can someone please help me

The length of MN is 68.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

LN = 6x-5, LM = x + 7, and MN = 3x + 20

As, M is in between L and N.

LM + MN = LN

x+7 + 3x+ 20 = 6x-5

4x + 27 = 6x -5

-2x = -32

x= 16

So, the length of MN = 3x + 20 = 3 * 16 + 20 = 68

Hence, the length of MN is 68.

Learn more about Algebra here:

https://brainly.com/question/13715639

#SPJ1

The value of the equation cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0

Now , the value of cos A + cos B = 2 cos ( A + B / 2 ) cos ( A - B / 2 )

Substituting the values in the equation , we get

cos x + cos ( x + 2π/3 + x + 4π/3 / 2 ) cos ( x + 2π/3 - x - 4π/3 / 2 )

On simplifying the equation , we get

cos  x + 2cos ( 2x + 2π / 2 ) cos ( -π/3 )

cos x + 2cos ( x + π ) ( -1/2 )

cos x + ( -cos x ) = 0

So , 0 = 0

Hence , the equation is solved

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

#SPJ1

The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².

In this problem we find a quadratic equation, of which we must infer the series of rigid transformations to be used to obtain a resulting expression. Rigid transformations are transformations applied on functions such that Euclidean distance is not changed. The most used rigid transformations are listed below:

After comparing the two expressions, we find that this procedure was applied in the following order:

Finally, we show the procedure to prove this manner:

y = x²

Step 1

y' = (x + 8)²

Step 2

y'' = 3 · (x + 8)²

Step 3

f(x) = 3 · (x + 8)² + 4

The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².

To learn more on rigid transformations: https://brainly.com/question/1761538

#SPJ1

Answer: 8/5

Step-by-step explanation:

Using supplementary angles, it is found that the value of x is of x = 10.75.

Supplementary angles are angles whose measures add to 180º.

An entire pizza is 360º, hence half the pizza is 180º, meaning that angles AOB and BOD are supplementary.

Their measures are given as follows:

Since they are supplementary, they add to 180º and we can add their measures and solve for x as follows:

2x - 4 + 14x + 12 = 180

16x = 172

x = 172/16

x = 10.75.

More can be learned about supplementary angles at https://brainly.com/question/12919120

#SPJ1

An isosceles triangle is a triangle with (at least) two equal sides. In the picture above, we have two equal side lengths and the remaining side length. .This property corresponds to two equal angles in a triangle.

verify the following equation:

Find the equation is possible or not?

Yes, it is possible to draw an isosceles obtuse triangle.

An isosceles obtuse triangle is a triangle in which one of its three angles is obtuse (between [tex]90[/tex] and [tex]180[/tex]degrees) and the other two are acute angles.

To learn more about the equation refer:

brainly.ph/question/6658482

#SPJ4

A recursive function allows us to find the value of any term in a geometric sequence by using the previous term in that exact sequence. If the common ratio of that geometric sequence is 9, then each term is nine times the previous term.

The general term for the geometric sequence is

an= a1 * r ^ (n-1)

where an is the nth term, a₁ is the first term, r is the common ratio, and n is its position or number. The term.

where a₁ = 3 and r = 3/2

Sequence: 3, 4.5, 6.75, 10.125, 15.1875, 22.78125, 34.171875, 51.2578125, 76.88671875 ...

3rd value: 6.75.

More problems related to a similar concept are solved in the link below.

https://brainly.com/question/11266123?referrer=searchResults

#SPJ4

Formula for arithmetic sequence 5,2,-1,-4, . . . . is an = 3n + 8.

An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

This is an A.P. series.

a = 5

d = -3

an = a + (n-1)d

an = a + (n-1)-3

an = a + 3n + 3

an = 5 + 3n + 3

an = 3n + 8

To learn more about A.P. series from given link

https://brainly.com/question/6561461

#SPJ4

Answer:

5 - 17 = -12

-12/4 = -3

Answer:

number is - 3

Step-by-step explanation:

let the number be n then the product ( multiplication ) of n and 4 is 4n , so

4n + 17 = 5 ( subtract 17 from both sides )

4n = - 12 ( divide both sides by 4 )

n = - 3

the number n is - 3

Parts of each Graph is,

a) Centre = C

   Radius = CA = CB = CD

   Diameter = BD

b) Centre = S

   Radius = SP = SQ = SR

   Diameter = PQ

The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle. Here, point P is the center of the circle.

The distance between the center of the circle to its circumference is the radius.

The diameter of a circle is the distance from a point on the circle to a point. radians away, and is the maximum distance from one point on a circle to another. The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere.

Therefore,

Parts of each Graph is,

a) Centre = C

   Radius = CA = CB = CD

   Diameter = BD

b) Centre = S

   Radius = SP = SQ = SR

   Diameter = PQ.

To learn more about radius, diameter visit : brainly.com/question/20488542

#SPJ9

Answer:

a) 13 = 2x - 5

Step-by-step explanation:

Given that,

→ Andrew ran 5 miles less than 2 times the no. of miles Bernadette ran.

