If f(1)=4 f(2)=5 and f(n)=f(n-1) + f(n-2) then find the value of f(5)

Vertical angles are : 1 and 6

supplementary angles : 1 and 2

linear pair : angle 4 and 8

adjacent angles: 21 and 22

A supplementary angle is an angle that, when added to another angle, results in a total angle measure of 180 degrees. In other words, if two angles are supplementary, the sum of their angle measures will be equal to 180 degrees.

For example, if angle A measures 100 degrees, its supplementary angle B would measure 80 degrees, since 100 + 80 = 180. Conversely, if angle B measures 120 degrees, its supplementary angle A would measure 60 degrees, since 120 + 60 = 180.

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Answer: $29.10

Step-by-step explanation:

1. Make a table, like the one shown in the image. You will need the item, its price, and how many are being bought.

2. Multiply the price and quantity of each item that is being bought.

3. Add all of the products together. This should get you the final price.

My steps are in the image. Hope this helps!

The equation relating T to H is H = 45 - 7T.

Temperature simply means the degree of hotness and coldness in a body.

In this case, they find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface.

Let T = the temperature (in Celsius).

Let H = the height above the surface (in kilometers).

The equation will be:

H = 45 - (7 × T)

H = 45 - 7T

The axes aren't given and can't be graphed.

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Answer:  [tex](h\circ m)(2) = 6[/tex]

=======================================================

Explanation:

The notation [tex](h \circ m)(2)[/tex] refers to function composition

It's the same as writing [tex]h(m(2))[/tex]

According to

m = {(3,4), (2,-2), (-2,6), (5,8)}

We have m(2) = -2 since x = 2 leads to m(x) = -2

Then the output -2 is treated as the input of the outer function h(x)

Looking through

h = {(1,5), (-2,6), (4, -3), (6,9)}

shows that h(-2) = 6

Therefore, [tex]h(m(2)) = h(-2) = 6, \ \text{ and } \ (h\circ m)(2) = 6[/tex]

Optionally we can write out a table like shown below.

The row highlighted shows the input x = 2 leading to m(x) = -2, which is then plugged into h(x) to get 6 as the final output. Think of it like a chain of dominoes.

We are given the following absolute value equation

Let us solve the problem then we will compare it with the given solution.

Now we will solve for the positive and negative sign separately

Comparing it with the given solution, there is an error on the left-hand side step 2. (the sign of 38 should be positive but in the figure, it is shown negative)

Now let us substitute the obtained x values into the original absolute value equation and check if they satisfy the equation.

For x = -4:

Hence, x = -4 is a valid solution.

For x = -38:

Hence, x = -38 is not a valid solution.

The above is an example of an extraneous solution.

An extraneous solution is a solution that we get during the process of solving an equation but it is not really the solution meaning that it does not satisfy the equation!

Therefore, x = -4 is the only solution to the given equation.

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

Given,

We have to expand the given polynomials and simplify them.

1. The polynomial: (a² - 3a)²

Here,

The polynomial is in the form of (a - b)²

So,

(a - b)² = a² - 2ab + b²

Then,

(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²

(a² - 3a)² = a⁴ - 6a³ + 9a²

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.

a = 1, b = -6 and c = 9

[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2

= 6/2 = 3

Then,

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) = 3

So,

(a² - 3a)² = 3a²

2. The polynomial: (1/2x³ + 6x)²

Here, the polynomial is in the form (a + b)²

(a + b)² = a² + 2ab + b²

Here,

(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²

(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

a = 1/4, b = 6 and c = 36

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]

= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12

Therefore,

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

Here,

(1/4x⁴ + 6x² + 36) = -12

Then,

(1/2x³ + 6x)² = -12x²

That is,

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

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The parallel between 2 highlights is called eduidistand

Answer:

the length of AB is 9

Step-by-step explanation:

an isosceles triangle is a type of triangle i which two of its sides are equivalent(equal). let AB=AC=x

perimeter=22

                  perimeter=AB+AC+BC

                                22=x+x+4

                                 22-4=2x

                                      18/2=2x/2

                                           9=x

Answer:

The equation of the line is;

Explanation:

Given that the line has a slope of;

And passes through the point;

Applying the point-slope equation of straight line;

substituting the given values and solving;

Therefore, the equation of the line is;

The Central Limit Theorem states that over a large number of samples, the sampling average of the sample means would be closer to the population mean.

