The diagram shows a hexagon-shaped tile used for flooring. Each hexagon tile has an area of 18/3 in 2 Find x.
Answers
Answer:
x = 12
Step-by-step explanation:
The hexagonal tile given here is made up of 6 triangles with equal bases and heights.
So, area of hexagonal tile will be equal to 6 times the area of one triangle.
Therefore,
[tex]18 \sqrt{3} = 6 \times \frac{1}{2} \times 2 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{x}{6} } \\ \\ 18 \sqrt{3} = 6 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{2x}{12} } \\ \\ \frac{18 \sqrt{3} }{6} = {( \sqrt{3)} }^{ \frac{x}{12} + \frac{2x}{12} } \\ \\ 3 \sqrt{3} = {( \sqrt{3)} }^{ \frac{3x}{12} } \\ \\ 3. {3}^{ \frac{1}{2} } = {3}^{ \frac{3x}{24} } \\ \\ {3}^{1 + \frac{1}{2} } = {3}^{ \frac{x}{8} } \\ \\ {3}^{ \frac{3}{2} } = {3}^{ \frac{x}{8} } \\ (bases \: are \: equal \: so \: exponents \: \\ will \: also \: be \: equal) \\ \implies \frac{3}{2} = \frac{x}{8} \\ \\ x = \frac{3 \times 8}{2} \\ \\ x = 3 \times 4 \\ \\ x = 12[/tex]
The area of the hexagon-shaped tile is the amount of space it occupies
The value of x is 2
The given parameters are:
[tex]\mathbf{Area = 18\sqrt 3}[/tex]
[tex]\mathbf{Base= (\sqrt 3)^{\frac x6}}[/tex]
[tex]\mathbf{Height = 2(\sqrt 3)^{\frac x{12}}}[/tex]
The shape is a regular hexagon (i.e. it has 6 equal sides).
So, the area of one of the segments is the total area divided by 6 and this is calculated as:
[tex]\mathbf{A(1) = \frac{18\sqrt 3}6}[/tex]
[tex]\mathbf{A(1) = 3\sqrt 3}[/tex]
A segment of the hexagon is a triangle, and the area of a triangle is:
[tex]\mathbf{Area = \frac 12 \times Base \times Height}[/tex]
So, we have:
[tex]\mathbf{3\sqrt 3= \frac 12 \times (\sqrt 3)^{\frac x6} \times 2(\sqrt 3)^{\frac{x}{12}}}[/tex]
This gives
[tex]\mathbf{3\sqrt 3= (\sqrt 3)^{\frac x6} \times \sqrt 3)^{\frac{x}{12}}}[/tex]
Apply law of indices
[tex]\mathbf{3\sqrt 3= (\sqrt 3)^{\frac x6 + \frac{x}{12}}}[/tex]
Add the exponents
[tex]\mathbf{3\sqrt 3= (\sqrt 3)^{\frac x4}}[/tex]
Express the equations as a base of 3
[tex]\mathbf{3^{\frac 32}= 3^{\frac x8}}[/tex]
Cancel out the base
[tex]\mathbf{\frac 32= \frac x8}[/tex]
Multiply through by 8
[tex]\mathbf{12= x}[/tex]
Rewrite as:
[tex]\mathbf{x = 12}[/tex]
Hence, the value of x is 2
Read more about areas at:
https://brainly.com/question/3365788
Related Questions
Multiply: (7y^3/5)(6x+5/21y)
Answers
Answer:
y²(6x+5)/15Step-by-step explanation:
We are to multiply the expression (7y^3/5)(6x+5/21y)
(7y^3/5)(6x+5/21y) = 7 * y * y * y/5 * 6x+5/21y
(7y^3/5)(6x+5/21y) = y²/5 * 6x+5/3
(7y^3/5)(6x+5/21y) = y²(6x+5)/5*3
(7y^3/5)(6x+5/21y) = y²(6x+5)/15
Hence the product is y²(6x+5)/15
Answer:
the correct answer would be d
Step-by-step explanation:
just took the test
Please help me with my homework this is 5th grade work btw
Answers
Answer:
21
Step-by-step explanation:
Can I have brainliest:)
Answer:
7 x 24
8 x 1
=
168/8= 21
The area of a regular hexagon inscribed in a circle with radius 2 is_____ . Round your answer to the nearest tenth.
Answers
Answer:
4
Step-by-step explanation:
Formula for area of hexagon is ((3*square-root 3)/2)*a^2.
