The area of the hexagon is 98 sq. m and option 3 is the correct answer.
What is a hexagon?The closed polygonal form of a regular hexagon has six equal sides and six equal angles. Any regular polygon has equal sides and angles on all sides. Regular pentagons, for instance, have 5 equal sides, while regular octagons have 8 equal sides. When these requirements are not satisfied, polygons might resemble many other asymmetrical forms. A regular hexagon is formed when six equilateral triangles are placed side by side. The regular hexagon's area then increases to six times that of the identical triangle.
Given that,
The scale factor of two similar hexagons is 3:7.
The ratio of the area will thus be,
(3/7)^2 = 9/49.
For the area of the smaller hexagon as 18 we have:
9/49 = 18/A
(9/49)A = 18
Multiplying both sides by 49/9, we get:
A = 98 sq. m
The volume of the hexagon cannot be determined by the given information.
Hence, the area of the hexagon is 98 sq. m and option 3 is the correct answer.
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Answer #14 using the picture
Answer:
(10,14)
Step-by-step explanation:
if you look there's a pattern
A route between Guilford and Bath has a distance of 180 kilometres.
Dave drives from Guilford to Bath. He takes 3 hours.
Olivia drives the same route. Her average speed is 15 kilometres per hour faster than Dave's.
(a) How long does it take Olivia to drive from Guilford to Bath?
Give your
answer in hours and minutes
Olivia will take time of 4 hour to drive from Guilford to Bath.
Explain the relation of speed and distance?Speed is the rate at which a distance changes over time. The speed is equivalent to s = D/T if D is the object's distance in time T. The units are the same as for velocity.Let the speed of Dave be 'x' km/h
Then,
Olivia's speed = ( x + 15 )km/h
Time = 3 hours.
Distance = 180 kilometres
Using relations:
Speed = distance /time
x + 15 = 180/3
x + 15 = 60
x = 60 - 15
x = 45 km/hr.
Time taken by Olivia to drive from Guilford to Bath.
45 = 180/t
t = 180 / 45
t = 4 hours.
Thus, it take Olivia 4 hour to drive from Guilford to Bath.
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Kevin and Randy Muise have a jar containing 54 coins, all of
which are either quarters or nickels. The total value of the coins
in the jar is $11.10. How many of each type of coin do they have
?
The number of each type of coin they have is 42 quarters and 12 nickels.
To find out how many of each type of coin Kevin and Randy Muise have, we can use a system of equations. Let's call the number of quarters "q" and the number of nickels "n". We can create two equations based on the information given:
q + n = 54 (the total number of coins)
0.25q + 0.05n = 11.10 (the total value of the coins)
Now we can use the substitution method to solve for one of the variables. Let's solve for "n" in the first equation:
n = 54 - q
Now we can substitute this value of "n" into the second equation:
0.25q + 0.05(54 - q) = 11.10
Simplifying and solving for "q":
0.25q + 2.7 - 0.05q = 11.10
0.20q = 8.40
q = 42
Now we can plug this value of "q" back into the first equation to find "n":
n = 54 - 42
n = 12
So Kevin and Randy Muise have 42 quarters and 12 nickels in their jar.
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Draw the image of the given rotation of the preimage
The answer of the given question based on the image of the given rotation of the preimage is given below,
What is Rotation?Rotation is a transformation in which an object or figure is turned around a fixed point or center by a certain angle or degree. The fixed point is known as the center of rotation, and the angle of rotation is measured in degrees or radians.
Based on the given rotation specification, "r(270,0)(x,y)", the preimage should be rotated 270 degrees counterclockwise around the origin.
To draw the image of the rotated preimage, you can use the following steps:
Plot the coordinates of the preimage points on a coordinate plane.
Draw line from of each point to origin.
Measure an angle of 270 degrees counterclockwise from each line, using a protractor or angle tool.
Draw a new line from each point to the endpoint of the measured angle. These lines represent the rotated points.
Label the new coordinates of the rotated points.
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33 pt= __qt __pt (convert units)
Converting 33 pints into quarts is 16.5 Quarts.
How to Convert 33 pints into quartsThe pint (symbol: pt) is a unit of volume or capacity in both the imperial and United States customary measurement systems.
The quart (abbreviation qt.) is an English unit of volume equal to a quarter gallon. It is divided into two pints or four cups.
To calculate 33 Pints to the corresponding value in Quarts,
We multiply the quantity in Pints by 0.5 (conversion factor).
In this case we should multiply 33 Pints by 0.5 to get the equivalent result in Quarts:
33 Pints x 0.5 = 16.5 Quarts
Hence, 33 Pints is equivalent to 16.5 Quarts.
