Answers
The area hexagon using Lin's and Andre's method is:
By Lin's method = 93.48inch^2
By Andre's method = 93.53 inch^2
What is Mensuration ?
The field of mathematics known as mensuration explores how to measure geometric objects and their attributes, such as length, volume, shape, surface area, lateral surface area, etc.
By Lin's method
He parted the hexagon into six equilateral triangle
So, area of equilateral triangle = √3/4 × (side)^2
Since the given side = 6inch
Therefore,
area of equilateral triangle = √3/4 × (6)^2
=√3/4 × 36
= √3 x 9
= 1.732 x 9
= 15.58inch^2
The area of hexagon will be = 15.58 x 6
= 93.48inch^2
Now, By Andre's method
he parted two triangle and one rectangle
The triangle has two equal side that means its an isosceles triangle
Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]
given,
base = 10.4 inch
side = 6 inch
Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]
= ½[√(6^2 - 10.4^2/4) × 10.4]
= ½[√(36 - 108.16 /4) ×10.4]
= ½[√(36 - 27.04) × 10.4]
= ½[√(8.96) × 10.4]
= ½[2.99 × 10.4]
= 15.56inch^2
for two triangles the area will be = 15.56 x 2
= 31.13 inch^2
Now, area of rectangle = length x width
where,
Length = 10.4 inch
Width = 6 inch
So,
area of rectangle = 10.4 x 6
= 62.4 inch^2
Then, The area of hexagon will be = area of rectangle + area of two triangle
= 62.4 inch^2 + 31.13 inch^2
= 93.53 inch^2
Hence, by both methods the area from Lin's method = 93.49 inch^2
and by Andre's method = 93.53 inch^2
To learn more about Mensuration click on the link
https://brainly.com/question/25292087
#SPJ9
Related Questions
Help quick!! I need someone to answer this for me.
Answers
Amari bought three chicken wings for $4.80 if Morris spent $27.20 how many chicken wings did she buy
Answers
Answer:
24 wings
Step-by-step explanation:
Answer:
17 wings
Step-by-step explanation:
1. first we multiply 3 by 27.20 you get 81.6
2. then we divide 81.6 by 4.80 and we get 17
17 wings
tell wheter the lines through the given points are parallel, perpendicular or neither.
a. Line 1: (2,-3), (-4, -6)
Line 2: (-3, 2), (2, -8)
b. Line 1: (-4, -5), (4, 1)
Line 2: ( 6, 10), (-3, -2)
c. Line 1: (0, -4), (-2, -8)
Line 2: (-1, 5), (1, 9)
Help I need this by tomorrow :c
Answers
Answer:
a. Perpendicular
Make sure to read the step-by-step explanation to figure out how to do the other 2.
Step-by-step explanation:
I will not be providing answers to all three, but I will answer the first one (this is, so you don't depend on people to solve this for you).
Parallel lines have one thing in common, their slope. Two lines that have the same slope never intersect because they are both facing the same direction and moving the same distance. So, you can find the slope of two lines by using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{-6-(-3)}{-4-2}=\frac{-3}{-6}=\frac{1}{2}\\m_2=\frac{-8-2}{2-(-3)}=\frac{-10}{5}=-2[/tex]
This is evidence that the two lines are not parallel. But, by finding the slope, we can conclude that it is perpendicular.
This brings me to how to identify perpendicular lines. The slope of perpendicular lines is negative reciprocals. A reciprocal is just a fraction that is flipped, and it's negative. For example, [tex]\frac{-2}{3}[/tex]'s negative reciprocal would be [tex]\frac{3}{2}[/tex]. The negative of -2/3 is a positive, and the reciprocal of 2/3 is 3/2. So, the negative reciprocal is 3/2.
How does this apply to what I said earlier?Well, [tex]-2[/tex] is the negative reciprocal of [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2, and the negative of 2 is -2. So, simply, lines 1 and 2 are perpendicular.
Use this method to solve the other questions. If they don't have the same slope and aren't negative reciprocals, then they are neither.
Answer:
Step-by-step explanation:
To solve this problem, we use the following formula:
[tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
a) (2,-3) (-4,-6)
[tex]x_1=2\ \ \ \ x_2=-4\ \ \ \ y_1=-3\ \ \ \ y_2=-6[/tex]
[tex]\displaystyle\\\frac{x-2}{-4-2} =\frac{y-(-3)}{-6-(-3)} \\\\\frac{x-2}{-6}=\frac{y+3}{-6+3} \\\\\frac{x-2}{-6} =\frac{y+3}{-3}[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{x-2}{2}=y+3\\\\0.5x-1=y+3\\\\0.5x-1-3=y+3-3\\\\0.5x-4=y\\[/tex]
⇔ Line 1: y=0.5x-4 m₁=0.5
(-3,2) (2,-8)
[tex]\displaystyle\\\frac{x-(-3)}{2-(-3)}=\frac{y-2}{-8-2} \\\\\frac{x+3}{2+3} =\frac{y-2}{-10} \\\\\frac{x+3}{5} =\frac{y-2}{-10} \\\\[/tex]
Multiply both parts of the equation by -10:
[tex]-2(x+3)=y-2\\-2x-6=y-2\\-2x-6+2=y-2+2\\-2x-4=y[/tex]
⇔ Line:y=-2x-4 m₂=-2
[tex]\displaystyle\\m_1=-\frac{1}{m_2}[/tex]
⇒ The given lines are perpendicular
b)
(-4,-5) (4,1)
[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+4}{4+4}=\frac{y+5}{1+5} \\\\\frac{x+4}{8} =\frac{y+5}{6} \\[/tex]
Multiply both parts of the equation by 6:
[tex]\displaystyle\\\frac{6(x+4)}{8} =y+5\\\\\frac{3}{4} x+3=y+5\\\\\frac{3}{4} x+3-5=y+5-5\\\\\frac{3}{4} x-2=y\\[/tex]
⇔ Line 1: y=(3/4)x-2 m=3/4
(6,10) (-3,-2)
[tex]\displaystyle\\\frac{x-6}{-3-6} =\frac{y-10}{-2-10} \\\\\frac{x-6}{-9} =\frac{y-10}{-12} \\\\[/tex]
Multiply both parts of the equation by -12:
[tex]\displaystyle\\\frac{-12(x-6)}{-9} =y-10\\\\\frac{4}{3}x-8=y-10 \\\\\frac{4}{3}x-8+10=y-10+10\\\\\frac{4}{3}x+2=y[/tex]
⇔ Line 2: y=(4/3)x+2 m=4/3
⇒ The given lines are neither perpendicular and neither parallel
c)
(0,-4) (-2,-8)
[tex]\displaystyle\\\frac{x-0}{-2-0} =\frac{y-(-4)}{-8-(-4)} \\\frac{x}{-2}=\frac{y+4}{-8+4} \\\\\frac{x}{-2}=\frac{y+4}{-4}[/tex]
Multiply both parts of the equation by -4:
[tex]2x=y+4\\2x-4=y+4-4\\2x-4=y[/tex]
⇔ Line 1: y=2x-4 m₁=2
(-1,5) (1,9)
[tex]\displaystyle\\\frac{x-(-1)}{1-(-1)} =\frac{y-5}{9-5} \\\\\frac{x+1}{1+1} =\frac{y-5}{4}\\\\\frac{x+1}{2} } =\frac{y-5}{4} \\[/tex]
Multiply both parts of the equation by 4:
[tex]2(x+1)=y-5\\2x+2=y-5\\2x+2+5=y-5+5\\2x+7=y[/tex]
⇔ Line 2: y=2x+7 m₂=2
m₁=m₂
⇒ The given lines are parallel
HELP ME I DONT UNDERSTAND THIS
Answers
Answer:
[tex]4r - 9s = k \\ ➪4r = 9s + k \\➪ r = \frac{9s + k}{4} [/tex]
Hope it helps
An angle measures 27.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answers
Answer:
∠1 = 103.9° ; ∠2 = 27.8°
Step-by-step explanation:
Supplementary angles = 180°
So, Let the angles be 'x'
Then, x + x -27.8° = 180°
2x - 27.8° = 180°
2x = 180° + 27.8°
2x = 207.8°
x = 207.8°/2
x = 103.9°
Therefore ∠1 = 103.9° ; ∠2 = 27.8°
I hope the answer is correct and has helped you!!!
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given equation.
5x+2y=10 and passes through (-6, 7)
Answers
y = -5/2x-8 is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.
Given that, the line 5x+2y = 10 passes through the point (-6,7) and is parallel to the given equation. Now, we have to write an equation in the slope-intercept form.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as: y = mx + b.
where, m is the slope of the line and b is the y-intercept of the line.
Let's proceed to find the equation.
5x+2y = 10
2y = -5x+10
y = -5/2x+10/2
y = -5/2x+5
Now, comparing with y = mx+b (slope-intercept form)
m = -5/2 and b = 5
As the two lines are parallel with each other then the slope of other line will also be same as m = -5/2
Now, the line passing through the point (-6,7)
⇒ x₁ = -6 and y₁ = 7
y-y₁ = m(x-x₁) ..........(1)
putting values in equation (1), we get
y-7 = -5/2(x-(-6))
⇒ y-7 = -5/2(x+6)
⇒ y = -5/2x-15+7
⇒ y = -5/2x-8
This is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.
Hence, y = -5/2x-8 is the required answer.
Learn more in depth about slope-intercept form at https://brainly.com/question/1884491
#SPJ1
Which of the following are rational numbers?
5.48
78.541
97
42.111...
Answers
Answer:
5.48, 78.541 and 97
Step-by-step explanation:
A rational number by definition refers to a number that is in the form of k/m and in which k and m are integers and m is not equal to 0.
Let me give you some examples:
1/32/41/59/3From our question,
5.48 = 137/25 hence rational number78.541 = 78541/1000; rational 97 = 97/1; rational 42.111..... = 4211111*/100000: irrational number. It is recurring hence not a rational number.Therefore 5.48, 78.541 and 97 are rational numbers
21. If x: y = 3: 4, find (3x + 4y): (5x + 6y).
Answers
Correct option is B)
Put x=3y=4
(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)
=(9+16):(15+24)
=25:39
PLS Heeeeeeelp!!!!!!!!!!
Answers
Answer 9 3/7
Step-by-step explanation:
[tex] \frac{30}{7} \times \frac{11}{5} \\ = \frac{330}{35} \\ = 9 \frac{15}{35} [/tex]
SIMPLIFIED WE GET:
[tex]9 \frac{3}{7} [/tex]
THE LAST OPTION IS THE ANSWER
Lisa walked 10,560 feet in 30 minutes. She walked at a constant rate.
At what rate did Lisa walk in miles per hour
Answers
convert feet to miles;
10,560 = 2 miles
30 minutes to miles;
2; therefore,
in 1hr she walked 4 miles
4 miles/hour
Answer:
Step-by-step explanation:
(EASY POINTS)
Solve for x in this figure.
x=
Answers
Answer:
x = 132°
Step-by-step explanation:
Sum of interior angles = (n - 2) x 180, where n is number of sides of the polygon.
Sum = (6 - 2) x 180 = 720°
sum = 160 +75 + 132 + 113 + 108 + x
sum = 588 + x
720 = 588 + x
x = 720 - 588
x = 132°
:)
Simplify the exponential expression (2x^2y^4)^3
Answers
Answer:
8x6y12
Step-by-step explanation:
I need help. What are the answers????
Answers
Answer:
5) a) x=55
Step-by-step explanation:
x=55
2x + 15 = 110 + 15
=125
Find the midpoint of each line segment
Answers
1) (4, 8)
2) (4, 8)
The midpoints are already given to you.
Answers:
(-1, 26) for problem 1(14, 12) for problem 2=======================================================
Explanation:
A = (9, -10)
B = (4,8)
C = (x,y)
A and C are the endpoints. B is the midpoint of segment AC.
The x coordinates of A and C are 9 and x respectively. Add them up and divide in half to get (9+x)/2. This is set equal to the x coordinate of point B and we solve for x.
(9+x)/2 = 4
9+x = 2*4
9+x = 8
x = 8-9
x = -1
The x coordinate of point C is -1.
Use the same idea for the y coordinates.
(-10+y)/2 = 8
-10+y = 2*8
-10+y = 16
y = 16+10
y = 26
Point C is located at (-1, 26)
The midpoint between (9, -10) and (-1, 26) is (4, 8)
Use the midpoint formula to confirm this.
------------------------
The steps for the second problem are going to follow the same outline.
A = (-6,4)
B = (4,8)
C = (x,y)
(-6+x)/2 = 4 solves to x = 14
(4+y)/2 = 8 solves to y = 12
Point C is located at (14, 12)
The midpoint between (-6, 4) and (14, 12) is (4, 8)
If T is the midpoint of SU,find x. ( ST=14x-6 and TU= 12x+5). What is the value of x?
Answers
the numerical value of x in fraction and decimal form are 11/2 and 5.5 respectively.
What is the numerical values of x?A midpoint is simply a point that divides a line segment into two equal halves.
Given the data in the question;
T is the midpoint of SUSegment ST = 14x - 6Segment TU = 12x + 5Numerical value of x = ?Since that T is the midpoint of segment SU, segment ST and segment TU are two equal halves of of segment SU.
Segment ST = Segment TU
Plug in the given values and solve for x
14x - 6 = 12x + 5
14x - 12x = 5 + 6
2x = 11
x = 11/2
x = 5.5
Therefore, 11/2 or 5.5 is the numerical value of x.
Learn more about midpoint of line segment here: brainly.com/question/4747771
#SPJ1
Solve the simultaneous equations 3 x + 2 y = 7
2 x − 3 y = − 4
Pls pls pls help me
Answers
On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2 .
In the question,
it is given that the simultaneous equations are
3x+2y=7 ....(i)
and
2x-3y=-4 ...(ii)
to solve these equations ,
we multiply equation(i) with 2 and
multiply equation(ii) with 3 .
So , the equations become
6x+4y=14 ...(iii)
and
6x-9y=-12 ....(iv)
we subtract equation (iv) from (iii) ,
So,
(6x+4y)-(6x-9y)=14-(-12)
Solving further ,
6x+4y-6x+9y = 14+12
4y+9y = 26
13y = 26
y = 26/13
y = 2
Substituting the value of y as 2 in equation (iii) , we get
6x+4(2) = 14
6x + 8 = 14
6x = 14-8
6x = 6
x=6/6
x=1
hence x=1 and y=2 .
Therefore , On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2 .
Learn more about Equations here
https://brainly.com/question/16848868
#SPJ1
The black triangle in the first quadrant is the original figure. Label each other triangle with its
transformation.
A. Translation of 6 to the left
B. Translation of 6 to the left and down 4
C. X-axis reflection
D. Y-axis reflection
E. Translation of 3 to the left and down 6
Answers
Also matching letter to triangle color
A green
B purple
C red
D navy blue
E light blue
benjamin wrote: -20+4x2+7-35=-19 where can he place the parentheses to make this statement true
Answers
-20+4(2+7)-35=-19
Step by step
-20+4(2+7)-35=-19
-20+4*9-35=-19
-20+36-35=-19
16-35=-19
-19=-19
What is the least common multiple of 8, 11, and 20?
PL help
Answers
Answer: 40
Step-by-step explanation:
The smallest number that all three numbers go into evenly is 40.
Therefore the LCM of 8, 11, and 20 is 40.
Answer:
440
Step-by-step explanation:
To find the Least common multiple (L.C.M) of 8, 11 and 20, it means that:
you list the first several multiples of each number, look for multiples common to both lists, Look for the smallest number common in both sides, the number is the LCM you are looking for.8 = 2,2,2
11 = 1, 11
20= 2,2,5
LCM of 8,11,20 = 2× 2 × 2 × 11 × 5
= 440
what is the value of cos 360
Answers
A bowl is used to serve punch for a party.
Which figure would be best to use to estimate the volume of the punch bowl?
C
Answers
Semicircle is the best figure to use to estimate the volume of the punch bowl.
What is meant by volume?Every three-dimensional object requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object within the boundaries of three-dimensional space. It is also known as the object's capacity. The liquid state has a definite volume but no definite shape. A solid state has a definite volume and a definite shape. Even if the containers are changed, the solid's shape and volume remain constant. Volume is a measurement of an object's capacity. For example, the volume of a cup is 100 ml if it can hold 100 ml of water up to the brim.To learn more about volume, refer to:
https://brainly.com/question/463363
#SPJ13
Please answer the two questions in the photo ( will mark brainliest if correct )
Answers
Answer: The rhombus below has two lines of symmetry, and the shape below has two lines of symmetry.
Step-by-step explanation:
Symmetry is when we split an object in half, in which both sides are equivalent. This definition must explain how the rhombus was most plausibly split, as well as the letter "H".
UGH I HATE MATH HELP
Answers
Hello!
What is the slope-intercept form:
[tex]y = mx + b[/tex]
m: is the slope[tex]m = \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-4}{0--2} =\dfrac{-5}{2}[/tex]
⇒ where (x₂,y₂) and (x₁,y₁) are random points on the line
b: y-intercept or the point that has an x-coordinate value of '0'⇒ thus our y-intercept is '-1'
Thus our line's equation in slope-intercept form:
[tex]y= -\dfrac{5}{2}x -1[/tex]
Hope that helps!
Given: -3(4x + 1) = 21
Prove: x = -2
Answers
Answer:
-3(4x + 1) = 21 given
4x + 1 = -7 Division Property of Equality
4x = -8 Subtraction Property of Equality
x = -2 Division Property of Equality
Answer:
see explanation
Step-by-step explanation:
prove by solving the equation
- 3(4x + 1) = 21 ( divide both sides by - 3 )
4x + 1 = - 7 ( subtract 1 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
thus solution is x = - 2
-3(3-8j) answer pls i need to make up my grade , what’s the answer?
Answers
Answer: if the j is supposed to be there, the answer is -9+24j. if the j is not there then just -9+24.
Step-by-step explanation: we distribute the -3 to the 3 and the -8. (-3x3=-9) and (-3x-8=24). when you multiply for divide by a single negative it is negative. when there are two negatives the answer will come out positive.
Which graph represents y=3√x+6-3?
Answers
The graph shown below represents the equation y =[tex]3\sqrt{x+6} -3[/tex]
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.
To learn more about coordinate plane visit :
brainly.com/question/13611766
#SPJ9
The volume of this cylinder is 6480π cm3.
Find the length of the radius,
The sides are equal to 180cm.
Answers
Answer:
The length of the radius is 10.7cm
Step-by-step explanation:
[tex]v = \pi {r}^{2} h[/tex]
6480=(22r*180)/7
6480*7=3960r
r=
[tex]r = \sqrt{45360 \div 396} [/tex]
radius=10.7The Hu family goes out for lunch, and the price of the meal is $59. The sales tax on the meal is 6%, and the family also leaves a 15% tip on the pre-tax amount. What is the total cost of the meal? The total cost of the meal is $ .
Answers
Answer:
$71.39
Step-by-step explanation:
So we can go ahead and add the extra money they paid (sales tax and tip).
15% + 6% = 21%
Then we can find 21% of 59 then that will be our extra money we're paying.
59 × 0.21 = 12.39
Then we add that amount to our 59 to get the total amount.
59 + 12.39 = 71.39
Write the negation of the following statement: No one has a pet water buffalo.
Answers
SOMEONE HAS A PET WATER BUFFALO.
THE GIVEN STATEMENT IS INDICATING THAT NOT EVEN ONE PERSON HAS A PET WATER BUFFALLO SO THE NEGATION SHOULD INDICATE THERE IS SOMEONE WHO DOES HAVE A PET WATER BUFALLO.
HOPE THIS HELPS
Given ΔRST is similar to ΔUVW with RT = 9 inches, UW = 5.4 inches, and RS = 6 inches.
Which is the length of UV¯¯¯¯¯¯¯¯
?
Responses
3.6 inches
3.6 inches
2.4 inches
Answers
Because triangle SRT and VUW are similar, all sides of triangle SRF are scaled up by an amount.
We calculate the scale factor : 9/5.4 = 5/3
-> The corresponding side of SR (UV) is scaled down 5/3 times from the length of SR
-> UV = 6 : 5/3 = 3.6 (inches).