Answer: (a) 720°, (b) 120°
Step-by-step explanation:
A hexagon is a polygon with six sides.
Formula for finding the interior angle of a polygon = ( 2n - 4 )complementary
= ( 2n - 4 ) 90
complimentary angle is 90° or
= ( n - 2 )supplementary
supplementary angle is 180° . Now solving the question now since n = 6
we now put it in any of the formula above
( 2 x 6 - 4 ) x 90 = ( 12 - 4 ) x 90
= 8 x 90
= 720° or
( 6 - 2 ) x 180 = 4 x 180
= 720°.
The second part of the question, each size of the interior angle
= ⁷²⁰/₆
= 120°
Translate into a variable expression.
the square of the difference between a number n and fifty
Answer:
f(n)= (n-50)²
Step-by-step explanation:
The difference between a number n and fifty:
n - 50Square of this difference:
(n-50)²It would look like this as variable expression:
f(n)= (n-50)²Isiah knows 1/4 is written .025 as a decimal how can you find a decimal for 5/4 without division
Answer:
0.25 x 5 = 1.25
This will not require any division. So, this is the answer. Hope this helps!
Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. What is the distance between the origin and the plane?
Answer:
The equation is:
(1/a)x + (1/b)y + (1/c)z = 1
Step-by-step explanation:
The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:
<0 - a, b - 0, 0 - 0>
<-a, b, 0> .....................(1)
The direction vector between (0, 0, c) and (0, b, 0) is given as:
<0 - 0, b - 0, 0 - c>
= <0, b, -c> .....................(2)
To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).
Doing this, we have:
<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>
To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:
(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0
(bc)x + (ac)y + (ab)z = (ac)b
Dividing both sides by abc, we have:
(1/a)x + (1/b)y + (1/c)z = 1
We will call π, the plane with points P, Q, R ( the intercepts )
The solution is:
π : -bc×x + ac×y -ab×z - bac = 0
c) d = | bac|/√ ( -bc)² + (-ac)² + ( -ab)²
The intercepts P Q R are three points of the plane, according to that
P ( 0, b, 0 ) intercept with y-axis
Q ( a, 0, 0 ) intercept with x-axis
R ( 0, 0, c ) intercept with z-axis
We will find the vectors PQ and PR both are on the plane
PQ = [ a, 0, 0 ] - [ 0, b, 0 ] ⇒ PQ = ( a , -b, 0 )
PR = [ 0, 0, c ] - [ 0, b, 0 ] ⇒ PR = ( 0, -b c )
The vectorial product of these two vector will give us, one normal vector to the plane.
i j k
PQ * PR = a -b 0 = i (-bc) - j ( ac - 0 ) + k ( -ab - 0)
0 -b c
PQ * PR = [ -bc, -ac, -ab ]
we call this vector n = [ -bc, -ac, -ab ]
Let´s now find a vector between P, and a general point T ( x , y , z ) on the plane.
PT = [ x, y, z ] - [ 0, b, 0 ] ⇒ PT = [ x-0 , y - b , z - 0 ]
PT = [ x, y-b, z ]
Vector PT is perpendicular to vector n, then their dot product must be 0
Then:
PT × n = 0
[ x, y-b, z ] × [ -bc, -ac, -ab ] = 0
x × (-bc) + ( y - b )× (ac) + z × (- ab) = 0
-bc×x + ac×y -bac - ab×z = 0
-bc×x + ac×y -ab×z = bac (1)
Finally, we got the implicit equation for plane π as:
π : -bc×x + ac×y -ab×z - bac
c) The distance (d) between the plane and the origin is:
d = | D | / | n |
| n | = √ ( -bc)² + (-ac)² + ( -ab)²
|D| = | bac| the right side of the equation (1)
Then
d = | bac|/√ ( -bc)² + (-ac)² + ( -ab)²
Related Link :https://brainly.com/question/3914382
X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 51, σ = 10, find P(36 ≤ X ≤ 56)
Answer:
0.6247
Step-by-step explanation:
The formula for calculating a Z-score is Z = (X - μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question,
μ = 51, σ = 10. We are to find P(36 ≤ X ≤ 56)
Step 1
Find the Probability of X ≤ 36
μ = 51, σ = 10
Z = (X - μ)/σ
Z = 36 - 51/ 10
Z = -15/10
Z = -1.5
We find the Probability of Z = -1.5 from Z-Table
P(X <36) = P(X = 36) = P(Z = -1.5)
= 0.066807
Step 2
Find the Probability of X ≤ 56
μ = 51, σ = 10
Z = (X - μ)/σ
Z = 56 - 51/ 10
Z = 5/10
Z = 0.5
We find the Probability of Z = 0.5 from Z-Table:
P(X < 56) = P(X = 56) = P(Z = 0.5)= 0.69146
Step 3
Find P(36 ≤ X ≤ 56)
P(36 ≤ X ≤ 56) = P(X ≤ 56) - P(X ≤ 36)
= P( Z = 0.5) - P(Z = -1.5)
= 0.69146 - 0.066807
= 0.624653
Approximately to 4 decimal places , P(36 ≤ X ≤ 56) = 0.6247
Achemistry student atrwered 81 questions correctly on a 90-question test. What
percent did the INCORRECT (WRONG)?