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The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different mileage and determines each car’s price using a used car website. The analysis is given in the computer output.
Which of the following represents the value of the average residual for a car’s price?
0.024
2164.1
3860.7
24157.2
The value of the average residual for a car’s price include the following: C. 3860.7.
What is a coefficient of determination?In Mathematics, a coefficient of determination (r² or r-squared) can be defined as a number between zero (0) and one (1) that is typically used for measuring the extent (how well) to which a statistical model predicts an outcome.
What is a residual value?In Mathematics, a residual value is a difference between the measured (given or observed) value from a residual plot and the predicted value from a residual plot.
Based on the computer output (see attachment), we can logically deduce that the coefficient of determination (r²) and average residual for a car's price are as follows;
r² = 68% = 68/100 = 0.68.
Average residual for a car's price, S = 3860.7.
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Use decomposition to find the area of the figure. A drawing of a right-angled trapezoid with length of two parallel sides measuring 10 yards and 13 yards. The height of the trapezoid is 8 yards. The area is
square yards. Skip to navigation
In the given problem, we need to find the area of the trapezoid in which the height is 8 yards. The area of the given trapezoid is 92 square yards.
If the length of a trapezoid's parallel sides and the distance (height) between them are known, the area of the shape may be determined.
A = (a+b)h/2 is the formula for a trapezoid's surface area.
where "a" and "b" are the lengths of the base of the trapezoid and "h" represents the height of the figure.
We have been given the values,
The length of the bases is 10 and 13 yards and,
the height of the trapezoid is 8 yards.
So, according to the formula for determining the area,
Area of a trapezoid,
"A" = {(10 + 13)8} / 2
⇒ A = {184}/2
⇒ A = 92 square yards.
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Select the correct answer from each drop-down menu
Answer:7.9
Step-by-step explanation:
square root of 63 is 7.9
Answer:
Step-by-step explanation:
[tex]\sqrt{63} =[/tex] [tex]\sqrt{7}[/tex]×[tex]\sqrt{9}[/tex]
= [tex]\sqrt{7}[/tex] × 3
= 3[tex]\sqrt{7}[/tex]
if your mom was given birth in year x and you were given birth in 2010 you and her have an age gap of 36 years what is her birth date
Answer:
2010-36=1974
She was born in 1974.
Answer:1974
Step-by-step explanation:
2010-36=1974
Pls help a brother out.
Where is your question so we may help
Answer:
Step-by-step explanation:
mark me brainliest so i can solve
Find the value of x. Then find the measure of each labeled angle .
Answer:M1=50 M2=130
Step-by-step explanation:
M2=130 because corresponding angles and M1=50 because 180-130=50
Bonsoir, j’ai besoin d’aide pour l’exo 135 je suis bloqué, merci d’avance
Answer:
Je suis désolé, mais je ne sais pas à quoi fait référence l'exo 135. Pouvez-vous me donner plus de détails sur ce que vous cherchez à comprendre ou résoudre ? Je suis heureux de vous aider si je peux comprendre la question.
y-3=1(x-2)
write an equation of a line
that is perpendicular to this line. Show your work.
The equation of a perpendicular line is y = -x + 2
How to determine the equation of a perpendicular lineFrom the question, we have the following parameters that can be used in our computation:
y - 3 = 1(x - 2)
We can use the point-slope form of a linear equation to write the equation of the perpendicular line:
y - y1 = m(x - x1)
By comparison, we have
m1 = 1
For perpendicular lines. we have
m = -1/m1
So, we have
m = -1
An example of an equation wit a slope of -1 is
y = -x + 2
Hence, the equaton is y = -x + 2
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what is
y = x
y = 2x -4
PLS I NEED HELP and i have sm more questions..
Answer:
(4, 4) in point form
x = 4, y = 4 in equation form
Explanation:
...
Quadrilateral HIJK is an isosceles trapezoid and mZJ = 5p + 1°. What is the value of p?
J
P =
K
Save answer
106⁰
I
H
The value of P for the given isosceles trapezoid is 21.
What is an isosceles trapezoid ?An isosceles trapezoid is a four-sided figure with two parallel sides (called bases) of different lengths, and two non-parallel sides of equal length.
The non-parallel sides are also called legs. The two parallel sides are connected by two diagonal lines that intersect each other at a midpoint, forming two congruent triangles.
