Find the area of a regular hexagon with the given measurement.
2 sqrt3 apothem
A =
...?
Answers
[tex]\sf tan(x^o)=\dfrac{Opposite}{Adjacent}[/tex]
[tex]\sf tan(30^o)=\dfrac{x}{2\sqrt{\sf 3}}[/tex]
We know that [tex]\sf tan(30^o)=\dfrac{1}{\sqrt{\sf 3}}[/tex]:
[tex]\sf \dfrac{1}{\sqrt{\sf 3}}=\dfrac{x}{2\sqrt{\sf 3}}[/tex]
Multiply [tex]\sf 2\sqrt{\sf 3}[/tex] to both sides:
[tex]\sf x=\dfrac{2\sqrt{\sf 3}}{\sqrt{\sf 3}}[/tex]
Simplify:
[tex]\sf x=2[/tex]
So half the side length of the hexagon is 2. That means the entire side length is 2 * 2 = 4.
Now use the formula:
[tex]\sf A=\dfrac{1}{2}ap[/tex]
This is used to calculate the area of any regular polygon. Where 'a' is the apothem and 'p' is the perimeter. The side length is 4, a hexagon has 6 sides, so the perimeter is 6 * 4 = 24. Plug in what we know:
[tex]\sf A=\dfrac{1}{2}(2\sqrt{\sf 3})(24)[/tex]
Simplify:
[tex]\boxed{\sf A=24\sqrt{\sf 3}}[/tex]
Answer:
41.57 unit²
Step-by-step explanation:
We know,
Area of a regular hexagon = [tex]3\times (sidelength)\times (apothem)[/tex].
The length of the apothem = [tex]2\sqrt{3}[/tex] units.
Since, we know, 'a regular hexagon splits into 6 identical equilateral triangles'.
As, the apothem of the regular hexagon = height of the equilateral triangle
So, height of the equilateral triangle = [tex]2\sqrt{3}[/tex] units.
As, in the equilateral triangle, 'One of the side length is the S, other will be [tex]\frac{S}{2}[/tex] and height is [tex]2\sqrt{3}[/tex] units'.
So, using Pythagoras Theorem, we have,
[tex]hypotenuse^{2}=perpendicular^{2}+base^{2}[/tex]
i.e. [tex]S^{2}=(\frac{S}{2})^{2}+(2\sqrt{3})^{2}[/tex]
i.e. [tex]S^{2}=\frac{S^2}{4}+12[/tex]
i.e. [tex]S^{2}-\frac{S^2}{4}=12[/tex]
i.e. [tex]\frac{3S^2}{4}=12[/tex]
i.e. [tex3S^2=48[/tex]
i.e. [texS^2=16[/tex]
i.e. S= 4 units
That is, the side length of the hexagon = 4 units.
Thus, the area of the hexagon is given by,
Area of a regular hexagon = [tex]3\times (4)\times (2sqrt{3})[/tex]
i.e. Area of a regular hexagon = [tex]12\times (2sqrt{3})[/tex]
i.e. Area of a regular hexagon = [tex]24sqrt{3}[/tex]
i.e. Area of a regular hexagon = 41.57 unit²
Hence, the area of the regular hexagon is 41.57 unit².
Related Questions
What is the inverse of the function f(x) = 4x + 8?
h(x) = x – 2
h(x) = x + 2
h(x) = x – 2
h(x) = x + 2
Answers
we have
[tex]f(x)=4x+8[/tex]
Step 1
Let
[tex]y=f(x)[/tex]
[tex]y=4x+8[/tex]
Step 2
exchanges the variable x for y and the variable y for x
[tex]x=4y+8[/tex]
Step 3
Isolate the variable y
[tex]4y=x-8[/tex]
[tex]y=\frac{1}{4}x-2[/tex]
Step 4
Let
[tex]h^{-1}(x)=y[/tex]
[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex] ------> the inverse function
therefore
the answer is
[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex]
The inverse of the function f(x) = 4x + 8 is h(x) = (x - 8) / 4.