Answer:
The student got 90% correct and 10% incorrect.
Step-by-step explanation:
Suzanne is cooking a roast. The table at the right gives the temperature F(1). in degrees Fahrenheit, of the roast at several times (in minutes) after she removes the roast from the oven Calculate the average rate of change for the temperature from 10 to 20 minutes. Include units in your answer!
Answer:
I use celcius so can u convert if I were to answer ?
Convert the equation:
[tex]6x ^{2} - 3y ^{2} + 12x - 18y - 3 = 0[/tex]
to the standard form of a hyperbola.
Answer:
(x+1)²/6 - (y+3)²/12 = 1
Step-by-step explanation:
The standard form of writing the equation of an hyperbola is expressed as;
(x-h)²/a² - (y-b)²/b² = 1 where (h,k) is the centre of the hyperbola.
Given the equation:
6x²-3y²+12x-18y-3 = 0
We are to convert it to the standard form of writing the equation of a hyperbola.
Collecting the like terms will give;
(6x²+12x)-(3y²+18y)-3 = 0
Divide through by 3
(2x²+4x)-(y²+6y)-1 = 0
Completing the square of the equation in parenthesis and adding the constants to the other side of the equation:
(2x²+4x)-(y²+6y+(6/2)²)-1 = 0+(6/2)²
(2x²+4x)-(y²+6y+9)-1 = 9
2x²+4x -{(y+3)²} = 9+1
2x²+4x - (y+3)² = 10
Divide through by 2
x²+2x -(y+3)²/2 = 5
(x²+2x+(2/2)²)-(y+3)²/2 = 5+(2/2)²
(x²+2x+1) - (y+3)²/2 = 5+1
(x+1)²-(y+3)²/2 = 6
Divide through by 6
(x+1)²/6 - (y+3)²/12 = 1
The resulting equation is the required standard form of a hyperbola with centre at (-1, -3)
HEEEELP ME PLEASEEEE :(
(The problem is in the picture)
Find the product 3 − 9 × 3
Answer:
24
Step-by-step explanation:
The answer is 24 because you have to use PEMDAS which is parenthesis, exponents, multiply and divide left to right (which means whichever one is first), lastly add and subtract left to right.
24 13/1,000 as a decimal number
Answer:
24.013.
Step-by-step explanation:
Simplify: 24 13/1,000 = 24013/1000. Than just use a calculator to make it into a decimal.
Which expression is the radical form of
Answer:
see below
Step-by-step explanation:
You know that the denominator of a fractional exponent is the same as a root index, so ...
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}\\\\\boxed{x^{\frac{2}{7}}=\sqrt[7]{x^2}}[/tex]
David washes all 24 windows in his house he washed 6 windows each mr big and 2 windows each afternoon
How many days did it take him to wash all of his windows?
Answer:
3 days
Step-by-step explanation:
6 in the morning and 2 at the afternoon which mean David washed 8 windows a day.