The following properties are characteristic of an isosceles trapezoid:
The opposite angles are supplementary (add up to 180 degrees).The diagonals are congruent to each other.The two non-parallel sides are congruent to each other.The angle between a non-parallel side and a base is congruent to the corresponding angle on the other side of the trapezoid.For this case, if m∠I = 106⁰, then m∠J = 106⁰
So the value of P is calculated as follows;
m∠J = 5p + 1 = 106
5p + 1 = 106
5p = 106 - 1
5p = 105
p = 105 / 5
p = 21
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I NEED HELP ASAP PLS
*problem in image*
The tallest tree that can be supported with the wire is 20 feet .
How to find the side of a right triangle?The tallest tree that can be supported with a 25 foot wire staked 15 feet away from the tree can be calculated as follows:
Therefore, the tallest tree can be found using Pythagoras's theorem,
Hence,
c² = a² + b²
where
a and b are the legsc is the hypotenuse25² - 15² = b²
b² = 625 - 225
b = √400
b = 20 feet
Therefore, the tallest tree is 20 feet.
From the diagram, the tallest tree that can be supported by a 25 feet wire is 20 feet. we had to use Pythagoras's theorem to find the tallest tree that 25 feet wire can hold.
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Help me please with this
Answer:
Mate the answer is c.
HELPPP
Martina will spend more than $36 on gifts. So far, she has spent $22. What are the possible additional amounts she will spend?
Use c for the additional amount (in dollars) Martina will spend.
Write your answer as an inequality solved for c.
If Martina has already spent $22 and will spend more than $36 in total, then we can set up an inequality to represent the possible additional amounts she will spend:
$22 + c > $36
To solve for c, we can isolate it on one side of the inequality by subtracting $22 from both sides:
c > $36 - $22
c > $14
Therefore, the possible additional amounts Martina will spend (represented by c) must be greater than $14. The inequality solved for c is c > $14.
Given the following functions f(x) and g(x), solve flg(10)]. F(x) = 10x + 8
g(x) = x+9
The value of function f[g(10)] = 198.
Given value of functions f(x) and g(x)
F(x) = 10x + 8
g(x) = x+9
To find f[g(10)], we need to first evaluate g(10), which means plugging in x=10 into the expression for g(x):
g(10) = 10 + 9 = 19
Now we can use this result to evaluate f[g(10)], which means plugging in x=19 into the expression for f(x):
Put the value of x=19 in F(x)
f[g(10)] = f(19) = 10(19) + 8 = 190 + 8 = 198.
Therefore, the function f[g(10)] value is = 198.
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Perform the indicated operation on the algebraic expressions. Sim (u-v)(u^(2)+uv+v^(2))
The simplified expression is u^(3) - v^(3).
To perform the indicated operation on the algebraic expressions, we need to multiply each term in the first expression by each term in the second expression and then simplify the resulting expression.
Step 1: Multiply each term in the first expression by each term in the second expression:
(u)(u^(2)) + (u)(uv) + (u)(v^(2)) - (v)(u^(2)) - (v)(uv) - (v)(v^(2))
Step 2: Simplify the resulting expression by combining like terms:
u^(3) + u^(2)v + uv^(2) - u^(2)v - uv^(2) - v^(3)
Step 3: Simplify further by canceling out terms that are equal but opposite in sign:
u^(3) - v^(3)
Therefore, the simplified expression is u^(3) - v^(3).
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Factoring out a monomial from a polynomial: Multiva Factor the following expression. 11u^(9)v^(8)-22u^(2)v^(2)y^(6)
The factored expression is 11u^(2)v^(2)(u^(7)v^(6) - 2y^(6)).
Factoring out a monomial from a polynomial involves finding the greatest common factor (GCF) of the terms in the polynomial and then dividing each term by the GCF to get the remaining polynomial. In this case, the GCF of the two terms in the expression is 11u^(2)v^(2). So, we can factor out this monomial from the polynomial as follows:
11u^(9)v^(8) - 22u^(2)v^(2)y^(6) = 11u^(2)v^(2)(u^(7)v^(6) - 2y^(6))
Therefore, the factored expression is 11u^(2)v^(2)(u^(7)v^(6) - 2y^(6)).
