Answers
Answer:
a) 120°
b) 16√3 ≈ 27.7 cm²
Step-by-step explanation:
a)Each exterior angle of a regular polygon measures 360° divided by the number of sides. For a hexagon, the exterior angle is 360°/6 = 60°. That means the adjacent interior angle is 180°-60° = 120°.
Angle ABC measures 120°.
__
b)The area of triangle ABC can be found using the formula ...
A = 1/2ab·sin(C) . . . . area of triangle with sides a, b, and angle C between them
A = 1/2(8 cm)(8 cm)sin(120°) = (32 cm²)(√3/2) = 16√3 cm²
The area of the triangle is 16√3 cm² ≈ 27.7 cm².
Answer:
∠ABC = 120°
ΔABC = 16√3 cm²
Step-by-step explanation:
Part (a)
Sum of interior angles of a regular polygon = (n - 2) × 180°
(where n is the number of sides)
⇒ Sum of interior angles of a regular hexagon = (6 - 2) × 180° = 720°
All the interior angles in a regular polygon are equal.
⇒ Interior angle = sum of interior angles ÷ number of sides
⇒ ∠ABC = 720° ÷ 6
⇒ ∠ABC = 120°
------------------------------------------------------------------------
Part (b)
Use the sine rule for area of a triangle:
[tex]\dfrac12ab \sin(C)[/tex]
(where a and b are the sides and C is the included angle)
Given:
a = 8b = 8C = ∠ABC = 120°Substituting values into the formula:
[tex]\implies \dfrac12\cdot 8 \cdot 8 \sin(120)=16\sqrt{3} \ \sf cm^2[/tex]
Related Questions
Decrease £15890.23 by 6.5%
Give your answer rounded to 2 DP.
Answers
Answer:
14,857.37
Step-by-step explanation:
15,890.23 - Percentage decrease =
15,890.23 - (6.5% × 15,890.23) =
15,890.23 - 6.5% × 15,890.23 =
(1 - 6.5%) × 15,890.23 =
(100% - 6.5%) × 15,890.23 =
93.5% × 15,890.23 =
93.5 ÷ 100 × 15,890.23 =
93.5 × 15,890.23 ÷ 100 =
1,485,736.505 ÷ 100 =
14,857.36505 ≈ 14,857.37
WILL GIVE BRAINLIEST, 5 STARS, THANKS!!!
Someone please factors these four problems all with step-by-step explanations!! I really don't understand how to do any of them, please help!!!
3x^2 + 10x+ 8
18x^2+39x-15
16x^2-25
6x^2-11x-10
PLEASEEEEE help me...!
Answers
Answer are in order:
[tex]\left(3x+4\right)\left(x+2\right)[/tex]
[tex]3\left(3x-1\right)\left(2x+5\right)[/tex]
[tex]\left(4x+5\right)\left(4x-5\right)[/tex]
[tex]\left(3x+2\right)\left(2x-5\right)[/tex]
Step-by-step explanation:
[tex]3x^2 + 10x+ 8[/tex]
[tex]\mathrm{Break\;the\;expression\;into \;groups}[/tex]
[tex]=\left(3x^2+4x\right)+\left(6x+8\right)[/tex]
[tex]\mathrm{Factor\;out\;x\;from\; 3x^2+4:}x(3x+4)[/tex]
[tex]\mathrm{Factor\;out\;2\;from\;6x+8:2(3x+4)}[/tex]
[tex]=x\left(3x+4\right)+2\left(3x+4\right)[/tex]
[tex]=\left(3x+4\right)\left(x+2\right)[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]18x^2+39x-15[/tex]
[tex]\mathrm{Factor\;out\;common\;term\;3:3(6x^2+13-5)}[/tex]
[tex]18x^2+39x-15[/tex]
[tex]\mathrm{Factor\;6x^2+13x-5:(3x-1)(2x+5)}[/tex]
[tex]=3\left(3x-1\right)\left(2x+5\right)[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]16x^2-25[/tex]
[tex]\mathrm{apply\;exponents\;rules}[/tex]