24/8=3
So it took him 3 days
Hope this helps! :)
(pls mark brainliest)
Answer:
3 days
Step-by-step explanation:
when you divide 24 by 8 you get 3
How to solve 1/2(x-3)=9 linear equation
Answer:
[tex] \boxed{ \bold{ \sf{ \boxed{x = 21}}}}[/tex]Step-by-step explanation:
[tex] \sf{ \frac{1}{2} (x - 3) = 9}[/tex]
Distribute 1/2 through the parentheses
⇒[tex] \sf{ \frac{1}{2} x - \frac{1}{2} \times 3 = 9}[/tex]
Multiply the fractions
⇒[tex] \sf{ \frac{1}{2} x - \frac{1 \times 3}{2 \times 1} = 9}[/tex]
⇒[tex] \sf{ \frac{1}{2} x - \frac{3}{2} = 9}[/tex]
While performing the addition or subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.
⇒[tex] \sf{ \frac{x - 3}{2} = 9}[/tex]
Apply cross product property
⇒[tex] \sf{x - 3 = 9 \times 2}[/tex]
Multiply the numbers
⇒[tex] \sf{x - 3 = 18}[/tex]
Move 3 to right hand side and change it's sign
⇒[tex] \sf{x = 18 + 3}[/tex]
Add the numbers
⇒[tex] \sf{x = 21}[/tex]
Hope I helped!
Best regards!!
Which equation represents the function represented by the table? 17 POINTS!!!
Answer:
f(x) = -x -1
Step-by-step explanation:
You can make the correct choice by seeing which equation works for the first line of the table.
f(-1) = -(-1) -1 = 0 . . . . . the first equation works
f(-1) = -(-1) +1 = 2 . . . not zero
f(-1) = -1 -1 = -2 . . . not zero
f(-1) = 1 -(-1) = 2 . . . not zero (same as second equation)
Answer:
f (x)= -x-1
Step-by-step explanation:
Solve the equation for the specified variable.
U = Y(b + R), for b
Answer:
b= u/y -r
Step-by-step explanation:
Cubes are to be stacked in perfectly square layers that can be 5x5 (25 cubes), 4x4 (16 cubes), 3x3 (9 cubes), 2x2 (4 cubes), and 1x1 (1 cube). Each layer above the bottom one must have fewer cubes in it than the layer below it. If you have 54 cubes, and all of them must be stacked, what is the smallest bottom layer you can possibly have?
Answer:
25 cubes
Step-by-step explanation:
Conditions are:
Each layer must be a perfect squareThe layers must be smaller starting from the bottom layerThere are 54 cubes and all of them must be stackedThen the the option is:
5*5 + 4*4 + 3*3 + 2*2 = 25 + 16 + 9 + 4 =54So the smallest bottom layer is 5*5 = 25 cubes and the layers from the bottom are:
25, 16, 9, 4 cubesEvaluate the expression (21 + 3) · 6 - 9
Answer:
135.
Step-by-step explanation:
(21 + 3) · 6 - 9
*21 + 3 = 24
24 · 6 - 9
**24 · 6 = 144
144 - 9
***144 - 9 = 135
Use compatable numbers, then divide. 448 ÷ 8 a. 450 ÷ 10 = 45 b. 500 ÷ 10 = 50
Answer: B
Step-by-step explanation: I think thats right
Use and accessibility of internet on mobile phone
Answer:
Through a cellular service provider, the phone connects to the Internet through data transfer the same way a PC does, but with a wireless link. ... Cell phones have an in-built antenna which is used to send packets of digital information back and forth with cell-phone towers via radio waves. so the use of the internet it allows u to download apps,visit sites, (ect.)
Hope this helps_ /(TwT)\_
desperate pls answer!!
Answer:
Step-by-step explanation:
a) Since the x's of the original equation are equal to the y's of the inverse equation, and vice versa, you can simply put the x-values of the table for the inverse equation into the y-values of the original equation. The same principle applies to the inverse equation. The table should look like the tables attached.
b) The x's and y's in the points of the inverse are switched. The points will be
(10, 27) --> (27, 10)
(3.5, 14) --> (14, 3.5)
(a, b) --> (b, a)
(x, y) --> (y, x)
Prove using the trigonometric identities the following equation
Answer:
Step-by-step explanation:
[tex]\frac{(1-cosA)^2+sin^2A}{sinA(1-cosA) }=\frac{1-2cosA+cos^2A+sin^2 A}{sinA(1-cos A)}[/tex]
[tex]=\frac{2-2cos A}{sinA(1-cosA)}[/tex]
[tex]=\frac{2(1-cosA)}{sinA(1-cosA)}=\frac{2}{sinA}=2cscA[/tex]
What is the equation of the line given the two points
(-1,-6) and (-3, -8)
Answer:
y=x-5
Step-by-step explanation:
First we need to find the slope.