Explanation:The inverse of the function f(x) = 4x + 8 can be found by switching the x and y variables and solving for y. So, we have:
x = 4y + 8
Now, we rearrange the equation to isolate y:
x - 8 = 4y
y = (x - 8) / 4
Therefore, the inverse function is h(x) = (x - 8) / 4.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation
(-2,3) ; y= 1/2x-1
A. y=1/2x+1
B. y=-2x-1
C. y=1/2x-1
D.y=-1/2x-1
Answers
to find the line that passes through the point (-2, 3), you'll want to use point-slope form: y - y1 = m(x - x1). your given point is (x1, y1) and your slope is 1/2, so plug all of your info in:
y - 3 = (1/2)(x + 2)
now, you must convert this to slope-intercept, y = mx + b. the first step is to distribute the 1/2 into your parentheses.
y - 3 = 1/2x + 1
y - 3 = 1/2x + 1 ... to isolate y, add 3
y = 1/2x + 4 should be your answer, but i see that it isn't an answer choice. it might be a glitch or a typing error in your program; i looked over my work for errors and i can't find one? i think you should ask your teacher for clarification if possible, and if not, i would choose A or C to submit your work to the best of your ability.
Math. Will Upvote. Please help
A function is a relation in which each element of the domain has exactly one element of the range assigned to it.
True Or False?
---
A function can only be represented by a straight line on the coordinate plane.
True Or False?
Answers
2) False. For example [tex]x^2[/tex] is a function, but is not linear. It is represented by a parabola.
explain how you can compare two different mixed numbers that have the same whole number part ?
Answers
The graph below shows the solution set of which inequality?
Answers
(-4)^2 >= 16
16 >=16
(4)^2 >= 16
16 >= 16
The answer is D
In the equation 6x – 2 = –4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain
Answers
Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.
Answer:
Spencer and Jeremiah both are correct
Step-by-step explanation:
We have given an equation 6x-2 = -4x+2
In this case spencer and jeremiah both are correct whether we first subtract 6x from both sides or we add 4x to both sides will not lead to any incorrection we will get the same result after simplification from both the methods
If we subtract 6x from both sides we will get 6x-6x-2= -4x-6x+2 after simplification we will get -2 = -10x+2
After further simplification we will get x=4/10=2/5
And if we add 4x on both sides we will get 6x+4x-2= -4x+4x+2 after simplification we will get 10x -2 =2 which eventually gives the result
x=4/10=2/5
Therefore, Both are correct
What is 16 divided by 4/9
Answers
We can re-write as: 16 * 9/4 = 4 * 9 = 36
So, your final answer is 36
Hope this helps!
The result of 16 times 9/4 is 36.
The original question appears to be asking how to divide 16 by the fraction 4/9, but it also contains an error in stating the mathematical expression. To divide 16 by 4/9, you need to multiply 16 by the reciprocal of 4/9, which is 9/4. Here's the step-by-step calculation:
Find the reciprocal of 4/9, which is 9/4. Reciprocal means exchanging the numerator and denominator.
Multiply 16 by the reciprocal (16 * 9/4).
Come up with the solution: (16 * 9) / 4 = 144 / 4 = 36.
Therefore, 16 divided by 4/9 equals 36.
which of the following is the sum of 16 4/7+3 3/7 reduced to lowest terms?
Answers
R=gs/g+s
solve for g
.
.
Answers
R. (g+s)=g.s
R.g+R.s=g.s
g.s-R.g=R.s
g (s-R)=R.s
g=R.s/(s-R)
Final answer:
To solve for g in the equation R = gs/(g+s), you can isolate g by multiplying both sides by (g+s) and rearranging the equation. The final solution is g = -Rs/(R - s).
Explanation:
To solve for g in the equation R = gs/(g+s), we can start by isolating g on one side of the equation. We can do this by multiplying both sides of the equation by (g+s), which cancels out the denominator on the right side:
R(g+s) = gs
Next, distribute the R to both terms on the left side of the equation:
Rg + Rs = gs
Now, we can rearrange the equation to isolate g on one side:
Rg - gs = -Rs
Factor out g on the left side:
g(R - s) = -Rs
Finally, divide both sides of the equation by (R - s) to solve for g:
g = -Rs/(R - s)
AB and BC are tangent to circle D. Find x if AB=3x+2 and BC=x+12. Find x.
Answers
so set the to lengths as equally and solve x from there
so that the answer is 3x+2=x+12
Answer:
The value for x will be 5.
Step-by-step explanation:
As the segment AB and BC are tangent to the circle D, it will have the same long. Due to segment longitude is written as function of the variable x, it requires to solve the following equation:
[tex]long(AB)= 3x+2= long(BC)= x+12[/tex]
[tex]3x+2=x+12[/tex]
[tex]3x-x= 12-2[/tex]
[tex]2x= 10[/tex]
[tex]x= 5[/tex]
If the probability of a win is 0.24 and the probability of a draw is 0.16, what is the probability of a loss
Answers
the probability of a loss is 0.6.