−4x−24x+24=10(12−2x) explain how you sloved it...i rllly need this!!!!
Answers
Answer:
x=-12
Step-by-step explanation:
first collect all the like terms -28x + 24 = 120-20x
then move variables and constants to the correct side -28x + 20x = 120-24
collect like terms again -8x = 96
divide both side by -8 so -8x/-x n 96/-8 you get x=-12 bc -8 time -12 = 96
Answer:
x = -12
Step-by-step explanation:
First, combine like terms
[tex]-4x-24x+24 = 10(12-2x)\\-28x+24 = 10(12-2x)[/tex]
Then, use the distributive property on the right side
[tex]-28x + 24 = 120 - 20x[/tex]
Now, add 28x to both sides to get the Xs all together
[tex]24 = 120 + 8x[/tex]
Next, subtract 120 from both sides:
[tex]-96 = 8x[/tex]
divide both sides by 8:
[tex]-12 = x[/tex]
This means the answer is x = -12
1) A triangular prism has a base measuring 8 inches and a side measuring 5
inches. It has a depth of 3 inches. What is the volume?*
O
40 cubic inches
O 20 cubic inches
O 24 cubic inches
60 cubic inches
Answers
Answer:
24 cubic inches
Step-by-step explanation:
Whenever you are finding the volume you have to multiply by two plus a number times two. For example, since there is two depths, you have to multiply 3 by 2 plus the next number. Then, since there is two sides, you multiply 5 by 2 plus the next number. Finally, since there is only one base, you don't have to multiply by two.
(3×2)+(5×2)+8=24
Hope I explained well enough for you to understand.
Plz help me with this Im timed will mark as brainliest
Answers
Answer:
It seems like John is trying to find the mean, or average.
Green is 82
blue is 320
red is 4
Step-by-step explanation:
82 is the score John must get to have the average of 80
320 is the number you must divide by 4 to get 80
What are the solutions to the equation?
4x3 = 36x
Enter your answers in the boxes.
X=
or x =
or X
Answers
Step-by-step explanation:
4x³ = 36x
4x³ - 36x = 0
4x(x² - 9) = 0
4x(x + 3)(x - 3) = 0
Hence x = 0, x = -3 or x = 3.
Help me please i need help
Answers
Answer:
The table is proportional all throughout the numbers except for the ratio 6:16
The ratio 6:16 should be 6:18
hii pls help i’ll give you brainliest if you give a correct answer.
Answers
Answer:
1. 19.375 inches taller
2. 8.808 km farther
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.19.375
2.8.808
for the reasoning you just show that you subtracted
please help! i have 5 mins to turn in!!! thanks :)
Answers
Find the 99th term of the sequence: -56, -59, -62, -65.
Answers
Reasoning How would the graph of y = - 3x + 2 change if - 3 were replaced by 4? How would it change if were replaced by 0? Explain.
Answers
Answer:
Please check the attached diagram.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the rate of change or slopeb is the y-interceptAnalysis of y = - 3x + 2
Given the linear function
y = - 3x + 2
comparing with the slope-intercept form y = mx+b
The slope m = -3
The negative slope indicates that as the line on the line graph moves from left to right, the line falls.
In other words, the negative slope indicates that when x increases, y decrease, and vise versa.
Please check the attached graph of the function y = - 3x + 2. It is clear that when x increases, y decreases, hence the line falls when the graph of the line moves from left to right.
The red line graph represents the linear function y = - 3x + 2.
Analysis of y = 4x + 2 (When -3 is replaced by 4)
Now, when we replace -3 by 4 in the equation y = - 3x + 2, the equation becomes
y = 4x + 2
comparing with the slope-intercept form y = mx+b
The slope m = 4
The positive slope indicates that as the line on the line graph moves from left to right, the line rises.
In other words, the positive slope indicates that when x increases, y also increases, and vise versa.
Please check the attached graph of the function y = 4x + 2. It is clear that when x increases, y increases, hence the line rises when the graph of the line moves from left to right.
The blue line graph represents the linear function y = 4x + 2.
Analysis of y = 2 (When -3 is replaced by 0)
Given the equation
y = - 3x + 2
If we replace -3 by 0, the equation becomes
y = 0x + 2
y = 2
In other words, y = 2 represents a horizontal line because the horizontal line is of the form
y = k
where k is the y-intercept
here k = 2 is the y-intercept of the line y = 2.
Thus, slope zero means the value of y does not change no matter what we take or change the x-value.
The graph of line y = 2 is also attached which represents a horizontal line with slope 0 and y-intercept 2.