(-8+6)/(-3+1)
-2/-2
So the slope is 1
Using -1,-6 because we know the slope is 1, if we add 1 to x, we add 1 to y
So the y intercept is 0,-5
The equation is y=x-5
First find the gradient
[tex] \frac{y2 - y1}{x2 - x1} = \frac{( - 8) - ( - 6)}{( - 3) - ( - 1)} = \frac{5}{2} [/tex]
then using the formula y-y1 = m(x-x1)
y - (-6) = 5/2(x-(-1))
y + 6 = 5/2 (x+1)
2y + 12 = 5x + 5
2y - 5x = 5-12
2y - 5x = -7
5x - 2y = 7
so equation of the line is 5x -2y = 7
Sorry if im wrong
PLEASE I NEED ASAP, I WILL GIVE BRAINLYEST, 35 POINTS!!!
Evaluate this expression then round your answer to the two decimal places
7^4/7^6
3lbs of sour candies cost 4.50. what is the unit price
Answer:
$1.50
Step-by-step explanation:
1.50 x 3 = 4.50
Answer:
1.50$ per pound
Step-by-step explanation:
Step 1: State what is known
They tell us that 3 pounds cost 4.50$
Step 2: Find how much 1 pound cost
We divide 4.50$ by 3 to find out how much 1 pound costs
4.5/3 = 1.5
Therefore 1 pound of sour candies cost 1.50$
Plz help fast
Thank you
Answer:
1.25 is largest, 1.1 is second, 0.924 third, 0.61 fourth, 0.5 fifth, 0.12 sixth.
Step-by-step explanation:
I will edit this post and explain later because you said you need the answer fast. :)
Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets
an average of 150,000 new views. The average ratio of likes-to-views of Dagogo's videos is 1 : 5. Dagogo
wants to reach a total of 9,000,000 views on his channel.
Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he
uploads?
Answer:
2,000
Step-by-step explanation:
I just completed it on Khan Academy and it was right. I hope this helps!
Answer:
2000 likes per minute
Step-by-step explanation:
thats the answer on khan
2) We are filling the storage room with packages of toilet paper. The packages measure 18
inches x 13 inches x 9 inches, the warehouse measures 12 feet by 20 feet by 8 feet. Inside
each box are 9 rolls of toilet paper. How many rolls are in this warehouse?
Answer:
14,175
Step-by-step explanation:
since measurement of packages are used in inches we will convert warehouse dimension in inches to keep the unit same.
1 foot = 12 inch
dimension of room
12 feet by 20 feet by 8 feet
dimension of room in inches
12 feet = 12*12 inches = 144 inches
20 feet = 12*20 inches = 240 inches
8 feet = 12*8 inches = 96 inches
volume of cube = length *width *height
dimension of room = 144 inches * 240 inches * 96 inches
= 3,317,760 cubic inches
volume of 1 package = 18 inches * 13 inches * 9 inches = 2,106 cubic inches.
let there be n packages in the room
volume of n package = n*volume of 1 package = 2,106*n cubic inches.
This volume of n packages should be equal to volume of warehouse
2,106*n= 3,317,760
=> n= 3,317,760/2,106 = 1,575.38
since package cannot be in fraction and value after decimal is less than 5 we will round the value to 1,575.
Thus, no of packages is 1,575
1 package has 9 rolls
1,575 package has 9*1575 rolls
thus, no of rolls in the warehouse = 14,175
what is the definition of addition
Answer:
the difinition of addition is adding two things together
Step-by-step explanation:
Answer: Hi!
The definition of addition is when you add two or more more numbers (positive or negative.)
Hope this helps!
What percent of the cube of 5 is 5?
Answer:
4%.
Step-by-step explanation:
The cube of 5 is 125.
So the required percentage is (5 * 100) / 125
= 500/125
= 4%.
if the farm needs to pack 12,70,224 litchis in boxes that hold 144 litchis ,how many boxes would be required .
For this, we will divide 1,270,224 by 144.
1,270,224 ÷ 144 = 8,821.
For this result, we can conclude that the number of boxes required to pack 1,270,224 litchis is 8,821 boxes.