→ Andrew ran a total of 13 miles.

Then the equation will be,

→ 13 = 2 times - 5

→ 13 = 2x - 5

Hence, option (a) is correct.

The total number of seats are there is row 16 is 65.

In Arithmetic Progression, the difference between two different arithmetic orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come along through a few specific terms in AP that had been labeled as:

As shown below, the AP can also be referred to in terms of common differences.

Now, as the values given in the question;

There are total 16 rows in the arena.

Thus, n = 16.

There are 20 seats present in row 1.

Consider the first term as 'a₁' = 20.

Similarly, there are 23 seats present at row 2.

Consider 'a₂' = 23 is the second term.

Now, calculate the common difference;

d = a₂ - a₁  

Put the values in the 'd'.

d = 23 - 20 = 3.

Now, compute the total number of seats in 16th row bu nth formula.

n-th term:  an = a + (n − 1) × d

a₁₆ = a₁ + (n - 1)d

a₁₆ = 20 + (16 - 1)3

a₁₆ = 20 + 45

a₁₆ = 65

Therefore, the total number of seats present in the 16th row is 65.

To know more about the arithmetic progression, here

brainly.com/question/24191546

#SPJ4

The height of the tree, which Dave is standing 66 feet away from, is 34 feet and 2.4 inches.

If Dave's and the tree's shadows end at the same point, then the length of the shadow of the tree must be the sum of Dave's shadow and his distance from the tree.

tree's shadow = Dave's shadow + distance from the tree

tree's shadow = 15 feet + 66 feet

tree's shadow = 81 feet

Using ratio and proportion, we can solve for the height of the tree.

Dave's height : height of tree = Dave's shadow : tree's shadow

let x = height of the tree

6 feet 4 inches : x = 15 feet : 81 feet

converting feet to inches (1 feet = 12 inches)

76 : x = 180 : 972

Solving for x by evaluating the proportion:

180 x = 76 (972)

x = 410.4 inches

x = 34 feet and 2.4 inches

Hence, the height of the tree is 34 feet and 2.4 inches.

To learn more about ratio and proportion: https://brainly.com/question/12024093

#SPJ4

The slope of the line through each pair of points (1,2) and (2,3) is 1.

Find the coordinates of two points along the selected line.

Find the difference in these two locations' y-coordinates (rise).

Find the difference in these two locations' x coordinates (run). Add the difference in x-coordinates (rise/run or slope) to the difference in y-coordinates.

The formula to calculate slope is -

m = y2 - y1 / x2 - x1

m = 3 - 2 / 2 - 1

m = 1  

To learn more about slope from given link

https://brainly.com/question/3493733

#SPJ4

The slope of the line that passes through the given points is equal to 3/5.

Given the following data:

Points on x-axis = (2, 5).

Points on y-axis = (1, 6).

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (5 - 2)/6 - 1)

Slope = 3/5

In conclusion, the slope of the line that passes through the given points is equal to 3/5.

Read more on slope here: brainly.com/question/3493733

#SPJ1

The words that are needed to complete the proof has been added below:

a. AE ≅ BD a. Given

b. A C=C E, B C=C D b. definition of midpoint

c. A E = B D c. definition of congruent segments

d. A C + C E = A E d. Segment Addition Postulate

e. A C + C E = B C + C D e. definition of congruent segments

f. A C + A C = C D + C D f. substitution

g. 2 A C  = 2 C D g. Simplify.

h. A C  = C D h. Division Property

i. AC ≅ CD i. definition of congruent segments

step I is the required proof

This is a term to compare segments that they are have similar properties such as equality in length. For instance using the line asked in the question, line AC is congruent to line CD means that the two lines are equal in length

Read more on proof of congruence here: https://brainly.com/question/2102943

#SPJ1

It has been proved that if the bisectors of ∠B and ∠C intersect each other at O, then; ∠BOC = 90°+  ¹/₂∠A

A △ ABC such that the bisectors of ∠ ABC and ∠ ACB meet at a point O.

To prove :

∠BOC = 90° + ¹/₂∠A

Proof :

In △BOC, we have

∠1 + ∠2 + ∠BOC = 180°

In △ ABC, we have, ∠A + ∠B + ∠C = 180°

∠A + 2(∠1) + 2(∠2) = 180°

¹/₂∠A + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90° -  ¹/₂∠A

Therefore, in equation 1,

90° -  ¹/₂∠A + ∠BOC = 180°

∠BOC = 90°+  ¹/₂∠A

Read more about Proving Angles at; https://brainly.com/question/13878372

#SPJ1

Answer:

Answer C is correct

Step-by-step explanation:

We know that,

[tex] \sf \: {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \\ \sf \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \: \: \: \: \: \: \: \: [/tex]

[tex]\sf (x) ^{0} = 1 \rightarrow \: Any \: number \: to \: the \: power \: 0 \: is \: 1[/tex]

Let us solve it now.

