Answer:
V≈83.14
AL=96
Surface A≈116.78
Base A≈10.39
Step-by-step explanation:
Step-by-step explanation:
base area of hexagonal prism =
6× ½×(2)(2)× sin 60° (regular prism)
= 12×½√3 = 6√3 sq. inches
Volume = base are x height
= 6√3 x 8 = 48√3 cu. inches
or 83.14 cu. inches
the lateral area = 6 × (2×8) = 96 sq. inches
total area = 2×(6√3) + 96
= (12√3 + 96) sq. inches
or 116.78 sq. inches
Consider the equations below:
y = 2x and 6x = 3y + 5
Are the lines parallel or perpendicular?
A Parallel because the product of the slopes is -1.
B Parallel because the slopes are the same.
C Perpendicular because the product of the slopes
is -1.
D Perpendicular because the slopes are the same.
==========================================================
Explanation:
Let's solve 6x = 3y + 5 for y
6x = 3y + 5
6x-5 = 3y
3y = 6x-5
y = (6x-5)/3
y = (6x)/3 - (5/3)
y = 2x - (5/3)
This final equation is in the form y = mx+b with m = 2 as the slope and b = -5/3 as the y intercept.
With the equation y = 2x, aka y = 2x+0, the m and b values are m = 2 and b = 0 respectively.
We see that both equations have the same slope (m = 2), but different y intercepts. Therefore, the two lines are parallel. If both y intercepts were the same as well, then we'd be talking about the same identical line.
If the slopes multiplied to -1, then the lines are perpendicular. In any other case, the two lines are neither parallel nor perpendicular.
In how many years the interest of Rs 25000 at 5.5% per year will be Rs3300?
Plzz help!!!
Answer:
37.82 year(s)
Step-by-step explanation:
double check tho, i might be using different method or my ans could be wrong since you gave literally no info on your specific task
i give brainlesss if u help me
Answer:
91,858
Step-by-step explanation:
This is the right answer
Answer: the answer is B hope it helps
Step-by-step explanation:
16,468 plus 75,390 = 91858
Given two points P(sinθ+2, tanθ-2) and Q(4sin²θ+4sinθcosθ+2acosθ, 3sinθ-2cosθ+a). Find constant "a" and the corresponding value of θ when these two points coincide. (0 ≤ θ < 2π)
Show your work, thanks!
Answer:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]
Step-by-step explanation:
we are given two coincident points
[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
since they are coincident points
[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
By order pair we obtain:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]
now we end up with a simultaneous equation as we have two variables
to figure out the simultaneous equation we can consider using substitution method
to do so, make a the subject of the equation.therefore from the second equation we acquire:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]
now substitute:
[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]
distribute:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
collect like terms:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
rearrange:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]
by Pythagorean theorem we obtain:
[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]
cancel 4 from both sides:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]
move right hand side expression to left hand side and change its sign:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]
factor out sin:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]
factor out 2:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]
group:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]
factor out -1:
[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
divide both sides by -1:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
by Zero product property we acquire:
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]
cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]
divide both sides by 2:
[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]
by unit circle we get:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
so when θ is 60° a is:
[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]
recall unit circle:
[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]
when θ is 300°
[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]
remember unit circle:
[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]
and we are done!
disclaimer: also refer the attachment I did it first before answering the question
Choose the correct graph of the given system of equations. (2 points)
y − 2x = −1
x + 3y = 4
a
graph of two lines, one with a positive slope and one with a negative slope, that intersect at the point negative 1, 1
b
graph of two lines that intersect at the point 1, 1
c
graph of two parallel lines with positive slopes
d
None of the above
it's b because the graph of two lines that intersect at the point one it's like
What do the following two equations represent?
Answer:
C)
Step-by-step explanation:
HELP PLEASE I SUCK AT THIS!<3
What is the area of the rectangle
Answer:
E. 54cm ^2
Step-by-step explanation:
when finding the area just multiply length over width .for example 9 is the length times it to the width 6 you get 54 so the area will be 54 cm
Answer:
E
Step-by-step explanation:
length times width
6 x 9 = 54
A bus departed from New York at 11 pm with 44 passengers. An hour later, a few passengers got off at New Jersey. The number of passengers who boarded the bus at New Jersey were twice the number of passengers who got off the bus. If the bus has 50 passengers now, how many passengers got off at New Jersey?
Answer:
6 passengers got off at New Jersey
Step-by-step explanation:
let the number of passengers who got off be x and let the number of passengers who boarded the bus be y
y=2x
44 - x + y=50
y=50-44+x
y=6+x
subst y=2x
2x=6+x
2x-x=6
x=6
please help me you get 20 points !
Evaluate 1/3m-1-1/2n when m=21 and n=12
Answer:
12
Step-by-step explanation:
Please help me with this
Answer:
33
Step-by-step explanation:
Which of these symbols stands for greater than?
Answer:
>
Hope this helps!!
Find the area of a circle with a diameter of 31.
Answer:
hope this helps
Step-by-step explanation:
31 divided by 2 = 15.5 then do 15.5 x 15.5= 240.25 then you do 240.25 x 3.14 = 754.385
Find the solution of the system of equations.
4x-10y=0
4x-9y=-2
Answer:
{x,y} = {-5,-2}
Step-by-step explanation:
plss help me answer this
Answer:
c≈5.2
Step-by-step explanation:
c=a2+b2=1.412+52≈5.19501
Joe tried to prove that the sum of a triangle's interior angle measures is 180°
Answer: Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5
Step-by-step explanation: Khan Academy
Joe made the mistake by guessing Angles ∠4 and∠2 are not alternate interior angles and neither are ∠1 and ∠5.
The correct option is (b).
What is Parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
WE have to prove that the sum of a triangle's interior angle measures is 180°
According to the figure <1 and <4 are the alternate interior angle and <2 and <5 are alternate interior angle.