[tex]=\left(4x\right)^2-5^2[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\left(4x\right)^2-5^2=\left(4x+5\right)\left(4x-5\right)[/tex]
[tex]=\left(4x+5\right)\left(4x-5\right)[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[tex]6x^2-11x-10[/tex]
[tex]\mathrm{Break\;the\;expression\;into\;groups}[/tex]
[tex]=\left(6x^2+4x\right)+\left(-15x-10\right)[/tex]
[tex]\mathrm{Factor\;out\;2x\;from\;6x^2+4x:2x(3x+2)}[/tex]
[tex]\mathrm{Factor\;out\;-5\;from\;-15x-10:-5(3x+2)}[/tex]
[tex]=2x\left(3x+2\right)-5\left(3x+2\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}3x+2[/tex]
[tex]=\left(3x+2\right)\left(2x-5\right)[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~Learn with Lenvy~
Question
A gift box in the shape of a rectangular prism measures 8 inches by 8 inches by 10 inches. What is the least amount of wrapping paper needed to wrap the gift box?
The least amount of wrapping paper need is
square inches
Question
A gift box in the shape of a rectangular prism measures 8 inches by 8 inches by 10 inches. What is the least amount of wrapping paper needed to wrap the gift box?
The least amount of wrapping paper need is
square inches
Question
A gift box in the shape of a rectangular prism measures 8 inches by 8 inches by 10 inches. What is the least amount of wrapping paper needed to wrap the gift box?
The least amount of wrapping paper need is
square inches
Answers
Answer:
448
Step-by-step explanation:
[(8x8)4]+[(8x10)2]
448
A man deposit Rs 60000 in a bank and earns simple interest at the rate of 10% per year. After 4 months, he withdraws all the money. How much does he receive?
Answers
Answer:
62000
We know that:
[tex]P=60000\\ R=10\ percent \\ T=4[/tex]
Formulate and substitute:
[tex]Substitute[/tex] [tex]P=6000\\ R=10\ percent\\ T=4[/tex] [tex]into\ formula[/tex]
[tex]F=P+Prt[/tex]
[tex]F=60000+60000rt[/tex]
Calculate
[tex]\frac{60000\times(12+4\times0.1)}{12}[/tex]
Calculate the product or quotient
[tex]\frac{60000\times(12+0.4)}{12}[/tex]
Calculate the sum or difference
[tex]\frac{60000\times12.4}{12}[/tex]
Cross out the common factor
[tex]5000\times12.4[/tex]
Calculate the product or quotient
[tex]62000[/tex]
I hope this helps you
:)
Which of the following equations would produce a parabola? Check all that apply. –5x2 4x – 7y 14 = 0 –x2 6x y2 – 8 = 0 9x2 – 12xy 4y2 4x – y 5 = 0 12x 6y – 5y2 14 = 0 20x2 10xy – y2 3x – 6y 5 = 0.
Answers
Equations 1 and 4 would produce a parabola as they follow the general equation of a parabola.
Given equations are:
[tex]1)-5x^2+4x-7y+14 = 0\\\\2)-x^2 + 6x +y^2-8=0\\\\3)9x^2-12xy+4y^2+4x-y+5=0\\\\4)12x+6y-5y^2+14=0[/tex]
What is the general equation of a parabola?The general equation of a parabola
[tex]y = a(x^2+h^2-2xh)+k\\[/tex] or [tex]x= a(y^2+k^2-2yk)+h[/tex]
where h and k are vertices of the parabola.
Each equation follows the same pattern as the general equation of a parabola except the second and third equation
Therefore, equations 1 and 4 would produce a parabola as they follow the general equation of a parabola.