To find the probability of a loss, we first need to understand that in this context, the sum of all possible outcomes (win, draw, and loss) must equal 1.
Given:
- Probability of a win = 0.24
- Probability of a draw = 0.16
Let's denote the probability of a loss as [tex]\( P(\text{loss}) \).[/tex]
We know that:
[tex]\[ P(\text{win}) + P(\text{draw}) + P(\text{loss}) = 1 \][/tex]
So, to find [tex]\( P(\text{loss}) \),[/tex] we rearrange the equation:
[tex]\[ P(\text{loss}) = 1 - (P(\text{win}) + P(\text{draw})) \][/tex]
[tex]\[ P(\text{loss}) = 1 - (0.24 + 0.16) \][/tex]
[tex]\[ P(\text{loss}) = 1 - 0.4 \][/tex]
[tex]\[ P(\text{loss}) = 0.6 \][/tex]
Therefore, the probability of a loss is 0.6.
Which function is the inverse of f(x) = 2x + 3? f-1(x) = –2x + 3 f-1(x) = 2x + 3
Answers
The inverse function is [tex]f^{-1}(x) = \frac{x - 3}{2}[/tex].
To find the inverse of the function [tex]f(x) = 2x + 3[/tex], follow these steps:
Replace [tex]f(x)[/tex] with [tex]y[/tex]:
[tex]y = 2x + 3[/tex]
Interchange the variables [tex]x[/tex] and [tex]y[/tex]:
[tex]x = 2y + 3[/tex]
Solve for [tex]y[/tex]:
[tex]x - 3 = 2y[/tex]
[tex]y = \frac{x - 3}{2}[/tex]
Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac{x - 3}{2}[/tex]
For a car traveling at a speed of 50 miles per hour, the relationship between the distance traveled, d, and the time traveled, t, is described by the function d = 50t. Which statement is true?
Answers
Answer:
The distance traveled is based on the time traveled.
Step-by-step explanation:
I did this question.
The inverse of the given function is t(d) = d/50. The time taken to travel 180 miles is 3.6 hours.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
Here, we have,
It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.
It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).
To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.
Step 1 of 2
The given function is d(t)=50t.
Consider d(t) as d and t as t(d) and rewrite the equation.
The rewritten function is d=50 t(d)
Divide by 50 on both sides of the equation.
d/ 50 =50 t(d)/50
t(d) = d/50
Step 2 of 2
Substitute 180 for $t$ in the simplified expression and interpret the results.
t(d) = 180/50
= 3.6
The time taken to travel 180 miles is 3.6 hours.
Hence, The inverse of the given function is t(d) = d/50. The time taken to travel 180 miles is 3.6 hours.
To learn more on speed click:
brainly.com/question/28224010
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Which is the graph of f(x)=(x-1)(x+4)
Answers
The quadratic function is described by the standard equation [tex]\boxed{ \ f(x) = ax^2 + bx + c \ }.[/tex]
We have the quadratic function [tex]\boxed{ \ f(x) = (x - 1)(x + 4) \ }.[/tex]
Let us configure it to obtain a standard equation.
[tex]\boxed{f(x) = (x - 1)(x + 4)}[/tex]
[tex]\boxed{f(x) = x^2 + 4x - x - 4}[/tex]
Hence, we get [tex]\boxed{\boxed{ \ f(x) = x^2 + 3x - 4 \ }}.[/tex]
We identify the coefficients a, b, and c. For this equation, [tex]\boxed{ \ a = 1, b = 3, and \ c = -4 \ }[/tex]The parabola opens upward because a > 0, resulting in a vertex that is a minimum.The y-intercept of the quadratic function f(x) = x² + 3x - 4 is (0, c), i.e., the point [tex]\boxed{ \ (0, -4) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - 1)(x + 4) \ }[/tex] we get the x-intercepts at [tex]\boxed{ \ (-4, 0) \ and \ (1, 0) \ }[/tex]The axis of symmetry is [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex], i.e., [tex]\boxed{ \ x = h = -\frac{3}{2(1)} \rightarrow h = -\frac{3}{2} \ }[/tex]The minimum value is [tex]\boxed{ \ k = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Finding the minimum value is as follows:
[tex]\boxed{ \ k = f (- \frac{3}{2}) = (- \frac{3}{2})^2 + 3(- \frac{3}{2}) - 4 = -\frac{25}{4} = -6\frac{1}{4} \ }, or[/tex][tex]\boxed{ \ k = \frac{3^2 - 4(1)(-4)}{-4(1)} = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]Notes:
The graph of a quadratic function is called a parabola.When a > 0, the parabola opens upward, resulting in a vertex that is a minimum.When a < 0, the parabola opens downward, resulting in a vertex that is a maximum.The value c is the y-intercept of the graph, because a y-intercept is a point on the graph where x is zero. In other words, the graph passes through the point [tex]\boxed{ \ (0, c) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - x_1)(x - x_2) \ }[/tex] we get x-intercepts at [tex]\boxed{ \ (x_1, 0) \ and \ (x_2, 0) \ }.[/tex] An x-intercept represents a point on the graph where y is zero.The axis of symmetry represent the line that passes through the vertex of parabola with equation [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Learn moreA line that is not parallel to either the x-axis or the y-axis https://brainly.com/question/4691222 Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) https://brainly.com/question/1332667The midpoint https://brainly.com/question/3269852Keywords: which is the graph of f(x) = (x - 1)(x + 4), the x-intercept, quadratic function, a standard equation, the y-intercept, the axis of symmetry, the vertex, parabola, upward, downward
The graph of f(x) = (x-1)(x+4) is an upward-opening parabola with roots at x = 1 and x = -4. It should be plotted carefully, labeling and scaling the axes to show maximum and minimum values, and ensuring it passes through the roots with the proper shape.
