6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x. ​

Answer:

1. Given.

2. Triangle Exterior Angle Theorem.

3. Definition of Equilateral Triangles.

4. Substitution Property of Equality.

5. Addition Property of Equality.

Two lines are said to be parallel if and only if the value of the angle between them is [tex]180^{o}[/tex].

Thus the required proofs for each question are stated below:

6. A bisector is a line that divides a given line or angle into two equal parts.

Thus to prove that: AD ║BC

Given that: AC ⊥ BD, then:

BX ≅ DX (midpoint property of a line)

<ADX ≅ <DBX (alternate angle property)

<DAX ≅ <BCX (alternate angle property)

<AXD ≅ <BXC (vertical opposite angle property)

Also,

ΔAXD ≅ ΔBXC (congruent property of similar triangles)

Therefore, it can be deduced that;

AD ║BC

7. Given: CD ≅ CE

<B ≅ <D

proof: AB ║DE

<ABC  ≅EDC

Thus,

CB  ≅ CA (congruent property of similar triangle)

<BAC  ≅ <EDC (alternate angle property)

ABC  ≅ <DEC (alternate angle property)

Also,

CA ≅ CB (congruent side of similar triangles)

ΔABc ≅ ΔCDE (congruent property of similar triangles)

Thus,

AB ║DE (congruent property)

8. Prove: AB ║ DE

Given: <1 ≅ < 3

Then,

<1 ≅ <2 ≅ <3 ≅ [tex]90^{o}[/tex]

So that,

BC ≅ EF

also,

<1 + <2 = [tex]180^{o}[/tex] (supplementary angles)

Therefore it can be inferred that;

AB ║ DE (congruent property of parallel lines intersected by transversals)

For more clarifications on parallel lines, visit: https://brainly.com/question/24607467

#SPJ1

The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.

According to the statement

We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.

So,

According to this representation,

A linear representation is a representation on a category of vector spaces or similar.

The other meaning is that when the growth increases linearly or at the constant speed.

In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.

linear representation explain this graph perfectly.

So, Linear model suits best to this graphical representation.

Learn more about Linear representation here

https://brainly.com/question/4074386

#SPJ1

The missing number in the given series is 24.

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.

Given the series,

4, ?, 144, 864, 5184, 31104

Multiplying with 6 in each term in the given sequence.

4×6 = 24

24×6 = 144

144×6 = 864

864×6 = 5184

5184×6 = 31104

Following the above sequence, we get the 2nd term is 24.

Hence the missing number is 24.

To learn more about the missing number from the given link :

https://brainly.com/question/27458314

#SPJ4

The amount of money that Miguel would save when he earns $120 is  $96.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

A ratio table can be described as table that shows equivalent values between two or more numbers and helps us to understand the relationship between the numbers.

The first step is to determine the ratio between the money earned and the money saved.

Ratio = money saved / money earned

8/10 = 0.8

Now, multiply the ratio gotten in the previous step by the amount earned to determine the amount saved.

Amount saved = amount earned x ratio

0.8 x 120 = $96

To learn more about ratios, please check: https://brainly.com/question/25927869

#SPJ1

Answer:

96

Step-by-step explanation:

I took the quiz edge 2022

Answer:

x=1, y=4;

x=2, y=13

Step-by-step explanation:

The slope is (B) -5/4.

To find the slope:

Therefore, the slope is (B) -5/4.

Know more about slopes here:

https://brainly.com/question/3493733

#SPJ4

The complete question is given below:

What is the slope of a line that is parallel to the line whose equation is y=45x−3?

A. −4/5

B. −5/4

C. 5/4

D. 4/5

Using proportions, it is found that Mrs. Wood should expect 1,898 books out of the 36,500 to have major damage.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, the proportion of books with major damage is:

43/(716 + 68 + 43) = 0.051995.

Hence, out of 36,500 books, the expected amount of books with major damage is:

0.051995 x 36,500 = 1898.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The total number of common tangents that can be drawn to the circles is 2.

A tangent serves as  line that touches the circle at a single point  whereby the  point where tangent meets the circle is the tangency.

A tangent to a circle can be described as the straight line  that touches the circle at only one point.

Therefore, from the definition, The total number of common tangents that can be drawn to the circles is 2.

Read more on the tangent here:

https://brainly.com/question/12926708

#SPJ1

Answer:

9.93 calories

Step-by-step explanation:

If 596 calories = 1h

then ?? calories =1m

since 1h=60 min

>>( 1/60)×596

=9.93 calories

The distance between points S' and S is 2.5 units.

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

Given that,

line segment ST is dilated to create line segment S'T' using the dilation rule DQ.

Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5 units, SS' = x units.

We need to find the value of x, the distance between points S' and S.

Since the line ST is dilated to S'T' with center of dilation Q, so the triangles STQ and S'T'Q must be similar.

We know that the corresponding sides of two similar triangles are proportional.

So, from ΔSTQ and ΔS'T'Q, we get

[tex]\frac{SQ}{S'Q} =\frac{TQ}{T'Q}[/tex]

[tex]\frac{SQ}{SQ+S'S} =\frac{TQ}{TQ+T'Q}[/tex]

[tex]\frac{2}{2+x} =\frac{1.2}{1.2+1.5}[/tex]

[tex]\frac{2}{2+x} =\frac{1.2}{2.7}[/tex]

[tex]\frac{2}{2+x} =\frac{12}{27}[/tex]

[tex]\frac{1}{2+x} =\frac{6}{27}[/tex]

12+6x = 27

6x = 15

x = 2.5

Hence, Thus, the required value of x is 2.5 units.

To learn more about proportionality theorem from the given link:

https://brainly.com/question/2475257

#SPJ4

Answer:

1.36mph

Step-by-step explanation:

The escalator is moving at 2ft/s, lets convert this to miles/second.

2ft/s = 0.000378788miles/s.

Now that we have the miles/second lets multiply this value by 3600 to get the miles/h, because there are 3600 seconds in an hour.

2ft/s=1.3636368miles/h

Or approximately 1.36miles/h.

Answer:

31: 98,765 x 9 + 3 = 888,888

32: 12.345 x 9 + 6 = 111,111

33: 3,367 x 15 = 50,505

34: 15,873 x 35 = 555,555

35: 33,334 x 33,334 = 1,111,155,556

36: 11,111 x 11,111 = 123,454,321

You skipped 37-39

40: 3 + 9 + 27 + 81 + 243 = 3(243-1)/2

41: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1 - 1/32

Step-by-step explanation:

It's just patterns bro

Get your associates, neighbors, friends, family, or even your local government concerned. It's much more comfortable and more useful to apply environmental attention and create a local project if you cooperate with others in our community.

Get your associates, neighbors, friends, family, or even your local government concerned. It's much more comfortable and more useful to apply environmental attention and create a local project if you cooperate with others in our community. Encouraging environmental awareness exists a vital aspect of being an environmental guardian.

Facilitate knowledge transfer from workers approaching retirement to workers of all ages. Work with families to support children in school and control illiteracy. Provide young people from deprived backgrounds the norms to study. Improve access to education for Aboriginal people.

To learn more about environmental problems refer to:

https://brainly.com/question/19098254

#SPJ9

The inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2

The function is given as:

f(x) = 1/2x + 1/4

Rewrite the function as

y = 1/2x + 1/4

Swap the positions of x and y

x = 1/2y + 1/4

Multiply through by 4

4x = 2y + 1

Subtract 1 from both sides

2y = 4x - 1

Divide by 2

y = 2x - 1/2

Rewrite as an inverse function

f-1(x) = 2x - 1/2

Hence, the inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2

See attachment for the graph of the inverse function

Read more about inverse function at

https://brainly.com/question/14391067

#SPJ1

Answer:

Step-by-step explanation:

e graph opens upward, and it has a vertex of (0,0)

What is vertex?

The vertex of an equation is the minimum or the maximum point on the graph of the equation

The equation of the graph is given as:

The above equation represents an absolute value function

An absolute value function is represented as:

So, by comparison, we have:

This means that the graph opens upward, and it has a vertex of (0,0)

See attachment for the graph of

Read more about absolute value functions at:

brainly.com/question/3381225

Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).

As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.

The horizontal distance between O and R is represented by "b".

The horizontal distance between T and S would therefore be:

= a + b

The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.

The coordinates of S is:

( a + b, d).

Find out more on shape coordinates at https://brainly.com/question/4599621

#SPJ1

The domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

So long as x ≥ -9/4, the function f(x) will be defined.

Given: "f(x) = Startroot 4 x + 9 Endroot + 2" should be written as

[tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

Note that [tex]$\sqrt{(4x + 9)}[/tex] exists a variation of the basic function [tex]y = \sqrt{x}[/tex], whose domain exists [0, ∞ ).

The domain of [tex]$f(x) = \sqrt{(4x + 9) }+ 2[/tex] exists seen by taking the "argument" 4x + 9 of [tex]\sqrt{(4x + 9)}[/tex]and setting it equivalent to zero:

4x + 9 ≥ 0

simplifying the equation, we get

4x ≥ -9

x ≥ -9/4

This exists the domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

So long as x ≥ -9/4, the function f(x) will be defined.

To learn more about the domain of the function refer to:

https://brainly.com/question/19638905

#SPJ4

Answer:

B

Step-by-step explanation:

I tink old up

no its BBBBB

Answer: $65

Step-by-step explanation:

Thomas saved $30

Matthew saved $35

 Saved up together in total is asking how much money they got together which addtion.

so we do 30 +35 which is $65

In triangle XYZ, angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c. Then, the side XZ which is the perpendicular, is opposite to ∠Y. Side XZ is adjacent to the ∠Y, and side ZY, which is the base, is also adjacent to ∠Y. We can say that ∠Y has been formed by the sides XZ and ZY.

It is given that,

In triangle X Y Z, angle X Z Y is a right angle or 90°.

The length of the hypotenuse XY is c.

⇒ The side with length c is adjacent to ∠Y.

The sides XZ and ZY form the right angle, thus one is base and the other is perpendicular.

Now, in relation to ∠Y, side ZY of length a is the base (adjacent to angle Y)

Similarly, side XZ of length b forms the perpendicular and is opposite to ∠Y.

Learn more about an angle here:

https://brainly.com/question/13954458

#SPJ1

the radius of the new circle =5cm

5cm is your answer love

Answer:

8

Step-by-step explanation:

AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.

P = 3 + 3 + 2 = 8.

The P(B|A) expressed in the simplest form will be (B) 2/7.

To find the P(B|A) expressed in the simplest form:

Given -

Total possible numbers = 2,3,4,5,6,7,8,9

Let the value of the number be AB.

Therefore, the P(B|A) expressed in the simplest form will be (B) 2/7.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ4

The complete question is given below:
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.

Event a = a first digit is an odd number

Event b = the second digit is an odd number

If a combination is picked at random with each possible locker combination being equally likely, what is P(B/A) expressed in the simplest form?

A.1/4

B.2/7

C.4/9

D.1/2

Answer:

54

Step-by-step explanation:

Answer: 12x-4, 14 counters, 8 more counters

Step-by-step explanation:  There are 2x yellow, 4x+6 red, and 6x-10 blue counters. We need to add all of this up to get the total number of counters. We first add the x's : 2x+4x+6x = 12x. Then we add the numbers. 6+ (-10) is -4. So, our expression is 12x-4. Next, we need to find out how many blue counters are in the bag. We know that there are 44 total counters and we need to find x because all the counters have x in them. 12x-4 = 44. We first add 4 to both sides to get 12x= 48 and x = 4. blue has 6x-10 counters so, blue has 24-10 = 14 counters. Red has 16+6 = 22 counters. 22-14 = 8 more counters

Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

Learn more about equation here-

https://brainly.com/question/3391581

#SPJ4

The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.

On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.

In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.

Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

Learn more about functions on:

https://brainly.com/question/15602982

#SPJ1

Answer:

  1.314 MJ

Step-by-step explanation:

As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.

There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.

The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.

The mass of the water being raised is the product of the volume of the cone and the density of water.

The cone volume is ...

  V = 1/3πr²h . . . . . . for radius 2 m and height 8 m

  V = 1/3π(2 m)²(8 m) = 32π/3 m³

The mass of water in the cone is then ...

  M = density × volume

  M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg

The center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.

The discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...

  W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J

As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.

  V(y) = (32π/3)(y/8)³

The differential volume at height y is the derivative of this:

  dV = π/16y²

The work done to raise this volume of water to a height of 10 m is ...

  (9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J

The total work done is the integral over all heights:

  [tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]

It takes about 1.31 MJ of work to empty the tank.

The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

For this question,

The curve is given as

x(t)=e^-t cos(t),

y(t) =e^-t sin(t),

z(t)=e^-t

The point is at (1,0,1)

The vector equation for the curve is

r(t) = { x(t), y(t), z(t) }

Differentiate r(t) with respect to t,

x'(t) = -e^-t cos(t) + e^-t (-sin(t))

⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)

⇒ x'(t) = -e^-t (cos(t) + sin(t))

y'(t) = - e^-t sin(t) + e^-t cos(t)

⇒ y'(t) = e^-t ((cos(t) - sin(t))

z'(t) = -e^-t

Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }

The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get

⇒  r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }

⇒  r'(t) = { -1(1+0), 1(1-0), -1 }

⇒  r'(t) = { -1, 1, -1 }

The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are

x = x₀+at

y = y₀+bt

z = z₀+ct

Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get

x = 1 + (-1)t

⇒ x = 1 - t

y = 0 + (1)t

⇒ y = t

z = 1 + (-1)t

⇒ z = 1 - t

Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

Learn more about parametric equation here

https://brainly.com/question/24097871

#SPJ4

Answer:

Step-by-step explanation:

12