Prove that: Cos x + Cos(x+ 2pi/3) + Cos (x + 4pi/3) =0

Answer:

48

Step-by-step explanation:

ABC is a right triangle so the masure of ∠A = 90°

The sum of interior angles in a triangle is equal to 180 so we will write an equation accordingly to find the

missing angle:

90 + 2x + 14 + 4x - 26 = 180 add like terms

78 + 6x = 180 subtract 78 from both sides

6x = 102 divide both sides by 6

x = 17

Now replace x with 17 to calculate the measure of m∠B

2*17 + 14 = 48

Answer:

Here,

MP=MN+NP=17+3y

or, 5y+9=17+3y

Now do equation and find the value of y.

Answer:

MP = 29

mp = mn + np

17 + 3y = 5y + 9

2y = 8

y= 4, NP = 3(4) = 12

so, MP = mn + np.... 12 + 17

MP = 29

The given equation is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.

Here we have the linear equation:

x - 2 = -2 + x

And we want to see how many solutions it has, so let's solve it.

IF we add 2 in both sides we will get:

x - 2 + 2 = -2 + x + 2

x + (-2 + 2) = x + (-2 + 2)

x = x

Now, that is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.

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Answer:

No Because 1/1 : 3/4 = 4/3 and 1/3 : 4/1 = 1/12

Answer:

x=3: 2(3) = 6.

Step-by-step explanation:

Answer:

10 24 32 are the answers

Step-by-step explanation:

My mom is a teacher lol

According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

Consider the algebraic relationships that exist for triangle medians.

The centroid of a triangle is 2/3 the distance from one vertex to the midpoint of the opposite side, according to the Centroid Theorem.

Given: [tex]$\triangle XYZ[/tex] with medians [tex]$\overline{X R}[/tex], [tex]\overline{Y S}$[/tex], and [tex]$\overline{Z Q}$[/tex].

By using Centroid Theorem, we get

1. XP = 2/3 XR

2. XR = XP + PR( Segment Addition Postulate)

3. XP = 2/3(XR+PR) (Substitution Property)

4. XP = 2/3 XP + 2/3 PR (Distributive Property)

5. 1/3 XP = 2/3 PR(Subtraction Property)

6. XP = 2PR (Multiplication Property)

7. XP/PR = 2 (Division Property)

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The distance between Amy's initial and final position is 1 mile and she is facing South direction

It is given that,

Amy first moves towards East direction in reference to her initial position  for 2 miles

The distance covered by Amy in East direction = 2 miles

Then,

Amy moves towards South direction in reference to her initial position(facing East side) for 3 miles

The distance covered by Amy in South direction = 3 miles

We need to find,

The distance between Amy's initial and final position which will be given by the displacement between both points

Let's say that the positive direction is East and the negative direction is south.

The distance covered by Amy in East direction = + 2 miles

The distance covered by Amy in South direction = - 3 miles

Then , +2 +(-3) = -1

Hence, the distance between Amy's initial and final position is 1 mile and she is facing South direction

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The slope of the line containing (7,-3) and (-8,-3) is  Zero(0).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = -3 , [tex]x_{2}[/tex] = -8 , and [tex]x_{1}[/tex] = 7 .

On substituting the values of variables in equation1, we will get

m = ( (-3)-(-3) ) / ( (-8)-(7) ) = (0/(-15)) = 0.

As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (7,-3) and (-8,-3) is  Zero(0).

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The measures of the angle and it's supplement are144°  and 36° respectively.

The measure of the supplement of an angle is four times the measure of the angle. (given)

Let us consider the value of the supplement be X°.

Therefore the value of the angle  is 4X°

 180 - X = 4X

  X = 36° (The value of supplement)

180°-X = 144°( The value of angle)

Hence the angles are 36° and 144° .

The measures of the angle and it's supplement are144°  and 36° respectively.

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Answer: Evaluate

6w=180

Divide both sides

6

6w = 6

180

​

Simplify

6

6w =30

Solution

w=30

Step-by-step explanation: hope this helps

Answer:

108°

Step-by-step explanation:

Since angle WYT and angle UYW lie on the same line, we can use linear pair fidn the answer.

That is: 180-72= angle UYW

Therefore angle UYW=108°

-Hence proved:)

Using arithmetic sequence concepts, the matching terms are given as follows:

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Hence, in this problem, the terms are classified as follows:

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Answer:

7+4 (11)

Step-by-step explanation:

I think you are asking about an equation that looks like this

x^7*x^4

When multiply exponents they are added together and the sum is what the new exponent is.

7+4=11

11 is the new exponent

x^11

So I believe the answer would be 7+4? But I don't fully understand what your question is.

P'''( 1 , -2 )     Q'''( 0 , 1)   R'''( -1 , 3 )    S'''( -2 , 0) are the coordinates of P''' Q''' R''' S''' .

What does the term "coordinates" mean?

( x , y)  →  ( x + 3 , y - 2 )

p' ( -2, -1 )     Q' ( 1 , 0)    R'( 3, -3 )   S'(0, -4 )

( x , y )  →   ( x , -2 - y)

p''(-2 , - 1 )   Q''( 1 , 0 )     R''( 3 , 1 )      S''( 0,2 )

( X , Y ) →  ( -Y , X )

P'''( 1 , -2 )     Q'''( 0 , 1)   R'''( -1 , 3 )    S'''( -2 , 0)

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The width of walkway is 3 feet.

What is rectangle ?

A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other. The diagonals of a rectangle bisects each other into equal segments.

We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.

Let us suppose the width of the walkway is x feet.

the length of garden and the walkway will be = 15+2x

and, the breadth of garden and the walkway will be = 12+2x

Now, area of the garden and the walkway around its perimeter is given by :

A = (15+2x)(12+2x)

A = 4x^2 + 54x + 180

Now, the area is given is given as 378 square feet. Hence, we have

4x^2 + 54x + 180 = 378

4x^2 + 54x -198 = 0

Using quadratic formula to find the roots of above equation we get :

x = 3, -33/2

Taking positive value of x that is 3 as area cannot be negative.

Therefore, the width of walkway is 3 feet.

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Answer:

k and 16

Step-by-step explanation:

I will cry

Nan

nnan

Nan

The area of triangle ΔABC with ∠C = 90°, ∠B = 75° an AB = 12 cm will be 18.16 square centimeters.

We have a right - angled triangle ΔABC.

We have to find the area of ΔABC.

Pythagoras theorem states - In a right - angled triangle ΔABC, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically -

h² = b² + p²

According to the question -

(Refer to the image attached)

∠C = 90°

∠B = 75°

AB = 12 cm

Now -

sin 75° = AC/AB

AC = AB sin(75°) = 12 sin(75°) = 12 x 0.97 = 11.64 cm

and

tan 75° = AC/BC

BC = AC/tan(75°) = 11.64/3.73 = 3.12 cm

Therefore, the area of triangle ΔABC -

A = 1/2 (AC x BC) = 0.5 x 3.12 x 11.64 = 18.16 cm²

Hence, the area of triangle ΔABC will be 18.16 cm².

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Answer:

Midpoint = (-1, 5)

Step-by-step explanation:

                     x₁  +  x₂         y₁   +   y₂

Midpoint = (--------------- , -----------------)

                          2                   2

                     -4  +  2         5  +   5

Midpoint = (--------------- , -----------------)

                          2                   2

                         -2                  10

Midpoint = (--------------- , -----------------)

                          2                   2

Midpoint = (-1, 5)

I hope this helps!

Answer:

In bold below.

Step-by-step explanation:

There are 12*12 = 144 square inches in a square foot.

So, there are 144 in^2 per 1 ft^2

So, we have:

               144 in^2

32 ft^2     -----------   =      4608 in^2.

                   1 ft^2

For yards it is 1 yd^2 per 9 ft^2 :-

                  1 yd^2

32 ft^2 =   ------------ =   3.56 yd^2.

                    9 ft^2

Answer:

2 or 1/3

Step-by-step explanation:

by getting the product and sum,then the roots

Answer:

skewed right, mean > median

Step-by-step explanation:

just did it

Answer:

skewed right, mean>median

Step-by-step explanation:

edge 2023

The midpoint is at (1/2 , -3, 7/2 )

In the given statement is

To find the midpoint of the line segment joining the pair of points

P(-2,-5,8) and Q(3,-2,-1)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] ,[tex]\frac{y_{1}+y_{2} }{2}[/tex] , [tex]\frac{z_{1}+z_{2} }{2}[/tex])

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points P(-2,-5,8) and Q(3,-2,-1)

Solving for the midpoint , we have,

m = ([tex]\frac{-2 + 3}{2} , \frac{-5+ (-2)}{2} , \frac{8 +(-1)}{2}[/tex])

m = (1/2 , -3, 7/2 )

Therefore, the midpoint is at (1/2 , -3, 7/2 )

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Step-by-step explanation:

The attached image should be what you're looking for.

The common ratio of the geometric sequence 4, 10, 25, 62.5, . . . is 2.5. The answer is B.

A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a common ratio.

a(n) = a r^(n-1)

Where:

a(n) = nth term

a = first term

r = common ratio

The common ratio must be the same for all pairs of succeeding term to be called a geometric sequence.

To find the common ratio, use the formula

a(n) = a r^(n-1)

let n = 2, a = 4, a(2) = 10

10 = 4(r^(2 - 1)

10 = 4(r)

r = 2.5

Or just simply divide each succeeding pairs of the sequence.

r = 10/4 = 2.5

r = 25/10 = 2.5

r = 62.5/25 = 2.5

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The probability that a particular one of them will sit in the chair closest to the dance floor is 1/4.

Linear Permutation:

Linear permutation defines the number of ordered arrangement of objects in a line while circular permutations is an ordered arrangement of objects in a circular manner.

Given,

Four friends are sitting at a table together at the prom.

Here we need to find  the probability that a particular one of them will sit in the chair closest to the dance floor.

Since the samples are arranged with a fixed reference point, this is a linear permutation.

So there are 4! or 24 ways in which the samples can be arranged.

The number of favorable outcomes is the number of permutations of the other 3 people given that a particular one of them will sit in the chair closest to the dance floor, 3! or 6.

Therefore, the probability is

=> 6/24

=> 1/4.

Therefore, the probability that a particular one of them will sit in the chair closest to the dance floor 1/4.

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the maximum time that he can have in his last race is 23 seconds.

We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:

(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8

(That is the equation for the mean of the 5 times)

Solving that for x we will get:

(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8

91 + x = 114

x = 114 - 91 = 23

So the maximum time that he can have in his last race is 23 seconds.

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The given conditional statement is true that is  If a number is divisible by 6, then it is divisible by 3".

A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as;

p⇒q, and read  "if p then q"

An example of a conditional statement is : p⇒q, that is:

if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that AB^2 = BC^2 + AC^2

"If a number is divisible by 3, then it is divisible by 6." is the inverse of the conditional statement "

Thus If a number is divisible by 6, then it is divisible by 3".

Therefore, the given conditional statement is true that is  If a number is divisible by 6, then it is divisible by 3".

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The slope-intercept form is y = mx + b.

If the value of m = -6 and b = 9 then 6x + y = 9 be the standard form.

Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.

Let the value of m = -6(slope)

b = 9 (y -intercept)

The slope-intercept form is given by,

y = mx + b

y = -6x + 9

Therefore,  y = -6x + 9  is the slope-intercept form

Standard form is given by, Ax + By = C

Since, slope-intercept form is y = -6x + 9

⇒ 6x + y = 9

Therefore, 6x + y = 9 is the standard form.

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The probability she will spell the word MATH P(MATH) is  1/12

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Given ; Alana has the letter tiles A, H, M , and T in a bag. If she selects a permutation of the tiles at random.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

Permutations of "MATH"

4P4 = 4! = 24

Two of the 'MATH" s we can get as a result

Then the probability she will spell the word MATH

P(MATH) = 2/24 = 1/12

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