Explanation:The graph of the function f(x) = (x-1)(x+4) can be determined by finding the roots and the shape of the curve. The roots of the function can be found when f(x) = 0, which occurs at x = 1 and x = -4. Therefore, these are the points at which the graph will intersect the x-axis. Since it's a quadratic function, its graph will be a parabola.
Additionally, because the coefficient of x² is positive, the parabola opens upwards. To graph this function accurately, one needs to plot the roots and then sketch the parabola, ensuring that it intersects these points and opens upwards. The vertex of the parabola can also be found by averaging the roots, which gives us the x-value of the vertex as (-4 + 1)/2 = -1.5, with the corresponding y-value obtained by evaluating f(x) at x = -1.5.
The resulting graph would start above the x-axis for x < -4, pass through the x-axis at x = -4, reach a vertex at x = -1.5, pass through the x-axis again at x = 1, and continue upwards for x > 1.
The graph should be accurately scaled and labeled with the function f(x) and the variable x, and include the maximum and minimum values on the axes based on the calculated points and the behavior of the quadratic function.
If max drives 25 miles per hour, how many minutes will it take him to drive 15 miles
Answers
Solve for x
6x + 3 - 1/2 x = -2x +5
Answers
6x + 3 - 1/2 x = -2x +5
6x - 1/2 x + 2x = 5 - 3
Now solve!
7 and 1/2 x = 2
x = 8
Hope this helps!
Find the equation of a line that satisfies the given conditions; x-intercept = 2, and y-intercept = -8
Answers
y-intercept = (0 , -8)
Slope of the line:
m = (-8 - 0) / (0 - 2)
m = 4
y = 4x - 8
The equation of a line with an x-intercept of 2 and a y-intercept of -8 is y = 4x - 8, which follows from applying the slope-intercept form and calculating the slope based on the intercepts.
To find the equation of a line with an x-intercept of 2 and a y-intercept of -8, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
We can determine the slope by recognizing that the line crosses the x-axis at (2,0) and the y-axis at (0,-8).
The slope m is the rise over the run, which in this case is (-8 - 0) / (0 - 2) = 4.
Therefore, the equation of the line is y = 4x - 8.
This equation satisfies the given conditions, as plugging in x = 0 gives the y-intercept of -8 and setting y to 0, and solving for x yields the x-intercept of 2.
Find the arc length of the curve y = ln (cos x) for 0 < x < pi/4
Answers
L = S(ln (cos x))'dx = S(-sinx / cosx)dx =
0 < x < pi/4 0 < x < pi/4
let be U=cosx dU= -sinxdx
so
S(-sinx / cosx)dx = SdU/U = LnU =0-1/2ln2-ln2 =1/2)Ln2
0 < x < pi/4 1>U>sqrt 2/2 1>U>sqrt 2/2
3x^2+5x-2=0 solve quadratic equation by factoring
Answers
trial and error
factor
(3x-2)(x+1) nope
(3x+2)(x-1) nope
(3x-1)(x+2) yes
(3x-1)(x+2)=0
set them to zero
3x-1=0
3x=1
x=1/3
x+2=0
x=-2
x=-2 and 1/3
Sams dog weighs 72 pounds. the vet suggests that for the dogs health tis weight should decrease by 12.5 percent. according to the vet what is a healthy weight for the dog?