So, Joe made the mistake by guessing Angles ∠4 and∠2 and ∠1 and ∠5 are alternate interior angles.
Learn more about parallel lines here:
https://brainly.com/question/16701300
#SPJ2
will give brainiest!
The Pythagorean Identity states that:
(sin x)2 + (cOS X)2 = 1
Given cos 0 = 6/10, find sin 0.
sin 0 = [ ? ] / [ ? ]
Simplify the fraction.
Answer:
[tex] \frac{4}{5} [/tex]
Step-by-step explanation:
[tex] ( \cos \theta) ^{2} + ( \sin \theta) ^{2} = 1 \\ \\ \therefore \: { \bigg( \frac{{6} }{10} \bigg)}^{2} + ( \sin \theta) ^{2} = 1 \\ \\ \frac{36}{100} + ( \sin \theta) ^{2} = 1 \\ \\ ( \sin \theta) ^{2} = 1 - \frac{36}{100} \\ \\ ( \sin \theta) ^{2} = \frac{100 - 36}{100} \\ \\ ( \sin \theta) ^{2} = \frac{64}{100} \\ \\ \sin \theta = \sqrt{\frac{64}{100} } \\ \\ \sin \theta = \frac{8}{10} \\ \\ \sin \theta = \frac{4}{5} [/tex]
To the nearest gallon, what is the volume of a cylindrical water heater 1.4 feet in diameter and 4 feet tall (1 cubic foot=7.48 gallons)
The answer would be 46 gal.
what is the standard deviation of 6, 2, 3, 1
Answer:
1.870828693387
Step-by-step explanation:
Standard Deviation, σ: 1.870828693387
Count, N:4
Sum, Σx: 12
Mean, μ: 3
Variance, σ2: 3.5
Steps
σ2 = Σ(xi - μ)2
N = (6 - 3)2 + ... + (1 - 3)2
4 = 14
4 = 3.5
σ = √3.5
= 1.870828693387
The area of a rectangular playground is 78 square meters. If the length of the playground is 13 meters, what is its width?
Answer: It’s 6 meters
Step-by-step explanation:
if we know the area and the length we need to divide the two to get the width.
78 divided by 13. = 6
Can someone help, please
easy math equation!
4. Write an equation of the line with slope 2/3 that goes through the point (-2,5).
Explanation please...........
Answer:
my school
Step-by-step explanation:
block me from sieng the image
Answer:
answer: Hi = 15
Step-by-step explanation:
the larger shape is the same as the smaller shape just flipped over and bigger of course so to find this out you have to take 2 simular angles and find out what multiplied by the small angle will get the big angle so I see angles gh and ba are simular I try 4.5 ÷ 1.5 = 3 so 3 is how much the shape is being multiplied by so bc is simular to hi so I do 5 x 3 = 15 and theres are answer 15 is the length of hi hope this helps you!
A polar bear weighs 3 times more than a baby elephant. Both of them together weigh 700 kilograms. How much does the polar bear weigh?
Answer:
The polar bear weighs 525kg
Step-by-step explanation:
C = Polar Bear
D = Baby Elephant
____________________________
(1) C + D = 700 kg
(2) C = 3D
________________________________
C = 700 - D
700 - D = 3D
700 = 4D
________________________________
525 + 175 = 700
Then we get our answer, the polar bear weighs 525kg, and the baby elephant weighs 175kg.
Hope this helps you :)
The graph shows a line and two similar triangles.
What is the equation of the line?
y = 3 x
y = one-third x
y = one-third x + 2
y = 3 x + 2
Answer:
y=1/3x+2
Step-by-step explanation:
1. Una proposición que necesita ser demostrada y que cuya demostración consta de un conjunto de razonamientos se llama:
A. Axioma. B. Hipótesis. C. Colorario. D. Teorema.
2. Una proposición tan sencilla y evidente por sí misma que se admite sin demostración:
A. Axioma. B. Hipótesis. C. Escolio. D. Teorema.
Answer:
1. D. Teorema.
2. A. Axioma.
Step-by-step explanation:
En matemáticas, un conjunto de proposiciones que deben estar respaldadas por una prueba adecuada basada en el razonamiento se denomina teorema. Se puede demostrar plenamente que todos los teoremas matemáticos son verdaderos mediante el razonamiento.
Sin embargo, un axión es evidente por sí mismo y no necesita ser probado. Es un hecho ya establecido.
Answer:
1. D. Teorema.
2. A. Axioma.
Step-by-step explanation:
Espero que esto ayude
What does the simple interest stand for? Interest = Principal x Rate x Time Interest = Per unit x Rate x Time Interest = Price x Rate x Total Interest = Principal x Rest x Total
9514 1404 393
Answer:
(a) Interest = Principal x Rate x Time
Step-by-step explanation:
The letters in the simple interest formula ...
I = Prt
stand for ...
Interest = Principal x Rate x Time
What is the equation for -8 = p - 13
Answer: 5 is your answer hope this helped
plz make brainly
Step-by-step explanation:
Calculate the theoretical probability of each of the following events:
You spin a spinner with 3 equal sections labeled blue, red, and purple, and it lands on purple.
Answer:
There is a 1/3 chance it lands on each section
Step-by-step explanation:
Help me ASAP I have a 67% I math the girlie needs help
Answer:
x=28
Step-by-step explanation:
4(x-5)=92
4x-20=92
add 20 to both sides
4x=112
divide 4 on both sides
x=28
Answer:
The value of x is 28
Step-by-step explanation:
4(x - 5) = 92
4x - 20 = 92
4x = 92 + 20
4x = 112
x = 112 ÷ 4
x = 28
Thus, The value of x is 28
-TheUnknownScientist