The green line graph represents the linear function y = 2.
Please check the graphs of all the lines.
will give brainlest!Solve the triangle, Round answers to the nearest tenth.
Answers
Answer:
C
Step-by-step explanation:
Answer:
Angle B should be 37°
Step-by-step explanation:
All i fugured out was the angle measure, which should be 90+53=143 and 180-143=37°, I’m just not sure what the other stuff means/needs.
A student conducts a survey on the eye color of a group of ninth-graders and then randomly selects a ninth-grader. Compare the experimental probability of choosing a ninth-grader with blue eyes to the experimental probability of choosing a ninth-grader with hazel eyes.
Eye Color Blue Brown Green Hazel
Number 37 62 13 15
Answers
Answer:
Hazel is 1 out of 8.46
Blue is 1 out of 3.43
Step-by-step explanation:
total number=37+62+13+15=127
Blue is 37 out of 127
Probability is 1 out of 3.43
Hazel is 15 of 127
Probability is 1 out of 8.46
answers for the 2 boxes :)
Answers
Step-by-step explanation:
Given
y = 2x + 1 .....i)
y = 3x +2 .....ii)
Putting equation II in equation i
3x + 2 = 2x + 1
3x - 2x = 1 - 2
x = -1
Now putting x = -1 in equation i
y = 2* (-1) + 1
= -2 + 1
= - 1
Therefore x = -1 and y = -1
Hope it will help :)
what is the square root of 49
Answers
Answer:
7
Step-by-step explanation:
√49 = 7
7² = 49
7 × 7 = 49
hope this helps...
The sum of the measures of three adjacent angles is 150' The measures of the angles are in the ratio of 1:2:3. What is the measure, in degrees of the
largest angle?
The measure of the largest angle is
degrees
Answers
Answer:
It is a 30, 60, 90 triangle.
Step-by-step explanation:
Hence, the measure of the largest angle is degrees is [tex]5[/tex] degree, [tex]10[/tex] degree and [tex]15[/tex] degree and the largest angle is [tex]15[/tex] degree.
What are the angles?
Angles are formed by two rays (or lines) that begin at the same point or share the same endpoint. The point at which the two rays meet (intersect) is called the vertex.
Here given that,
The sum of the measures of three adjacent angles is [tex]150[/tex] degree. The measures of the angles are in the ratio of [tex]1:2:3.[/tex]
Let one angle is [tex]x[/tex], second is [tex]2x[/tex] and the thirs one is [tex]3x[/tex].
As given that the sum of three angles is [tex]150[/tex] degree but we know that the sum of three angles is [tex]180[/tex] degree then,
[tex]x+2x+3x=180-150\\\\x+2x+3x=30\\\\6x=30\\\\x=\frac{30}{6}\\\\x=5[/tex]
when
[tex]x=5\\\\2x=2(5)\\\\2x=10[/tex]
when
[tex]x=5\\\\3x=3(5)\\\\3x=15[/tex]
Hence, the measure of the largest angle is degrees is [tex]5[/tex] degree, [tex]10[/tex] degree and [tex]15[/tex] degree and the largest angle is [tex]15[/tex] degree.
To know more about the angles
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One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?
Answers
Given :
One root of a third degree polynomial function f(x) is –5 + 2i.
To Find :
The number and nature of all roots for this function.
Solution :
We know, there are exactly three roots in any third degree polynomial.
Also, we know complex roots always comes in pair i.e. the other root is the conjugate of each other .
So, other root is , -5 - 2i .
Also, since complex roots come in conjugate pair. So, third root cannot be complex.
Therefore, 2 roots are complex and 1 is real.
Answer:
f(x) has two imaginary roots and one real root.
Step-by-step explanation:
B on edge.
The length of a triangle is 1 1/8 cm longer than the width. The perimeter is 13 1/4 cm. What are the width and length of this triangle?
Answers
Answer: See explanation
Step-by-step explanation:
I think your question should be a rectangle and not a triangle. A triangle has 3 sides and not 2 sides. In order to solve the question, I'm assuming that you wanted to write rectangle.
Note that the perimeter of a rectangle:.= 2(length + breadth)
Let the width be x
Since the length is 1 1/8 cm longer than the width, therefore, the length is 1 1/8 + x.
