EASY 5 POINTS!!!! A new park in the shape of a hexagon will have 66 sides of equal length. On a scale drawing, the coordinates of the vertices of the park are: (6.5,5)6.5,5, (18.5,0)18.5,0, (6.5,-5)6.5,-5,
(-6.5,-5)-6.5,-5, (-18.5,0)-18.5,0, and (-6.5,5)-6.5,5. How long is each side of the park?
Answers
To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.
The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.
The distance formula given two points is:
d^2 = (x2 – x1)^2 + (y^2 – y^1)^2
Now we calculate the distance between 2 points:
d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2
d^2 = 169
d = 13
Therefore the length of each side of the park is 13 units.
Answer:
13 units
To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.
Explanation:To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:
Take the coordinates of two adjacent vertices of the hexagon.Use the distance formula, which is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.Plug in the coordinates and calculate the distance.Repeat the process for different pairs of adjacent vertices to make sure all sides have the same length.By following these steps, you should be able to determine the length of each side of the hexagon.
Related Questions
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?
Answers
5.92 / 16 = 0.37 per oz.....37 cents per oz
Answer:
$,37 dollars per ounce of strawberries
Step-by-step explanation:
We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:
5,92/16= ,37
SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.
A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram?
Answers
Answer:
7
Step-by-step explanation:
find the equation of a line containing the given point and slope (10,5); m=9/20
Answers
Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
Answers
line l is the orange line, intersecting the positive x-axis and the positive y axis.
The angle with measure ∅ is the angle made by the line and the positive x-axis. It is the obtuse (>90° angle) shown in the picture.
the slope of the line l is tan∅
PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2
Answers
1.
the line of symmetry is x=2, means that the x coordinate of the vertex is x=2.
the point x=2 is the midpoint of the roots [tex]x_1[/tex] and [tex]x_2[/tex].
so
[tex] \frac{x_1+x_2}{2}=2 [/tex]
[tex]x_1+x_2=4[/tex]
Remark: in the x-axis, if c is the midpoint of a and b, then [tex]c= \frac{a+b}{2} [/tex]
2.
since [tex]x_1[/tex] and [tex]x_2[/tex] are roots
[tex]a(x_1)^{2} -8(x_1)-3=0[/tex] and [tex]a(x_2)^{2} -8(x_2)-3=0[/tex]
3.
equalizing:
[tex]a(x_1)^{2} -8(x_1)-3=a(x_2)^{2} -8(x_2)-3[/tex]
[tex]a(x_1)^{2} -8(x_1)=a(x_2)^{2} -8(x_2)[/tex]
[tex]a(x_1)^{2}-a(x_2)^{2} =8(x_1) -8(x_2)[/tex]
in the left side factorize a, in the left side factorize 8:
[tex]a[(x_1)^{2}-(x_2)^{2}] =8(x_1 -x_2)[/tex]
in the right side use the difference of squares formula:
[tex]a(x_1 -x_2)(x_1 +x_2) =8(x_1 -x_2)[/tex]
simplify by [tex](x_1 -x_2)[/tex]
[tex]a(x_1 +x_2) =8[/tex]
substitute [tex](x_1 +x_2)[/tex] with 4:
[tex]a*4 =8[/tex]
a=2
Answer: C)2
Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)
Answers
1 kg = 2.25 pounds
5*2.25 = 11.25 pounds
11.25/5 = 2.25 bags
so you would need 3 bags
at 5 lbs per bag.....2 full bags + 1.25 lbs in the other bag...so it would be 3 bags with 1 bag partially full or 2 bags, leaving out 1.25 lbs
What is the next number in the series? 71 62 53 44 35 ?
Answers
To further prove this;
71 --> 62.
-10 and + 1.
62 --> 53.
-10 and +1
and so on.
However, if that's a little too complicated, there's an alternate method.
All you have to do is subtract 9 from the current number.
To further prove this;
71 - 9 = 62
62 - 9 = 53
53 - 9 = 44
and so on.
So, let's subtract 9 from our most current number, 35.
35 - 9 = 26.
The upcoming number in your sequence is 26.
I hope this helps!
If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?
Answers
g(x) = f(-x); -x has been substituted in for x.
Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?
Answers
0.04f+.08e=800
However, e=2f so the above equation becomes:
0.04f+0.08(2f)=800
0.04f+0.16f=800
0.2f=800
f=$4000, since e=2f
e=$8000
So Susan invested $4000 at 4% and $8000 at 8%.
Final answer:
To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.
Explanation:
Susan has invested $x at 4% interest rate and $2x at 8% interest rate.
Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.
Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.
If p is a positive integer,then p(p+1)(p-1) is always divisible by?
Answers
I am not quite sure what the choices are, but the answer to that problem is:
If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.
The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.
For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.
And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.
Answer: From the choices, select the even number
Final answer:
If p is a positive integer, p(p+1)(p-1) is always divisible by 3.
Explanation:
If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.
This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.
In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.
The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8
Answers
xy = c, where c is a constant
when y = 40 and x = 5 -> c = 40*5 = 200
So xy = 200
Then, when x = 8, y = 200/8 = 25
Answer: 64
Step-by-step explanation:
i put it into math-way
Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°
Answers
[tex]u = \ \textless \ cos(45),sin(45)\ \textgreater \ [/tex]
In same way you can find component form of u+v
[tex]u+v = \ \textless \ 2cos(90), 2sin(90)\ \textgreater \ [/tex]
By property of vector subtraction:
v = (u+v) - u
[tex]v = \ \textless \ 2cos(90) - cos(45), 2sin(90) - sin(45)\ \textgreater \ [/tex]
[tex]v = \ \textless \ -\frac{\sqrt{2}}{2}, 2-\frac{\sqrt{2}}{2} \ \textgreater \ [/tex]
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
Answers
In this case, we can use the z statistic to find for the proportion of students who failed the exam. The formula for z score is given as:
t = (x – u) / s
where,
x = the sample score = 60
u = sample score mean = 82
s = standard deviation = 11
Substituting all given values into the equation:
t = (60 – 82) / 11
t = - 2
Based from the standard proportion distribution tables for z, this corresponds to:
P = 0.0228
This means that 2.28% of the students failed the exam or equivalent to:
failed students = (0.0228) * 85 = 1.938
approximately 2 students failed the exam
Answer:
2 students failed the exam
Step-by-step explanation:
Poisson suppose you have 5 cakes made ready to sell. what is the probability that you will sell out?
Answers
Assume further that the mean number of cakes sold per day is lambda.
Let k=5 = number of cakes sold during the day, then the Poisson pmf (probability mass distribution) is given by
P(k)=lambda^k*e^(-lambda)/k!
or
P(5)=lambda^5*e^(-lambda)/5!
=lambda^5*e^(-lambda)/120
If the average number of cakes sold is 4 per day, then
P(5)=4^5*e^(-4)/120
=0.156 is the probability of selling exactly 5 cakes.
The probability of selling 5 cakes or more (i.e. the sixth and subsequent customers will be told to come back the next day) is then
P(k>=5)=1-(P(k=0)+P(k=1)+P(k=2)+P(k=3)+P(k=4)
=1-(0.018316+0.073263+0.146525+0.195367+0.195367)
=0.371163
(for mean number of cakes sold per day = 4 )
53 ℃ below zero degrees
Answers
hope this helps
If f(x)=2x^2sqrt(x-2), complete the following statement f(6)
Answers
f(6) = 2(6^2) + 5 sqrt (6 - 2)
f(6) = 2(36) + 5 sqrt 4
f(6) = 72 + 5 * 2
f(6) = 72 + 10
f(6) = 82
The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
How to determine the function value?The function is given as:
[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]
Substitute 6 for x
[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]
Evaluate the difference
[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]
Evaluate the exponents
f(6)=2 * 36 + 5 * 2
Evaluate the sum of products
f(6) = 82
Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
Read more about functions at:
https://brainly.com/question/13136492
#SPJ2
Explain why we need more than one digit to express certain quantities
Answers
A new crew of painters can paint a small apartment in 12 hours. AN EXPERIENCED crew can paint the small apartment in 6 hours. How many hours does it take to paont the apartment when the two crews work together?
Answers
so.. in 1 hour, they have done 1/t of the whole work.
now, the new crew, working by itself can do the whole job in 12 hours, that means, in 1 hour, they have done only 1/12 of all the work.
the experienced crew, can do the job in 6 hours, that means in 1 hour, they have done 1/6 of all the work.
now, let's add their rates for 1 hour worth, to see what we get.
[tex]\bf \begin{array}{clclcllll} \cfrac{1}{12}&+&\cfrac{1}{6}&=&\cfrac{1}{t}\\ \uparrow &&\uparrow &&\uparrow &&\\ new\ crew&&experienced&&total\\ rate/hr&&rate/hr&&work/hr \end{array}\\\\ -------------------------------\\\\ \textit{let's multiply both sides by \underline{12t}, to toss away the denominators} \\\\\\ t+2t=12[/tex]
and pretty sure you know how much that is.
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
Answers
Answer: The required value is
[tex](f-g)(x)=x^2+8.[/tex]
Step-by-step explanation: The given functions are:
[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]
We are given to find the value of [tex](f-g)(x).[/tex]
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
[tex](s-t)(x)=s(x)-t(x).[/tex]
Therefore, we have
[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]
Thus, the required value is
[tex](f-g)(x)=x^2+8.[/tex]
Answer:
3x2 - 6 its the answer
What is the answer to this question?
Answers
Now that you know the formula, plug in and solve.
SA = 2(5)(8) + (5)^2
SA = 80 + 25
SA = 105
Now that you see that the question is asking for the answer in yards, you convert feet into yards.
3 feet = 1 yard.
105 is divided by 3 and you get 35.
The answer is 35 square yards.
Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056
Answers
Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?
Answers
the rate of the 5000ft is "10 feet per hour less than twice the first rate", so hmm twice the first rate is 2x, 10 less than that is 2x - 10.
so, the 5000ft were climbed in 5000/(2x-10)
the number of hours it lasted climbing? well, simply add them up.
Answer: The expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
Step-by-step explanation:
Since we have given that
Distance covered by mountaineer = 1000 feet
Speed at which he climbed = x feet per hour
Time taken by him would be
[tex]\dfrac{1000}{x}[/tex]
Additional distance covered by him = 5000 feet
Speed at which he climbed this time = 2x-10
So, Time taken is given by
[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]
Hence, the expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?
Answers
now, 4 years later in 2010, t = 4, there are 900 skaters, and the rate of decrease is 5%.
[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &900\\ I=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &4\\ \end{cases} \\\\\\ 900=I(1-0.05)^4\implies 900=I(0.95)^4\implies \cfrac{900}{0.95^4}=I \\\\\\ 1105\approx I\qquad thus\qquad \boxed{A=1105(0.95)^t}[/tex]
[tex]\bf \\\\ -------------------------------\\\\ \textit{now in 2006, 4 years earlier, year 0, t = 0} \\\\\\ A=1105(0.95)^0\implies A=1105\cdot 1\implies A=1105[/tex]
The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898
Answers
The probability that the mean leg length is less than 20 cm is practically 0.
Explanation:To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.
We can standardize the sample mean using the formula:
z = (x - μ) / (σ / sqrt(n))
Where:
z: the z-scorex: the value of the sample meanμ: the population meanσ: the population standard deviationn: the sample sizeSubstituting the given values:
z = (20 - 43.7) / (4.2 / sqrt(9))
z = -23.7 / (4.2 / 3)
z = -23.7 / 1.4
z ≈ -16.93
Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.
Please help quick !!
Answers
√3/2
√3=1.73205080757
1.73205080757/2
=0.866025404
1) IS CORRECT
Solve the rest using the same technique.
Hope this helps! A thanks/brainliest answer would be appreciated :)
How do you solve this
Answers
(5x^7y^2)/2
When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75
Answers
$29.75 divided by 5 books is $5.95, answer A.
36.75 - 5b = 7
-5b = 7 - 36.75
-5b = - 29.75
b = -29.75 / -5
b = 5.95 <=== 5.95 per book
What is the integral of 1/x?
Answers
Final answer:
The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.
Explanation:
The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:
[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]
The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.
The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?
Answers
Final answer: 2.77 oz
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.
Which equation can be used to solve for x, the increase in side length of the square in inches?
x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0
Answers
Then the enlarged side becomes (x+4) and the square = (x+4)²
The final area should be (x+4)² = 81
Let's expand:
x²+ 8x + 16 = 81
x² + 8x + 16 - 81 = 0
x² + 8x - 65 = 0
Answer:
[tex]x^2+8x-65=0[/tex]
Step-by-step explanation:
Side length of square = 4 inches
Let x be the increase in length
So, New length = x+4
Area of square = [tex]Side^2[/tex]
Area of enlarged square = [tex](x+4)^2[/tex]
Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]
Area of enlarged square = [tex]x^2+16+8x[/tex]
We are given that The final area needs to be 81 square inches.
So, [tex]x^2+16+8x=81[/tex]
[tex]x^2+16+8x-81=0[/tex]
[tex]x^2+8x-65=0[/tex]
So, Option C is true
Hence equation can be used to solve for x, the increase in side length of the square in inches is [tex]x^2+8x-65=0[/tex]