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what is the rate of traveling 372 miles in 6 hours
Answer:62 miles/hour
Step-by-step explanation:372 miles / 6 hours = 62 miles/hour 62 * 15 = 930 A driver travels 372 miles in 6 hours. At that rate, the driver will travel 930 miles in 15 hours
Answer: 62 mph
Step-by-step explanation:
372/6=62
:)
Complete each operation with functions. Shown bellow 1. g(a) = 2 - 1 f(a) = -2-4 Find (g-f)(1) 2. h(t) = 2t +1 g(t) = 2t + 2 Find (h-g)(t) 3. g(a) = -30 - 3 f(a)= a +5 Find (g -f(a) 4. g(x) = 2x-5 h(x) = 4x +5 Find g(3) - h(3) 5. h(x) = 3x +3 g(x) = -4x + 1 Find (h+g)(10) 6. f(x) = 4x - 3 g(x) = x + 2x Find (f-g)(4)
The following operations with functions:
1. (g-f)(1) = 7
2. (h-g)(t) = -1
3. (g -f(a) = -38 - a
4. g(3) - h(3) = -16
5. (h+g)(10) = -6
6. (f-g)(4) = 1
Complete each operation with functions.
1. (g-f)(1) = g(1) - f(1) = (2-1) - (-2-4) = 1 + 6 = 7
2. (h-g)(t) = h(t) - g(t) = (2t+1) - (2t+2) = -1
3. (g-f)(a) = g(a) - f(a) = (-30-3) - (a+5) = -33 - a - 5 = -38 - a
4. g(3) - h(3) = (2(3)-5) - (4(3)+5) = (6-5) - (12+5) = 1 - 17 = -16
5. (h+g)(10) = h(10) + g(10) = (3(10)+3) + (-4(10)+1) = (30+3) + (-40+1) = 33 - 39 = -6
6. (f-g)(4) = f(4) - g(4) = (4(4)-3) - (4+2(4)) = (16-3) - (4+8) = 13 - 12 = 1
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A square-based pyramid has a base side length of 10 cm and a height of 12 cm.
Find the Volume of this pyramid.
Answer: In the given square-based pyramid: The edge length of the square base (a)=10 m ( a ) = 10 m . The slant length of the pyramid (l)=12 m
Step-by-step explanation:
Answer:
I found this i hope it is correct
Step-by-step explanation:
The volume of a square-based pyramid is given by the formula:
V = (1/3) * base area * height
The base area of the pyramid is the area of a square with side length 10 cm:
base area = 10 cm * 10 cm = 100 cm^2
Substituting the given values into the formula:
V = (1/3) * 100 cm^2 * 12 cm
V = 400 cm^3
Therefore, the volume of the pyramid is 400 cubic centimeters.
The area of a rectangle is 228 square feet. If the length of the rectangle is 12 feet what is the width of the rectangle
Answer: 19
Step-by-step explanation: The formula for the area of a quadrilateral is length x width.
Here, we have the width missing. So our equation would be,
12x=228.
dividing both sides by 12 gives us x=228/12.
solving this, we get x=19.
So, your answer will be 19.
Answer:
The width of the rectangle is 19 feet
Step-by-step explanation:
The formula for the area of a rectangle is length times width which can be expressed as
[tex]A=lw[/tex]
We can rearrange the equation and solve for the width.
Divide both sides of the equation by [tex]l[/tex].
[tex]\frac{A}{l}=w[/tex]
Now we have an equation to evaluate the width.
Numerical Evaluation
Substituting our values into the equation yields
[tex]\frac{228}{12}=w[/tex]
[tex]w=19[/tex]
Show that ∑F(i) = F(n+2) - 1. Consider the following disk transportation problem: You are given three pegs named A, B and C. On peg A sit n disks in strict decreasing order of size, with the smallest disk on the top and the largest disk on the bottom. You are required to transport the disks from peg A to peg C, while respecting the following rules: (a) In each move, exactly one disk can be moved. (b) No disk may ever be placed on top of a smaller disk. (c) Each move consists of taking the uppermost disk from one of the pegs and placing it on top of another peg i.e., a disk can only be moved if it is the uppermost disk on a peg. Write down a recurrence relation for computing the total number of moves required to transfer the n disks from peg A to peg C. Hint: Do you see why peg B is required?
Therefore, ∑F(i) = F(n+2) - 1 is true for the disk transportation problem.
The disk transportation problem described in the question is a classic example of the Tower of Hanoi puzzle. The goal of the puzzle is to move all the disks from peg A to peg C while following the rules mentioned in the question. The recurrence relation for computing the total number of moves required to transfer the n disks from peg A to peg C can be written as follows:
F(n) = 2F(n-1) + 1
This recurrence relation can be derived by considering the fact that to move n disks from peg A to peg C, we first need to move the top n-1 disks from peg A to peg B using peg C as an intermediate peg. This requires F(n-1) moves. Next, we need to move the largest disk from peg A to peg C, which requires 1 move. Finally, we need to move the n-1 disks from peg B to peg C using peg A as an intermediate peg, which again requires F(n-1) moves. Therefore, the total number of moves required to transfer the n disks from peg A to peg C is F(n) = 2F(n-1) + 1.
Now, to show that ∑F(i) = F(n+2) - 1, we can use the recurrence relation F(n) = 2F(n-1) + 1 and the fact that F(1) = 1. By substituting n = 1, 2, 3, ..., n-1, n in the recurrence relation and adding all the equations, we get:
∑F(i) = 2∑F(i-1) + n
Using the fact that F(1) = 1 and rearranging the terms, we get:
∑F(i) = F(n+1) - 1
Therefore, ∑F(i) = F(n+2) - 1 is true for the disk transportation problem.
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does the table represent a proportional relationship between x and y?
x y
4 3
8 7
12 11
16 15
20 19
Answer:
Yes
Step-by-step explanation:
They both are added by 4
Four different exponential functions are represented below.
Drag the representation of each function into order from greatest y intercept to least y-intercept.
Answering the question, we may state that According to the graph, from function largest y-intercept to smallest y-intercept, we have:
[tex]f(x) = 5 f(x) = 2 f(x) + 1 f(x) = 1/2 f(x) = 1/5 (x)[/tex]
what is function?Mathematicians investigate the relationships between numbers, equations, and related structures, as well as the locations of forms and possible placements for these items. A set of inputs and their corresponding outputs are referred to as a "function" in this context. If each input results in a single, unique output, the relationship between the inputs and outputs is known as a function. Each function has its own domain, codomain, or scope. A common way to denote functions is with the letter f. (x). is an x for entry. One-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
According to the graph, from largest y-intercept to smallest y-intercept, we have:
[tex]f(x) = 5 f(x) = 2 f(x) + 1 f(x) = 1/2 f(x) = 1/5 (x)[/tex]
As a result, the sequence is:
[tex]f(x) = 5^(x) (highest y-intercept) (highest y-intercept)[/tex]
[tex]f(x) = 2^(x) + 1 f(x) = 1/2^ (x)[/tex]
[tex]f(x) = 1/5^(x) (lowest y-intercept) (lowest y-intercept)[/tex]
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If a+b=4, and a^2+b^2=12, then what is a^4+b^4
? (A) 112 (B) 136 (C) 144 (D) 256 (E) None of these
If a+b=4, and a²+b²=12, then what is a⁴+b⁴ is (B) 136.
To find the value of a⁴ + b⁴, we can use the identity (a² + b²)² = a⁴ + 2a²b² + b⁴. We are given that a² + b² = 12, so we can plug that value into the identity to get:
(12)² = a⁴ + 2a²b² + b⁴
144 = a⁴ + 2a²b² + b⁴
We can also use the identity (a + b)² = a² + 2ab + b² to find the value of 2a²b². We are given that a + b = 4, so we can plug that value into the identity to get:
(4)² = a² + 2ab + b²
16 = a² + 2ab + b²
Subtracting a^2 + b^2 from both sides gives us:
16 - (a² + b²) = 2ab
16 - 12 = 2ab
4 = 2ab
2 = ab
So we can plug the value of 2ab back into the first identity to get:
144 = a4⁴ + 2(2)² + b⁴
144 = a^⁴ + 8 + b⁴
Subtracting 8 from both sides gives us:
136 = a⁴ + b⁴
So the value of a⁴ + b⁴ is 136, which is option (B).
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Inventory Analysis
A company reports the following:
Cost of goods sold
$259,150
51,830
Average inventory
Determine (a) the inventory turnover and (b) the number of days' sales in inventory. Round interim
calculations to the nearest dollar and final answers to one decimal place. Assume 365 days a year.
5 ✔
94,589 X days
a. Inventory turnover
b. Number of days' sales in inventory
The inventory turnover is 5 days and the number of days sales is 73 days if we assume 365 days a year.
The given data is as follows;
Cost of goods sold = $259,150
Average inventory = 51,830
a. Inventory turnover
Inventory turnover is calculated by dividing the cost of goods sold by the average inventory of the report.
Inventory turnover = (Cost of goods sold) / (Average inventory )
Inventory turnover = $259,150 / $51,830
Inventory turnover = 4.99 = 5
b. Number of days' sales in inventory
Assuming that 365 days in a year.
The number of days' sales in inventory is calculated by dividing the number of days in a year by the Inventory turnover
Number of days' sales = 365 days / (Inventory turnover)
Number of days' sales = 365 days / 4.999 = 73.015
Therefore we can conclude that the Inventory turnover is 5 and the Number of days' sales is 73 days.
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