To get more about parabola visit:
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Answer:
A. –5x2 + 4x – 7y + 14 = 0
C. 9x2 – 12xy + 4y2 + 4x – y + 5 = 0
D. 12x + 6y – 5y2 + 14 = 0
I got it right on edge trust me
What is The longest line segment that can be drawn in a right rectangular prism that is 13 cm long 12 cm wide and 11 cm tall
Answers
Answer:
13√2
Step-by-step explanation:
The longest segment that can be drawn is a "diagonal" connecting two opposite "corners" at the top and bottom.This is similar to finding the length of a diagonal of a rectangle using the Pytagoren Theorem. However, this distance is in 3-space and is given by:d =√(152 + 82 + 72) = √338 = √(169 * 2) = 13√2 cm.
I need help with question 5 please help me
Answers
The radius of a circle is 6 kilometers. What is the circle's circumference?
Answers
Answer:
37.699km
Step-by-step explanation:
C=piDor2piR
D=2R(6×2)=12
C=22/7×12or2×22/7×6
ans=37.699
The population of Florida has increased, on average, at a rate of 8% per year since 1953. In 1993, the population of Florida was 13 million.
What was the population in 1953?
*show work & will give brainliest*
Answers
Answer:
598,402
Step-by-step explanation:
Let y = population at year x
x is the number of years since 1953, so for 1993, x = 40
a = population in 1953
y = a(1.08)^x
In 1993, the population is 13,000,000, so y = 13,000,0000 when x = 40.
13,000,000 = a(1.08)^40
13,000,000 = 21.7245a
a = 598,402
Answer: 598,402
James had $400 in his bank account. After
paying bills for 4 months, his balance is now
$160. What is his rate of change in dollars per month?
A.40
B.-40
C.60
D.-60
Answers
Answer:
C
Step-by-step explanation:
400-160=240
240/4=60
Solving proportions
Answers
Answer:
[tex]2x - 12 = 9x - 63 \\ \\ 63 - 12 = 9x - 2x \\ 51 = 7x \\ x = 7.2[/tex]
What is the value of the expression?
A++
1
A
mloo Loonloon
(B)
32
Answers
Step-by-step explanation:
1) Simplify the fractions....
\begin{gathered}2^{-3} = 1/8\\2^{-2} = 1/4\end{gathered}
2
−3
=1/8
2
−2
1/8 + 1/4 = 3/8
Hope its Helps you60 percent of $2million
Answers
Answer: $1,200,000
Step-by-step explanation:
50% would be 1 million, and 10% of 2 million would be 200,000, so if you add those two together, you get the total of $1,200,000
A polynomial function p (x) has degree 3, and its zeros are –3, 4, and 6. What do you think is the equation of p (x)? Do you think there could be more than one possibility? Explain
Answers
Answer:
[tex]\bold{Cubic \: eq {}^{n} = x {}^{3} - ( \alpha + \beta + \gamma )x + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - ( \alpha \beta \gamma )} \\ [/tex]
Sum of zeroes ,
[tex] \alpha + \beta + \gamma = ( - 3) + 4 + 6 = 7[/tex]
sum of product of zeroes taken two at a time ,
[tex] \alpha \beta + \beta \gamma + \gamma \alpha = ( - 3)(4) + (4)(6) + (6)( - 3) \\ = > - 12 + 24 - 18 \\ = > - 6[/tex]
product of zeroes ,
[tex] \alpha \beta \gamma = ( - 3)(4)(6) = - 72[/tex]
Substituting the values in the equation above , we get
[tex]\bold{x {}^{3} - ( \alpha + \beta + \gamma )x {}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - ( \alpha \beta \gamma ) }\\\\\bold{ ⇢ x {}^{3} - 7x {}^{2} + ( - 6)x - ( - 72)} \\\\\bold\blue{ ⇢x {}^{3} - 7x {}^{2} - 6x + 72}[/tex]
hope helpful~
Question 9 of 25
Which parent function is represented by the graph?
104
10
10
-10
A. The absolute value parent function
B. The linear parent function
C. An exponential parent function
D. The quadratic parent function
Answers
C. An exponential parent function
The given function is an exponential parent function the correct option is C.
What is the exponential parent function?Algebraic expressions appear in the exponent of exponential functions. The formula for their parent function is y = bx², where b is any nonzero constant. The graph of the parent function, y = ex².
In the graph, we can see that the function is varying exponentially from -10 to 10.
Therefore, the given function is an exponential parent function the correct option is C.
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Angle Pairs ( Lines cut by a Transversal )
i don't really get it. an explanation would be nice, too, if possible..
- due in 3 hours
please answer ONLY if you know, thank you :)) !!
What are pair relation exists between angle 8 and angle 3? Use the figure below as a reference.
What are pair relation exists between angle 6 and angle 2? Use the figure below as a reference.
What are pair relation exists between angle 5 and angle 3? Use the figure below as a reference.
What are pair relation exists between angle 8 and angle 2? Use the figure below as a reference.
What are pair relation exists between angle 7 and angle 3? Use the figure below as a reference.
What are pair relation exists between angle 6 and angle 1? Use the figure below as a reference.
What are pair relation exists between angle 5 and angle 4? Use the figure below as a reference.
What are pair relation exists between angle 6 and angle 4? Use the figure below as a reference.
What are pair relation exists between angle 7 and angle 1? Use the figure below as a reference.
What are pair relation exists between angle 8 and angle 1? Use the figure below as a reference.
Answers
Answer:
See below
Step-by-step explanation:
What are pair relation exists between angle 8 and angle 3? Use the figure below as a reference.
Answer: Exterior alternate angles
Exterior alternate angles are equal in measure.
[tex]\implies m\angle 8 = m\angle 3[/tex]
What are pair relation exists between angle 6 and angle 2? Use the figure below as a reference.
Answer: Interior angles on the same side of transversal.
Interior angles on the same side of transversal are supplementay.
[tex]\implies m\angle 6 + m\angle 2 =180\degree[/tex]
What are pair relation exists between angle 5 and angle 3? Use the figure below as a reference.
Answer: Corresponding angles
Corresponding angles are equal in measure.
[tex]\implies m\angle 5 = m\angle 3[/tex]
What are pair relation exists between angle 8 and angle 2? Use the figure below as a reference.
Answer: Corresponding angles
Corresponding angles are equal in measure.
[tex]\implies m\angle 8 = m\angle 2[/tex]
What are pair relation exists between angle 7 and angle 3? Use the figure below as a reference.
Answer: Exterior angles on the same side of transversal
Exterior angles on the same side of transversal are supplementay.
[tex]\implies m\angle 7+ m\angle 3=180\degree[/tex]
What are pair relation exists between angle 6 and angle 1? Use the figure below as a reference.
Answer: Corresponding angles
Corresponding angles are equal in measure.
[tex]\implies m\angle 6 = m\angle 1[/tex]
What are pair relation exists between angle 5 and angle 4? Use the figure below as a reference.
Answer: Interior angles on the same side of transversal
Interior angles on the same side of transversal are supplementay.
[tex]\implies m\angle 5+ m\angle 4=180\degree[/tex]
What are pair relation exists between angle 6 and angle 4? Use the figure below as a reference.
Answer: Alternate angles
Alternate angles are equal in measure.
[tex]\implies m\angle 6 = m\angle 4[/tex]
What are pair relation exists between angle 7 and angle 1? Use the figure below as a reference.
Answer: Exterior alternate angles
Exterior alternate angles are equal in measure.
[tex]\implies m\angle 7 = m\angle 1[/tex]
What are pair relation exists between angle 8 and angle 1? Use the figure below as a reference.
Answer: Exterior angles on the same side of transversal.
Exterior angles on the same side of transversal are supplementay.
