= $1,500
We know that the inventory turnover formula is given by :-
[tex]\text{Inventory turnover}=\frac{\text{ Cost of product sold}}{\text{Average value of inventory}}[/tex]
[tex]\\\Rightarrow\ \text{Inventory turnover}=\frac{\$6,000 }{\$1500}\\\\\Rightarrow\ \text{Inventory turnover}=4[/tex]
Therefore, the stock turnover for a product that has sales of $6,000 and an average value of inventory investment of $1,500 = 4
Consider the arithmetic series:
1 + 9 + 17 + 25 + ...
Write a formula for the sum of the first n terms in this series.
A) 4n2 - 3n
B) 6n2 - 7n
C) 8n2 - 5n
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[tex] S_{n}= \frac{n}{2}(2a_{1}(n-1)*d) [/tex]
where,
d = Common Difference = Difference of any two consecutive terms.
So,
d = 8
a1 = First term = 1
Using the values, we get:
[tex] S_{n}= \frac{n}{2}(2*1+(n-1)*8) \\ \\ S_{n}= \frac{n}{2} (2+8n-8) \\ \\ S_{n}= \frac{n}{2}(8n-6) \\ \\ S_{n}=n(4n-3) \\ \\ S_{n}==4n^{2}-3n [/tex]
The above equation gives the formula for n terms of an Arithmetic Series.
So, option A is the correct answer
Which additional information is needed to solve this problem?
John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?
A.
total amount John can save in 1 week
B.
the cost of the game
C.
amount John earns per hour babysitting
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The answer is B.
the cost of the game.
We need to know the cost of the game in order to find out how many weeks John has to save money. If we don't know this price, we'll never know whether John has saved enough money.
We can find out the total amount of money John can save in 1 week (so A. is not the answer). The amount of money John earns per hour doesn't matter to answer the question (so C. is wrong).
~ Hope this helps you!
What is the slip of the line given by the equation y=-1/3 x
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[tex]\bf y=\stackrel{slope}{-\cfrac{1}{3}}x~~\stackrel{y-intercept}{+0}[/tex]
Tom has been given 35 chores to complete today this morning he finished seven of them how many chores does he now have left to do
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QS is the perpendicular bisector of PR solve for x
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3x=90
so the answer is x=30
2x - 20 = 70 - x
3x - 20 = 70
3x = 90
x = 30
PLS HELP! Tanisha is planning a party. She will serve hamburgers, potato salad, strawberry shortcake, and lemonade. Including Tanisha, 28 people will be at the party. Tanisha expects that each person will drink two 8−ounce glasses of lemonade at the party, and makes 448 ounces of lemonade. Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 ounces of lemonade. Does Tanisha need more lemons?
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448 ÷ 80 =5.8
⇒ There are 5.6 80-ounce of lemonade.
80 ounces of lemonade needed 8 lemons.
448 ounces of lemonade needed 8 x 5.6 = 44.8 lemons.
Tanisha has 38 lemons.
She does not have enough lemons.
She needs 44.8 - 38 = 7 more lemons.
Answer: Tanisha needs more lemons. She needs 7 more.
Answer: 7 more lemons
Step-by-step explanation:
Since she needs 448 ounces of lemonade you have to divide which is 5.6 . As a result there are 5.6 80 ounces of lemonade. 80 ounces needs 8 lemons. 448 ounces of lemonade are needed 8 x 5.6 = 44.8 lemons. Tanisha only has 38 lemons, which isn't enough. 44.8 - 38 = is about 7 more lemons.
Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F
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Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F'?
we know that
the transformation has the following rule
(x,y)--------> (x+6,y-6)
so
(-9,2)-----> (-9+6,2-6)------> (-3,-4)
the answer is
(-3,-4)
Answer:
-6,-6
Step-by-step explanation:
(-9,2) + (-8,3) = (-6,-6)
correct on the test :)
simplify radical (1-cos0)(1+cos0)/ cos^2 0
HELP ME PLS!! ASAP
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(1-cos)(1+cos)=1-cos² which equals to sin²
√sin²/cos²= sin/cos which equals to tan
HEEEELLLPP!!!!!!!!!!!!!!!WILL GIVE THE BRAIN!!!!!POINTS!!!!!!!
plz
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It is the local minimum as it is the minimum point in the neighboring. The term local is used, as it is the lowest point within a short interval and not for the entire function.
The interval which correctly shows the local minimum is [-3, -1]
So, the correct answer is option Third
Use addition to solve the linear system of equations. Include all of your work in your final answer.
x - y = 4
x+ 2y = 4
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x - y = 4-------> multiply by -1-----> -x+y=-4-----> equation 1
x+ 2y = 4------> equation 2
add equation 1 and equation 2
-x+y=-4
x+2y=4
-----------------
0+3y=0-----> y=0
x+2y=4------> x+0=4------>x=4
the solution is the point (4,0)
someone please help asap! Which statement is most likely true for this distribution?
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Answer:
C) The mean is greater than the median.
Step-by-step explanation:
This distribution is right skewed; that means it has a longer tail to the right and the data is "bunched up" at the left.
In a right skewed distribution, the majority of data points are at the smaller end; for this reason, the median will be towards the left side of the graph.
The higher numbers in the "tail" will bring the mean up, making it larger than the median.
The correct statement for the distribution is the mean is greater than the median.
What is mean and median?
The mean is the average of a data set. The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
The median is the middle term of a distribution.
It measure determines the middle value of a dataset listed in ascending order.
Therefore, from the distribution the data are rightly skewed. The higher numbers in the "tail" will bring the mean up, thereby making it larger than the median.
learn more on mean and median here: https://brainly.com/question/14299269
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Henry has a defined benefit plan that promises a 2.5% annual retirement benefit based on the average of his last five years of salary. At retirement Henry has 21 years of service and an average salary over the last five years of $95,000. What will his annual benefit be?
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Henry's annual retirement benefit will be $2,375.
We have,
To calculate Henry's annual retirement benefit, we need to find 2.5% of his average salary over the last five years.
First, let's calculate 2.5% of $95,000:
2.5% = 2.5/100 = 0.025
Annual benefit = 0.025 * $95,000
Annual benefit = $2,375
Therefore,
Henry's annual retirement benefit will be $2,375.
Learn more about expressions here:
https://brainly.com/question/3118662
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A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. tables Which of the following correctly represents the given data in the problem?
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D) a = 24, c = 48, e = 22, i = 80
Need help with math thank u
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2,-4
These are two answers
It is infinitely many solutions