[tex] \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times ( {b}^{5} {c}^{4} )^{0} \\ \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{3} \times {a}^{5} \times {b}^{12} \times {c}^{2} \times {c}^{2} \times 1\\ \sf {a}^{3 + 5} \times {b}^{12} \times {c}^{2 + 2} \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} \times {b}^{12} \times {c}^{4} \times 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} {b}^{12} {c}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

x=9

Step-by-step explanation:

[tex]\sqrt{x+5}=\sqrt{2x-4} \\ \\ x+5=2x-4 \\ \\ x=9 [/tex]

On substituting this back into the equation, we see x=9 satisfies it.

The missing term in the sequence is A5 = 5 .

Let's assume for the sake of simplicity that the third term they provided you was >3, and the twenty-fifth is >25. As a result, you put 3 as A sub-one rather than specifying that A sub-3 is 3 and A sub-25 is 25. Here's where things become tough. Set A sub-23 to 25. (why? because 1 to 23 and 3 to 25 are equally distant.

A3=3, A25=25 } A1=3, A23=25

Apply the equation An = A1 + (n-1)D.

(Read: A-sub n = A sub 1 - the nth term - D)

A23(A sub-23)= 3 Plus (23-1)

D 25 = 3 + 22D \s-3 -3

22 = 22D

D = 1

Once more, An = A1 + (n-1)D.

A3 = A1 + (3-1) X 1

3 = A1 + 2

-2 -2

A1 = 1

An = 1 + (n-1) X 1

An = 1 + 1n - 1

An = 1n + 0

So you are left with the general formula An = 1n. You can use this formula to find any term in the sequence, all you got to do is plug in (An) the number you want. In this case, plug in A sub-5 if you want to find the fifth term. You get

An = 1n

A5 = 1X5

A5 = 5

The fifth term in the sequence is 5. (it goes 1,2,3,4,,5,..)

To learn more about similar question from the given link:

brainly.com/question/2505012

#SPJ4

Answer:

Side length of a square game board is 11.916 inches. Explanation: If the area is 142 ∈2 , as area is square of side length of a square,

Step-by-step explanation:

Applying the midpoint formula, the coordinates of point M are: (-3, -4).

The midpoint formula is given as, (x, y) = [(x2 + x1)/2, (y2 + y1)/2].

Given the following:

N(x, y) = (1.5, 2.5)

P(x1, y1) = (6, 9)

M(x2, y2) = (?, ?)

Plug in the values into the midpoint formula

N(1.5, 2.5) = [(x2 + 6)/2, (y2 + 9)/2]

Isolate each coordinate

1.5 = (x2 + 6)/2

2(1.5) = x2 + 6

3 = x2 + 6

3 - 6 = x2

x2 = -3

2.5 = (y2 + 9)/2

5 = y2 + 9

5 - 9 = y2

y2 = -4

Therefore, applying the midpoint formula, the coordinates of point M are: (-3, -4).

Learn more about the midpoint formula on:

https://brainly.com/question/13115533

#SPJ1

The isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

Draw an isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin.

The coordinate of the origin is (0, 0)

We can take the coordinate of point A and B as (-1, 1) and (1, -1)

The right angle triangle is shown in the attahced picture.

Thus, the isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.

Learn more about the right-angle triangle here:

brainly.com/question/3770177

#SPJ4

Regarding the piecewise curve and probabilities, we have that:

a) The figure is a value density curve because the area under the figure is of 1.

b) The probability is: P(0.6 ≤ X ≤ 0.8) = 0.2.

c) The probability is: P(0 ≤ X ≤ 0.4) = 0.6.

d) The probability is: P(0 ≤ X ≤ 0.2) = 0.3.

e) The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, to the left of x = 0.4, we have a linear curve with:

Then, considering the constant:

To represent a distribution, it's area over the entire interval has to be of 1. The area is composed by.

Hence the total area is:

A = 0.8 x 1 + 0.5 x 0.4 x 1 = 1.

Hence:

The figure is a value density curve because the area under the figure is of 1.

For itens b to d, the probabilities are also given by areas, hence:

For item e, we have that:

The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.

More can be learned about piecewise functions at https://brainly.com/question/24734454

#SPJ1

Answer:

Step-by-step explanation:

42=24+9h

To calculate the geometric mean, we take their product instead: 1 x 5 x 10 x 13 x 30 = 19,500 and then calculate the 5-th root of 19,500 = 7.21. This is equivalent to raising 19,500 to the 1/5-th power. Another way to calculate the geometric mean is with logarithms, as it is also the average of logarithmic values converted back to base 10.

The equation of the circle that passes through the point (-6 , -4) and has a center located at the origin is x^2 + y^2 = 52.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , -4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-6 - 0)^2 + (-4 - 0)^2

radius= √36 + 16

radius = √52

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = √52

(x - 0)^2 + (y - 0)^2 = (√52)^2

x^2 + y^2 = 52

Learn more about equation of a circle here: https://brainly.com/question/14150470

#SPJ4