The Central Limit Theorem states that for a random variable X, with mean given by [tex]\mu[/tex] and standard deviation given by [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

This means that over a large number of trials, i.e., of samples from the population, the mean of the sample means will be close to the population mean, with a small standard error, as the standard error is inversely proportional to the square root of the sample size.

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shooting percentage: 0.425 (decimal)

To express in percentage:

0.425 x 100 = 42.5%

(3) He made 42.5% of the baskets he attempted.

And also

17/40 = 0.425

(4) He made 17 out of every 40 baskets he attempted

Answer:

l = 2 in

h = 4 in

w = 2 in

Surface Area = 40

Step-by-step explanation:

If “l” is the length, and “h” is the height and “w” is the width of the rectangular prism, the surface area is given by the formula,

The surface area of a rectangular prism = 2 (lw+lh+hw) square units.

The 'x' and 'y' variables are highlighted in the box

Answer:

x = 7

y = 15

Step-by-step explanation:

Disclosure:  After I had completed my answer, I found that Answerwell had already posted a solution.  It is more straightforward than my approach.  While the answers are the same, I'm still adding mine because 1) I worked hard on it, and 2) it illustrates there can be different ways of reaching a solution.

See attached worksheet.

Answer:

It would be MOP is adjacent

Step-by-step explanation:

The movies for the movie marathon can be chosen in 120  different ways .

In the question ,

it is given that

total number of movies = 10 movies

number of movies that need to be played in specific order = 7 movies .

we have to find how many different ways can the movies be selected for the movie marathon .

we can solve this with Combination ,

where n = 10  and r = 7

So C(n,r) =  C (10,7)

= 10! / (3! * 7! )

= (10*9*8*7!)/(3! * 7! )

= ( 10*9*8) / (3*2 )

= 10 * 3 * 4

= 120 ways .

Therefore , The movies for the movie marathon can be chosen in 120  different ways .

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Graph is attached below.

Given,

y = 2x - 4

We have to draw a graph according to this

Here,

x E {-2; "-1;" 0; 1; 2}:

Image is attached.

How to draw a graph?

First, label and draw your X and Y axes at a straight angle. Axis Y is vertical, whereas axis X is horizontal. Write the scale for each axis down the line and mark the junction as 0, then draw a line. Calculate the values of Y for various values of X after drawing the axes.

So, the graph is given below.

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When QP bisects DQL, then the angles DQP and angle PQL is 23°.

Given that,

In the picture we can see the diagram,

The QL  line is there and the QD line.

QP line bisect the angles DQL

The angle DQP is 5x-7

The angle PQL is 11+2x

We have to find the x value and the angles DQP and PQL.

We know,

From the bisection we can say the angle are equal to each other

The angle DQP=The angle PQL

5x-7=11+2x

5x-2x=11+7

3x=18

x=18/3

x=6

Substitute x value in angles DQP and angle PQL.

The angle DQP=5x-7=5(6)-7=30-7=23°

The angle PQL=11+2x=11+2(6)=11+12=23°.

Therefore, the angles DQP and angle PQL is 23°.

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Answer: The perimeter of the triangle is 69 cm.

Step-by-step explanation:

Let us consider the side of the triangle be 3x ,4x and 5x.

According to the question,

The longest side of the triangle be 30 cm.

. 5x=30cm

x=6 cm

So the side of the triangle are 18cm ,24 cm and 30 cm.

The perimeter of the triangle is the sum of sides of the triangle.

so perimeter is =15+24+30=69 cm



1) The area of a sector of a circle can be found with the following formula:

2) Thus the area of the sector is 25π cm²

=========================================================

Explanation:

A hand of two pairs is when we have 2 cards of the same value, and another 2 of the same value, then the fifth card is something else entirely.

An example hand is:

-------------

We use the nCr formula since order doesn't matter.

C(n,r) = (n!)/(r!*(n-r)!)

For any suit, there are n = 13 cards. We make r = 2 selections for each of the two pair.

C(n,r) = (n!)/(r!(n-r)!)

C(13,2) = (13!)/(2!*(13-2)!)

C(13,2) = (13!)/(2!*11!)

C(13,2) = (13*12*11!)/(2!*11!)

C(13,2) = (13*12)/(2!)

C(13,2) = (13*12)/(2*1)

C(13,2) = (156)/(2)

C(13,2) = 78

There are 78 ways to select which two ranks will be chosen to represent each of the two pair.

Let's say one of the ranks of the two pair is a king. There are n = 4 kings and we select r = 2 of them. That gives C(4,2) = 6 ways to select those two kings. We'll also have 6 ways to select the other two cards in the other pair.

Therefore, we have 78*6*6 = 2808 ways to pick the first four cards that consist of the two pair (eg: 2 kings and 2 queens).

-----------------

So far we've considered just the two pairs. We have one card left to select. There are 13-2 = 11 cards of any particular suit that weren't part of the two pair. There are 4 suits to pick from, which means we have 11*4 = 44 cards to pick from for that fifth and final slot.

-----------------

Summary so far:

That gives 2808*44 = 123,552 different two pair hands possible.

This is out of C(52,5) = 2,598,960 hands

Divide those two values to get the final answer

(123,552)/(2,598,960) = 0.04753901560624

This then rounds to 0.04754 as the final answer.

Answer:

none (as shown) or

one if all uppercase letters

Step-by-step explanation:

A line of symmetry is a line you could place on a shape (usually a square, rectangle, triangle, etc, but here the "shape" is the word checkbook) which, if you folded the shape on the line, the two halves of the shape would exactly match each other.

"checkbook" does NOT have any lines of symmetry. BUT,

CHECKBOOK

does have a line of symmetry, horizontally, right thru the middle.

The building is 5.88 units tall.

It is given that the ball is dropped from a tall building.

The formula in the box relates the distance in meters "d" fallen to the time in seconds "t".

The formula is given below :

d = 4.9*t

The ball falls for a total of 1.2 seconds before hitting the ground.

The ball will travel a distance in the time interval from when the ball is dropped until it hits the ground.

The time for which the ball travels the distance is 1.2 seconds.

The distance travelled by the ball is :

d = 4.9*t

d = 4.9*1.2

d = 5.88

Hence, the ball travels a distance of 5.88 after it is dropped from the top of the building and before hitting the ground.

The height of the building is equal to the distance calculated.

The height of the building is 5.88.

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Hill's Criteria of Strength is the only criteria that must be met 100% for a causal relationship to be possible.

The Criteria of strength is Hill's first test for causation. He stated that the likelihood of an association being causative increases with the size of the connection between exposure and disease. Hill used Percival Pott's investigation into the prevalence of scrotal cancer in chimney sweeps to highlight this issue. Since the correlation between that occupation and sickness was so strong (almost 200 times more than in other jobs), it was concluded that chimney soot was probably a contributing factor. On the other hand, Hill argued that minor connections are less indicative of causation since they are more likely to be explained by other underlying factors (such as bias or confounding).

To evaluate possibly causative associations, it is essential to define what is meant by a "strong" correlation. Scientists may now distinguish between strong and weak associations using more mathematically sound criteria than Hill had in mind because of developments in statistical theory and computing capacity. Strength is no longer just understood as an association's magnitude. Furthermore, multi-factorial disorders and the existence of determinant risk variables that are tiny in magnitude but statistically significant have received more attention from researchers. The recognized standard for determining the strength of an observed correlation and, hence, its potential causation, is statistical significance today rather than the magnitude of the association.

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The expression -3.1^4x * -3.1^2x + 7 has an equivalent of 887.503681x^2 + 7

From the question, the expression is given as

-3.1^4x * -3.1^2x + 7

Evaluate the exponents in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 92.3521x * 9.61x + 7

Evaluate the products in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 887.503681x^2 + 7

Hence, the equivalent expression of -3.1^4x * -3.1^2x + 7 is 887.503681x^2 + 7

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Using the relation between velocity, distance and time, it is found that:

a. The equation used to find the distance of the flowerbed from the​ hive is: d = 540 feet per minute x 1.6 minutes.

b. The distance of the flower bed from the hive is: 864 feet.

Velocity is given by the distance divided by the time, as follows:

v = d/t

In the context of this problem, we have that:

The times are as follows:

The sum of this times is of 22 - 18 = 4 minutes, hence:

[tex]t_1 + t_2 = 4[/tex]

During the first step, that is, from hive to flowerbed, the velocity is 1.5 times greater than during the second step, thus the second time is 1.5 times the first time, that is:

[tex]t_2 = 1.5t_1[/tex]

Then the first time is calculated as follows:

[tex]1.5t_1 + t_1 = 4[/tex]

[tex]2.5t_1 = 4[/tex]

[tex]t_1 = \frac{4}{2.5}[/tex]

[tex]t_1 = 1.6[/tex]

The velocity during this time was of 9 feet per second = 540 feet per minute, for 1.6 minutes, hence the equation is:

d = v x t

d = 540 feet per minute x 1.6 minutes.

d = 864 feet.

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Answer:

Given, 3x−2<2x+1

⇒3x−2x<1+2

⇒x<3orx∈(−∞,3)

The lines y=3x−2 and y=2x+1 both will intersect at x=3

Clearly, the dark line shows the solution of 3x−2<2x+1.

solution

Step-by-step explanation:

The algebraic expression is equivalent to the expression below is 36x+110

According to the Distributive Law, multiplying a number by a collection of numbers is equivalent to performing each multiplication independently.

For instance, given the standard expression C(D + E). Using the distributive law;

C(D + E) = CD + DE

Using this rule to the given expression shown below;

11(4x + 10) - 8x

Apply the distributive property;

11(4x + 10) - 8x

11(4x) + 11(10) - 8x

44x + 110 - 8x

Collect the like terms

44x + 110 - 8x

44x-8x+110

36x+110

This gives the resulting equation of the linear function after expansion

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The height, h of the parallelogram is 4 feet.

A parallelogram is a quadrilateral with opposites sides equal to each other. Opposite sides of a parallelogram are also parallel to each other.

Opposite angles of a parallelogram are congruent. The consecutive or adjacent angles of a parallelogram is supplementary.

Therefore, the height of the parallelogram can be found as follows:

The sum of angles in a parallelogram is 360 degrees.

Hence,

sin ∅ = opposite / hypotenuse

where

sin ∅ = 3 / 6

sin ∅ = 1 / 2

∅ = sin⁻¹ 0.5

∅ = 30

Therefore,

30 + 30 + 2x = 360

where

60 + 2x = 360

2x = 360 - 60

2x = 300

x = 300 / 2

x = 150

Let's find the height of the parallelogram using trigonometric ratios,

sin 30° = h / 8

cross multiply

h = 8 sin 30°

h = 8 × 0.5

Therefore,

h = 4 ft

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Three people: Alan, Betty, Carol

Alan has 9 shares.

Betty has 10 shares.

Carol has 11 shares.

Therefore, there are a total of 9 + 10 + 11 = 30 shares.

Since the profit is $67,500, let's divide this one by the total number of shares.

The profit per share is $2,250.

Since Alan has 9 shares, let's multiply $2,250 to 9.

Therefore, Alan's share must be $20,250.

Let's do the same with Betty and Carol.

To summarize, Alan will receive $20,250, Betty will receive $22,500, and Carol will receive $24,750 from the proft