[tex]\implies m\angle 8+ m\angle 1=180\degree[/tex]
[tex] \: [/tex]
Solution :
⠀
1. What are pair relation exists between angle 8 and angle 3?
Alternate exterior angles. A pair of angles in which one arm of each of the angles is on the opposite sides of the transversal and the other arm in opposite direction is called a pair of alternate exterior angles.⠀
2. What are pair relation exists between angle 6 and angle 2?
∠6 + ∠2 = 180°. Therefore, ∠6, ∠2 is a pair of interior angles on the same side of the transversal.⠀
3. What are pair relation exists between angle 5 and angle 3?
Corresponding angles.A pair of angles in which one arm of each angle of a pair is on the same of the transversal and the other arm of the angles of the pair are directed in the same direction are known as Corresponding angles.⠀
4. What are pair relation exists between angle 8 and angle 2?
Corresponding angles.A pair of angles in which one arm of each angle of a pair is on the same of the transversal and the other arm of the angles of the pair are directed in the same direction are known as Corresponding angles.⠀
5. What are pair relation exists between angle 7 and angle 3?
∠7 + ∠3 = 180°. Therefore, ∠7, ∠3 is a pair of exterior angles on the same side of the transversal.⠀
6. What are pair relation exists between angle 6 and angle 1?
Corresponding angles.A pair of angles in which one arm of each angle of a pair is on the same of the transversal and the other arm of the angles of the pair are directed in the same direction are known as Corresponding angles.⠀
7. What are pair relation exists between angle 5 and angle 4?
∠5 + ∠4 = 180°. Therefore, ∠6, ∠2 is a pair of interior angles on the same side of the transversal.⠀
8. What are pair relation exists between angle 6 and angle 4?
Alternate interior anglesA pair of angles in which one arm of each of the angles is on the opposite sides of the transversal is called a pair of alternate interior angles.⠀
9. What are pair relation exists between angle 7 and angle 1?
Alternate exterior angles. A pair of angles in which one arm of each of the angles is on the opposite sides of the transversal and the other arm in opposite direction is called a pair of alternate exterior angles.C = 4+0. 10t what is the charge to rent a paddle boat for 20 minutes?
Answers
What is 300 x 2? Thank you!
Answers
Answer: 600!
Step-by-step explanation:
Point L is on line segment KM. Given LM = 5 and KM=9, determine the length KL.
Answers
Answer:
KM=LM+KL. If KM is 9 and LM is 5, then KM-LM=KL. So 9-5=4. KL is 4.
Step-by-step explanation:
The value of KL will be equal to 4 in the line segment KM.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that point, L is on line segment KM. Given LM = 5 and KM=9. The value of the line segment KL will be calculated as below:-
KM = LM + KL.
If KM is 9 and LM is 5, then,
KM-LM=KL.
KL = 9-5=4.
KL = 4
Therefore, the value of KL will be equal to 4 in the line segment KM.
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Sammy starts with $50 in her saving account and adds $50 each week. Write an equation that Sammy can use to show how much money she has after a certain number of weeks
Answers
Known facts:
50 dollars is the initial amount in the saving account50 dollars is added every week into the savings account.Variables:
x: # of weeksy: total amount of money in savingsSet equation based on known facts and variables:
y = 50x + 50, 50x is the rate at which it grows depending on
the week and 50 is the initial amount there
Hope that helps!
Which quadratic equation is equivalent to (x – 4)2 – (x – 4) – 6 = 0?
(u – 4)2 – (u – 4) – 6 = 0 where u = (x – 4)
u2 – (u – 4) – 6 = 0 where u = (x – 4)
u2 – 16 – u – 6 = 0 where u = (x – 4)
u2 – u – 6 = 0 where u = (x – 4)
Answers
Answer:
see below.
Step-by-step explanation:
letting u = x - 4 means the equation can now be expressed as a quadratic
u² - u - 6 = 0 ← quadratic equation in u
Answer: (D)
Step-by-step explanation:
HOW DO I DO THIS QUESTION
The GCD and LCM of three numbers are 3 and 1008 respectively.If two of the numbers are 48 and 72.Find the least possible value of the third number
Answers
Answer:
21
Step-by-step explanation:
We decompose prime factors of 48, 72, and 1008
48=2*2*2*2*3
72=2*2*2*3*3
1008=2*2*2*2*3*3*7
Let's compare 48, 72 with GOD(3) and LCM(1008), we can find that there must be at least 2 prime factors in the third number that is 3 and 7.
And let's find out the LCM of 48 and 72. Quite obvious the answer is 144.
Since the LCM should be the consequence of 144 multiplied by another prime factor.
Then let's try 144*7. Amazingly 144*7=1008. DONE!
A triangle has two side lengths of 5 and 13. What value could the length of the third side be?
Answers
Answer:
Step-by-step explanation:
USing the net below, Find the surface area of the triangular prism.
Answers
Answer:
Area of a triangle=1/2bh
>>1/2×3×6=9
Area of rectangle=L×B
=7*6=42
=7×4=28
Surface Area=2(9)+2(42)+2(28)
=18+84+56=158cm^2
You're an automotive body repairer who is writing an estimate for a customer. You
figure the repair work will cost about $450.00 before tax. If the tax rate is 6%, how
much will the customer pay after tax?
$477.00
$720.00
$588.00
Answers
Answer:
$100.70
Step-by-step explanation:
The difference between the total price ($434.50) and the sales price ($415) is the tax ($19.50). To find the sales tax as a percentage of the sales price, divide the sales tax by the sales price and then multiply by 100:
19.50415(100)=4.70
Please answer this friends I am stuck ?
Answers
Answer:
10°C average temperature
Step-by-step explanation:
Average Temperature = Lowest + 17
= -7 + 17
= 17 - 7
= 10°C average temperature
Mary wants to have $8500 to travel to South America when she is 21. She currently has $6439 in a savings account earning 4% annual compound interest.
will she have enough for the trip when she is 21?
what would the graph look like? (describe not graph!!)
Answers
Answer:
This is how i think you do this
Step-by-step explanation:
6439e^.04x8= 8867.32, or
e^.04= 1.0408 = 6439 x (1.0408^8) = 8,867.33.
the first one would be if she is receiving multiple payments ove the year, and the second one is just the "4% commended annually per year". its been a minute since ive actually had to do this, but that seems right to me. so she will have enough.
Please Help 20 Points
Answers
Answer:
3x^2+4x+1Step-by-step explanation:Given the polynomial function 4x + 3x^2 - 1Rearranging in descending order means that we are to arrange the degree power from the highest to the lowest.The term with the highest degree is 3x^2Followed by 4xThen the constant 1Adding according to the descending powersThe polynomial in descending order will be 3x^2+4x+1D is the answer:)I do need help with this problem that includes pi. ^_^
Answers
Solution:
Note that:
Circumference = 50.24 ft = 2πr = πdDia. = 16 ft.Divide the diameter both sides.
50.24 ft = πd=> 50.24/d ft = πd/d=> 50.24/d ft = πSubstitute the diameter in the equation.
=> 50.24/16 = π (Option A)The Snowy Pines Historical Center kept track of the amount of snow that fell in their town each year for the past century. This box plot shows the results.
Yearly snowfall (in.)
0
4
8
12
16
20
What fraction of the time did Snowy Pines get at least 14 inches of snow?
Answers
Answer: 1/4
Step-by-step explanation:
Find the part of the box plot that represents at least 14 inches of snow. In a box plot, each whisker represents 1/4 of the data. So, Snowy Pines got at least 14 inches of snow 1/4 of the time.
PLEASE FORGIVE ME IF THIS IS WRONG