Answers
It would be: x*87.5 / 100 = 72
x = 7200/87.5
x = 82.285
So, your final answer is 82.285
Which of the expressions are NOT polynomials? Check all that apply.
A. x^2-(square root of x)-3
B. 4 - 3x + 5x^6
C. 5x^1/2 + 4x^2
D. 14x^7
E. x^2-x-12/x+3
F. 8x^10 + 2x^5 ...?
Answers
A. x^2-(square root of x)-3
C. 5x^1/2 + 4x^2
E. x^2-x-12/x+3
(method: check polynomials lesson)
Answer:
A, C, E are not polynomials
Step-by-step explanation:
Identify the expressions that are not polynomials
A. x^2-(square root of x)-3
Polynomial cannot have a square root. so it is not polynomial
B. 4 - 3x + 5x^6
C. 5x^1/2 + 4x^2
A polynomial does not have fractional exponent
D. 14x^7
E. x^2-x-12/x+3
Polynomial cannot have x in the denominator
F. 8x^10 + 2x^5
the sum of 3 less than 5 times a number and tge number is increased by 9 is 24. what is the number ?
Answers
Quadrilateral ABCD is a square.
BC = 10
What is the length of AC?
Answers
So if BC is 10, then AC is also 10.
quadrilatarel squares all sides same
AB=BC=AC=AD=10
in which of the following are 1/2,5/6,and 5/8 arranged in order
Answers
1/12, 5/8, 5/6
The following is from greatest to least:
5/6, 5/8, 1/2
I hope this helps!
(Least to Greatest) 1/2,5/8,5/6
(Greatest to Least) 5/6,5/8,1/2
The ratio of areas between two similar triangles is 1:4. if one side of the smaller triangle is 2 units, find the measure of the corresponding side of the other triangle.
Answers
smaller side = 2
bigger side = 8 since 2/8 = 1/4
1/4 = 2/x
x=4*2=8
The rabbit population on a small island is observed to be given by the function P(t) = 130t − 0.4t^4 + 1200 where t is the time (in months) since observations of the island began.
(a) When is the maximum population attained (Round your answer to one decimal place.)
What is the maximum population? (Round your answer to the nearest whole number.)
(b) When does the rabbit population disappear from the island? (Round your answer to one decimal place.) ...?
Answers
The population is maximum when P'(t) = 0
P'(t) = 130 - 1.6t^3 = 0
1.6t^3 = 130
t^3 = 81.25
t = ∛81.25 = 4.3 months.
Maximum population P(t)max = 130(4.3) - 0.4(4.3)^4 + 1200 = 1,622
b.) The rabbit population will disappear when P(t) = 0
P(t) = 130t - 0.4t^4 + 1200 = 0
t ≈ 8.7 months
Answer:
Step-by-step explanation:
P(t)=130t -0.4t^4 +1200
The population will be max when first differential of p(t) =0
So p'(t) =130-1.6t^3=0
1.6t^3=130
t^3 =130/1.6
t^3 =81.25
t = cube root of 81.25
t =4.3 months
P(max) =130(4.3) -0.4(4.3)^4 +1200
= 559-136.75+1200
=1622
Population will disappear when p(t) =0
d(n)=3(−2)^ n−1
What is the 4th term in the sequence?
Answers
3.(-8)=-24
Answer: -24
Step-by-step explanation:
3(-2)^(4-1)=3*-8=-24
the jeans you would like to buy are on sale for $28. write an equation that will help you determine how much you save by getting the jeans on sale. p= regular price and c= cost savings
Answers
the answer would be p-28=c
Mark Me Brainliest !
Answer:
P - 28 = C
Step-by-step explanation:
P (Regular Price )
C ( Cost Savings )
You Noticed These Jeans You Liked.
You Couldn't Afford Them So You Waited Til The Price Dropped.
When Prices Drop Its Either 1 of 2 Reasons
Holiday Seasons Or Price Elasticity
So These Jeans Become $28 On The Market.
Simply You Figure Out How Much You'll Save By Comparing The Original Price To The Discounted Price.
There For Your Answer Will Be The Following :
Regular Price - Discounted Price = Cost Savings
If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.
Answers
= -7 / pi*5*8
= - 0.56 cm/min
Hope this helps
radius: r
diameter: e
time: t
[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]
S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e
dS/dt = 7cm^2 / min
de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] / [2pi*10cm] = 0.11 cm/min
What is f(x) = 2x2 + 28x – 5 written in vertex form?
Answers
Answer:
b
Step-by-step explanation: