Answers
Check the picture below.
let's recall that a circle has 360°, so that means every two radii coming from the center of the hexagon, will split those 360° in 6 even pieces, 360/6 = 60, namely those two radii make up a 60° central angle, as you see in the picture.
running a perpendicular from the center, we end up with a 30-60-90 triangle, as you see there, and thus we can use the 30-60-90 rule to get the length of "a".
now, keeping in mind that the perimeter of the polygon is simply 4+4+4+4+4+4 = 24.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}dp~~ \begin{cases} d=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ d=2\sqrt{3}\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(2\sqrt{3})(24)\implies A=24\sqrt{3}[/tex]
Related Questions
A bottlenose dolphin is 10 feet below sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation, y, after x seconds?
A.
y = 9x − 10
B.
y = -9x − 10
C.
y = 9x + 10
D.
y = -9x + 10
Answers
Diving means it is moving down so it would be a negative value.
You would need to multiply the rate by the number of seconds it dives, so you would have -9x for that part.
The dolphin started at 10 feet below sea level which would be written as -10.
To find the elevation you would need to add both parts together, which would give you:
y = -9x -10
The answer is B.
Answer:
the answer is b :)
Step-by-step explanation:
if f(×)=4×^2+1 and g(x)=×^2-5 find (f-g)(×)
Answers
Answer:
[tex]\large\boxed{(f-g)(x)=3x^2+6}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=4x^2+1,\ g(x)=x^2-5\\\\\text{Substitute:}\\\\(f-g)(x)=(4x^2+1)-(x^2-5)=4x^2+1-x^2-(-5)\\\\=4x^2+1-x^2+5\qquad\text{combine like terms}\\\\=(4x^2-x^2)+(1+5)=3x^2+6[/tex]
Estimate how many times larger 5x10^8 is than 24x10^6. A) 10 times larger
Answers
i believe its 20 times larger
Identify the vertex and the y-intercept of the graph of the function.
y = –0.25(x – 4)^2 2 – 2
vertex, (2, –4); y-intercept, –6
vertex, (–4, 0); y-intercept, –6
vertex, (4, –2); y-intercept, –6
vertex, (–2, 4); y-intercept, –6
Answers
Answer:
vertex, (4, –2); y-intercept, –6
Step-by-step explanation:
The equation is written in vertex form [tex]y = a(x-h)^2 + k[/tex] where the vertex is (h,k).
The vertex here is (4, -2). This means the solution is vertex, (4, –2); y-intercept, –6.
Answer:
vertex, (4, –2); y-intercept, –6.
Step-by-step explanation:
[tex]y=-0.25(x-4)^{2}-2[/tex]
[tex]y=-0.25(x^{2}-8x+16)-2[/tex]
[tex]y=-0.25x^{2}+2x-4-2[/tex]
[tex]y=-0.25x^{2}+2x-6[/tex]
the vertex is [tex](\frac{-b}{2a},y(\frac{-b}{2a}) )[/tex] where a=-0.25 and b=2. So,
[tex]\frac{-b}{2a}= \frac{-2}{-0.5}=4[/tex]
[tex]y(\frac{-b}{2a})=-0.25(4)^{2}+2(4)-6= -4+8-6=-2 [/tex]
Then, the vertex is (4,-2) and the intercept is y(0)= -0.25(0)+2(0)-6 = -6. So, the answer is the third option.
What is the term for a transformation that changes the size of a figure? rotation dilation reflection translation
Answers
The term that changes the size of a figure is called Dilation
Step-by-step explanation:A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A description of a dilation includes the scale factor and the center of the dilation. A dilation stretches or shrinks the original figure. Remember that to dilate something in the coordinate plane, multiply each coordinate by the scale factor
The term for a transformation that changes the size of a figure is dilation. Dilation involves stretching or shrinking a figure while maintaining its shape, using a scale factor greater than 1 for enlargement or between 0 and 1 for reduction.
The term for a transformation that changes the size of a figure is dilation.
Dilation is a geometric transformation that alters the size of a figure while keeping its shape intact. It involves stretching or shrinking the figure by a scale factor, which can either be greater than 1 (resulting in an enlargement) or between 0 and 1 (resulting in a reduction). In a dilation, all points of the original figure move away from or toward a fixed center called the "center of dilation," and their distances from the center are multiplied by the scale factor.
In contrast, other transformations have different effects:
Rotation involves turning a figure about a fixed point.
Reflection flips a figure over a line, creating a mirror image.
Translation shifts a figure in a specific direction without altering its size or shape.
So, the transformation that changes the size of a figure is dilation.
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A cube has a total surface area of 54 square inches.
What is the volume of the cube?
Answers
Answer:
V = 27 in³Step-by-step explanation:
The formula of a surface area of a cube:
[tex]S.A.=6a^2[/tex]
a - edge
We have S.A. = 54 in². Substitute:
[tex]6a^2=54[/tex] divide both sides by 6
[tex]a^2=9\to a=\sqrt9\\\\a=3\ in[/tex]
The formula of a volume of a cube:
[tex]V=a^3[/tex]
Substitute:
[tex]V=3^3=27\ in^3[/tex]
Which option below best describes why the domain of g(x) = 5–x is all real numbers but the range of g is not all real numbers? The domain of g is all real numbers because every real number . However, the range of g is not all real numbers because the
Answers
Answer:
The function is
g(x) = 5^(-x)
This question can be easily solved by using a graphing calculator
and plotting the graph of g(x)
In the image below, we can see that for each value of x , there is a corresponding value for g(x)
This means that the function does not have any discontinuities. Therefore,
The domain of g(x) is all real numbers (x ∈ R)
The range is related to the values that can be achieved by g(x),
Since it is a positive exponential function, all values will be g(x)>0
And the range would be (0,∞)
The domain of g(x) = 5-x is all real numbers because any real number can be an input, but the range is not all real numbers since the output is limited to values equal to or less than 5.
The function g(x) = 5-x has a domain of all real numbers because you can plug in any real number for x and it will result in a valid output. In contrast, the range of g is not all real numbers because the function g(x) can only produce certain values based on the operations involved. For instance, if x is a real number, the expression 5-x will always result in values less than or equal to 5, since you are subtracting a real number from 5. Thus, the output will never be greater than 5, so the range is all real numbers less than or equal to 5.
2. Which is a disadvantage of purchasing and owning a home?
A.An individual assumes all responsibility for maintenance and repair of owned property.
B.An individual has more freedom and choice for owned property than rented lodging.
C.An individual pays less in property taxes as a homeowner than a renter.
D.An individual builds equity by owning a home.
3. Use the table to answer the question.
The table shows the Final Settlement Statement for the purchase of a home.
How much cash did the borrower pay upfront?
A.$605.36
B.$3,491.04
C.$25,985.68
D.$95,505.36
4. Use the table to answer the question.
The table shows the Final Settlement Statement for the purchase of a home.
What amount goes in line 8?
A.$120,440.04
B.$121,491.04
C.$123,909.44
D.$125,882.47
Answers
2. Which is a disadvantage of purchasing and owning a home?
A. An individual assumes all responsibility for maintenance and repair of owned property.
3. How much cash did the borrower pay upfront?
D.$95,505.36 (500 + 94400 + 605.36)
4. What amount goes in line 8?
B.$121,491.04 (95505.36 + 25985.68)
The main disadvantage of home-ownership is that the individual is responsible for all maintenance and repair costs. As for the borrower's upfront payment and the amount in line 8 on the Final Settlement Statement, these would be specified in the settlement statement and cannot be precisely determined without such information.
Explanation:2. The main disadvantage of purchasing and owning a home is: A. An individual assumes all responsibility for maintenance and repair of owned property. This can be expensive and time-consuming, especially if the property is older or requires frequent repairs.
3 & 4. Without the table showing the Final Settlement Statement for the purchase of a home, it would be impossible to indicate precise answers to questions 3 and 4 related to upfront cash paid by the borrower, and the amount going in line 8. These values are calculated based on several variables, which should be tabulated clearly in the Final Settlement Statement.
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use 3.14 for pi to estimate the area of a circle if the diameter is given 28.2m round the answer to the nearest hundredth if necessary
Answers
Answer:
= 624.26 m²
Step-by-step explanation:
The area of a circle is given by the formula;
A = πr² ; where r is the radius
Radius = 1/2 diameter
= 3.14 × 14.1 ×14.1
= 624.26 m²
Final answer:
To estimate the area of a circle with a diameter of 28.2m, calculate the radius (14.1m), then use the formula A = πr² with pi as 3.14 to get an area of approximately 624.33 m² after rounding to the nearest hundredth.
Explanation:
To estimate the area of a circle with a given diameter of 28.2m, we first need to calculate the radius, which would be half of the diameter. Thus, the radius (r) is 28.2m / 2 = 14.1m.
Next, we use the formula for the area of a circle, which is A = πr². Plugging in the numbers, we get A = (3.14)×(14.1m)².
Carrying out the multiplication, we have A = 3.14 × 198.81m² = 624.3254m². We round this result to the nearest hundredth to get 624.33 m² as the estimated area of the circle using 3.14 for pi.
Write the equation for 5x + 2y = 3 in slope-intercept form.
y = 5/2 x - 3/5
y = -5/2x + 3/2
y = -2/5x +3/5
Answers
the answer is :
y = -5/2x + 3/2
Answer:
Choice b is correct.y = -5/2x+3/2 is the slope intercept form of given equation.
Step-by-step explanation:
We have given the equation:
5x + 2y = 3
We have to write the equation in slope intercept form.
The general slope intercept form of equation is :
y = mx+c
Where m = slope and c is the y-intercept.
We have given the expression:
5x + 2y = 3
2y = 3-5x
y = (3-5x)/2
y = 3/2-5/2x
y = -5/2x+3/2
y = -5/2x+3/2 is the slope intercept form of given equation.
Where m = -5/2 and y-intercept = 3/2
How do I work this problem out
Answers
Answer:
6^2 + 8^2 = c^2
36+ 64 = c^2
100 = c^2 | sqrt
10 = C
Let's Find Angles :
sin BCA = 6/10 = 0.6 => 37 degree
90 degree + 37 degree = 127 degree
Angle BAC = 180 degree - 127 degree = 53 degree
The side AC is 10
Step-by-step explanation:See the image attached
Last month, 17 people showed up to help a local charity. This month, 55 people volunteered. What is the percentage increase?
Answers
Step-by-step explanation:
The formula for percent change is
change/original.
So let's subtract 17 from 55 to find the change. 55-17=38
This is the change. Now we divide it by the original, 17.
38/17=2.235294
We're not done yet! We have to move the decimal point over to the right 2 spaces to make it a percentage. So, the percentage increase is
about 223.53 percent
Find the diameter of a circle with an area of 380.13m^2
Answers
Answer:
22
Step-by-step explanation:
Divide the area (in square units) by Pi (approximately 3.14159).
Example: 380.13/3.14 = 121.06
Then square the answer.
121.06 squared = 11.0
That answer is the radius, double that to get the diameter.
11.0 * 2 = 22
Final answer:
To calculate the diameter of a circle with an area of 380.13 m², solve for the radius using the formula r = √(A/π) and then double that value to find the diameter, resulting in a diameter of approximately 22.00 meters.
Explanation:
To find the diameter of a circle with a given area, we start with the formula for the area of a circle, which is A = πr², where A is the area, π (Pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. Given the area A = 380.13 m², we can solve for the radius r by rearranging the area formula to r = √(A/π) and then calculating the diameter D by doubling the radius (D = 2r).
Step 1: Calculate the radius.
r = √(A/π) = √(380.13 m² / 3.14159) ≈ 11.00m
Step 2: Calculate the diameter.
D = 2r = 2 × 11.00m = 22.00m
Need help with my precal please!
Answers
Answer:
y = 3x - 1
Step-by-step explanation
We manipulate the scatter plot feature in Ms. Excel then we simply add the linear trend line displaying the equation on the chart.
The excel output is attached below.
The relation exhibited by the data set is y = 3x - 1; given the value of x, the value of y is obtained by multiplying x by 3 and subtracting 1 from the result.
Write 58% as a fraction in simplest form
Answers
Answer:
29/50
Step-by-step explanation:
58/100 simplified is 29/50
Write the expression: y divided by the quantity x minus 5.
HURRY PLEASE IM IN CLASS THANKS
Answers
Answer:
please mark me brainiliest
y/x-5
Step-by-step explanation:
Answer: y ÷ x -5
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
"y" is a variable that is divided by the quantity "x" (also a variable) minus 5 (subtraction).
Mathematically speaking:
y ÷ x -5
In conclusion, the expression is y ÷ x -5
Feel free to ask for more if needed or if you did not understand something.
HELP ASSAP WILL MARK BRAINIEST!!!!! Just need the slope
Answers
Answer:
1/4
Step-by-step explanation:
2/8 = 1/4
The line goes up 2 and over 8 repeatedly, so the slope is 2/8, which can be simplified to 1/4.
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carmen participated in a read-a-thon.MR.cole pledge $4.00 per book and gave carmen $44.00.How many books did carmen read
Answers
Answer:
11 books
Step-by-step explanation:
because if she gets $4 per book and gets $44 in total then that means she has read 11 books because 4 times 11 is 44.
maria earned $42 for 6 hours of work .how much will she get for 15 hours of work ?
Answers
Answer: 105
Step-by-step explanation:
6 hours
7 x 6 = 42
15 hours
7 x 15 = 105
Answer:
105
Step-by-step explanation:
If she works 7 days a week than you get 7 x 15 witch = 105
Which describes the relationship between 1 and 2
A. 1 and 2 are complementary angles
B. 1 and 2 are equivalent angles
C.1 and 2 are adjacent angles
D.1 and 2 are supplementary angles
Answers
C is the correct answer
1 and 2 are adjacent angles. (C)
four students each ate 1 1/2 cupcakes. How many cupcakes did they eat in all
Answers
Multiply the number of cupcakes each by the number of people:
1 1/2 x 4 = 6 total cupcakes.
4 * 1 1/2 = x
(4 * 1) + (4 * 1/2) = x
4 + 2 = x
6 = x
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(65 + (1/5 x5) +6) divided by 9
Answers
1/5x5=1,65+1+6=72, and 72÷9=8. The answers 8.
What would the answer be because I already tried everything and I just can’t get it
Answers
Answer:
e = 56
Step-by-step explanation:
Use cross multiplication.
28 * 14 = 7e
Simplify
392 = 7e
Divide each side by 7
e = 56.
Answer:
cross muiltiply the euqation
28 * 14 = 7e
e= 56
give thanks :D
Twelve of the fifty dogs in the show were some breed of terrier. What percent is this?
Answers
Answer:
That would be 24%.
x - y = 3 x + y = 5 Which of the following systems is equivalent to the given system? 2x - y = 18 and x + 2y = 10 4x - 3y = 18 and x + 2y = 10 2x - 3y = 3 and x + 2y = 5
Answers
The equivalent system to given equations is: 2x - y = 3 and x + 2y = 5. We assess this by finding the solution of the given system (x = 4, y =1) and verifying these values in all given options.
Explanation:The given system is: x - y = 3 and x + y = 5. To find an equivalent system, we need to find a system that has the same solution as the given one.
If we add these two equations, we have 2x = 8, so x = 4. If x = 4, we can put x = 4 into the second equation 4 + y = 5, hence y = 1.
Now we test these solutions in the given options. After testing, we find that the equivalent system is: 2x - y = 3 and x + 2y = 5.
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The average earning of a shop for first three weeks of a month are 2750 per week. If the earnings of next 2 weeks are 4750 rupees then find total earnings of the 5 weeks.
A. 3000 B. 17500
C. 17750 D. 13000
E. none
Answers
Answer:
D. 13000 is the correct option out of the choices!
The total earnings of the 5 weeks will be 13,000.
What is Addition?A process of combining two or more numbers is called addition.
We have to given that;
The average earning of a shop for first three weeks of a month are 2750 per week.
And, The earnings of next 2 weeks are 4750 rupees.
Now,
Since, The average earning of a shop for first three weeks of a month are 2750 per week.
Hence, The total earnings in first three weeks = 3 × 2750
= 8,250
And, The earnings of next 2 weeks are 4750 rupees.
Hence, The total earnings = 8250 + 4750
= 13,000
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Two numbers have a product of 12 but their sum is -7. What are the numbers?
Answers
Answer:
-4 and -3
Step-by-step explanation:
-4 + -3 = -7
-4 * -3 = 12
Negative times negative equals a positive.
Answer:
-3 and -4
Step-by-step explanation:
Two numbers have a product of 12 but their sum is -7
Answers are -3 and -4
Double check:
(-3) x (-4) = 12
and
(-3) + (-4) = -7
What is the measure of YOZ given that WX =YZ
Answers
Answer: The answer is B - 95.
Answer: A. [tex]=105^{\circ}[/tex]
Step-by-step explanation:
Given: Circle with center O , having two congruent arcs as :-
[tex]\overarc{WX}\cong\overarc{YZ}\\\\\angle{XOW}=105^{\circ}[/tex]
We know that " If two arcs of a circle are congruent then their corresponding central angles are congruent".
[tex]\angle{XOW}\cong\angle{YOZ}\\\\\Rightarrow\ \angle{YOZ}=105^{\circ}[/tex]
Hence, the measure of [tex]\angle{YOZ}=105^{\circ}[/tex].
What is the slope of the line represented by the equation
3
x
+
4
y
=8
Answers
Answer:
Step-by-step explanation:
3x + 4y = 8
4y = 8 - 3x
y = 2 - (3/4)x
So the slope of the given line is -(3/4).
Final answer:
The slope of the line represented by the equation 3x + 4y = 8 is -3/4. We found this by rearranging the equation into slope-intercept form, y = mx + b, and identifying the coefficient of x as the slope.
Explanation:
To find the slope of the line represented by the equation 3x + 4y = 8, we first need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m represents the slope of the line, and b represents the y-intercept. Let's solve for y:
3x + 4y = 84y = -3x + 8y = (-3/4)x + 2The slope-intercept form of the line is y = (-3/4)x + 2, so the slope is -3/4. This means for every increase of 1 on the horizontal axis (x), there is a decrease of 3/4 on the vertical axis (y).
WNCI is having a promotion in which every 42nd caller receives a free concert ticket to JAY-Z and every 72nd caller receives a backstage access pass. Which caller will be the first one to win both?
Answers
Answer:
504th caller
Step-by-step explanation:
To determine who would win both the free concert ticket AND the backstage access pass, we need to find the first number that is divisible by both 42 and 72 at the same time.
That's called the Least Common Multiple (LCM), and it can be found with this formula:
[tex]lcm(a,b) = (\frac{|a * b|}{gcd(a,b)} )[/tex]
Where gcd is the Greatest Common Divisor, meaning what's the greatest number that divides both numbers without any leftover.
In the case of 42 and 72, the GCD is 6.
So, let's take the formula again, punching in the numbers this time and solving it.
[tex]lcm(42,72) = (\frac{|42 * 72|}{6} ) = \frac{3024}{6} = 504[/tex]
And 504 does divide both 42 (result is 12) and 72 (result is 7).