Therefore, perimeter = 2(1 1/8 + x + x) = 13 1/4
2(1 1/8 + 2x) = 13 1/4
2 2/8 + 4x = 13 1/4
2 1/4 + 4x = 13 1/4
4x = 13 1/4 - 2 1/4
4x = 11
x = 11/4
x = 2 3/4
Therefore, the width is 2 3/4cm
Length = 2 3/4 + 1 1/8
= 2 6/8 + 1 1/8
= 3 7/8cm
Whats the surface area?
Answers
Answer:
Total Area = 1070 m^2
Step-by-step explanation:
we have 4 different surfaces
the "ramp" the triangles (2) one for each sidethe bottom rectanglethe back rectangle1. the ramp
[tex]A_r = 15\times 30\\\\A_r = 450[/tex]
2. the triangles
since they are the same we just multiply by two
[tex]A_t = \frac{8\times 10}{2}\\\\A_t = \frac{80}{2}\\\\A_t = 40[/tex]
so the areas of the two triangles is
[tex]2A_t = 2(40)\\\\2A_t = 80[/tex]
3. the bottom rectangle
[tex]A_{bot} = 10\times 30\\\\A_{bot} = 300[/tex]
4. the back rectangle
[tex]A_{back} = 8\times 30\\\\A_{back} = 240[/tex]
now add them together
[tex]A_T=A_r+2A_t+A_{bot}+A_{back}\\\\A_T = 450+80+300+240\\\\A_T = 1070\: m^2[/tex]
You are trying to decide whether to use Uber or Lyft during a vacation. Uber charges $3 to pick up plus an additional $0.25 for each mile driven. Lyft does not charge to pick up but they have a rate of $0.75 for each mile driven.
Let x = the number of miles traveled and y = the total cost for the trip.
Will the cost of the two companies ever be the same? If so, at how many miles and what is that cost? If not, explain your reasoning. Show all work that leads to your answer.
Answers
Answer:
6 Miles and the cost is $4.50
Step-by-step explanation:
3+0.25=0.75x
3+0.50x
6=x
0.75x+?
0.75 x 6= 4.50
Laptops that sell for $660 are on sale with a percent discount of 7%. Find the sale price. Round your answer to the nearest cent, if necessary
Answers
Answer:
$613.80
Step-by-step explanation:
7% of 660 = 0.07 × 660 = 46.2
660 - 46.2 = 613.80
If 4 people want to share a 15-pound sack of rice equally by weight, how
many pounds of rice should each person get?
(PLS HURRY UP)
Answers
Solve each equation mentally: J + 7 = 13
Answers
Answer:
j=6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
13-7=6
Which of the following equations have exactly one solution?
Choose all answers that apply:
A
- 6x – 15 = 6x + 15
B
6x + 15 = 6x + 15
62 - 6 = 15.2 + 15
D
62 - 6 = 60 - 15
Answers
Answer:
The answer is B
Step-by-step explanation:
I got this answer from Khan Academy.
Hope this helps! :)
I need 4 1/2 teaspoons of butter but i only have 1/8 measuring cup how many 1/8 of butter do i need?
Answers
Answer:
2 1/2
Step-by-step explanation:
Answer:
36 cups
Step-by-step explanation:
You only have ⅛ measuring cup. Now, since you need 4½ teaspoons of butter, the number of ⅛ measuring cups needed to achieve that will be;
4½ ÷ ⅛ = 9/2 × 8/1 = 36 cups
Thus, you will need 36 number of ⅛ cups
Sara's family traveled 5 7 of the distance to her grandfather's house on Saturday. They traveled 1 2 of the remaining distance on Sunday. What fraction of the total distance to her grandfather's house was traveled on Sunday?
Answers
Answer:1/7
Step-by-step explanation:2/7 is the remainder of the leftover 5/7. Half of 2 is one, leaving u with 1/7.
Find the range of the function y=1/2x-3 if the domain is {-2, 0,4}
A. {-7, -3, 5}
B. {-4, -3, -1}
C. {1, -3, 4-11}
D. {-2, -3, -5}
Answers
Answer:
i think it is B
Step-by-step explanation: don't ask for an explanation cuz i wont give one
Ana walked 13/3 miles. How many whole miles did ana walk?What portion of an additional mile did she walk
Answers
Answer: 4 whole miles and 1/3 of an additional mile
Step-by-step explanation:
13/3=4 1/3
Answer:
4 whole miles and 1/3 of an additional mile
Step-by-step explanation:
13\3=4 1\3
Determine the inverse of the following.
y =- log(x - 1) + 2
Answers
Answer:
[tex]f^{-1}[/tex](x)=[tex]10^{-x+2}[/tex]+1
Step-by-step explanation:
