Find h(1) if h(x)=4x2 +3x - 2

The permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3

We have:

[tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex]

Apply the following permutation formula

[tex]^{n}P_r = \frac{n!}{(n- r)!}[/tex]

So, we have:

[tex]\frac{(n + 1)!}{(n + 1 - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]

Evaluate the difference

[tex]\frac{(n + 1)!}{(n - 2)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]

Expand

[tex]\frac{(n + 1)!}{(n - 2)(n - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)(n - 3)!}[/tex]

Multiply through by (n - 3)!

[tex]\frac{(n + 1)!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]

Expand

[tex]\frac{(n + 1) * n!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]

Divide through by n!

[tex]\frac{(n + 1)}{(n - 2)} - 1 = \frac{3}{(n - 2)}[/tex]

Take the LCM

[tex]\frac{n + 1 - n + 2}{(n - 2)} = \frac{3}{(n - 2)}[/tex]

Evaluate the like terms

[tex]\frac{3}{(n - 2)} = \frac{3}{(n - 2)}[/tex]

Both sides of the equations are the same.

Hence, the permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3

Read more about permutation at:

https://brainly.com/question/11732255

#SPJ1

Answer:

D) -12

Step-by-step explanation:

[tex]3(x-4)+(2-x)-x^2[/tex]

Replace X With 5

[tex]3(5-4)+(2)(5)-5^2[/tex]

[tex]=-12[/tex]

I Hope This Helps

Please Mark Me As Brainliest :)

Answer: C, {(1, -4), (4, -1)}

Step-by-step explanation: Where the two graphs meet are their solutions, and the points where they meet are {(1, -4),(4,-1)}.

Based on the calculations on these invertible functions, f⁻¹(f(6.022)) is equal to 6.022 and f⁻¹(-10) + f(-6) is equal to -16.

An invertible function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a function and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property, we have:

f⁻¹(f(6.022)) = 6.022.

From the table, we have:

f⁻¹(-10) = -6

f(-6) = -10

Therefore, f⁻¹(-10) + f(-6) is given by:

f⁻¹(-10) + f(-6) = -6 - 10

f⁻¹(-10) + f(-6) = -16.

Read more on invertible function here: https://brainly.com/question/15635761

#SPJ1

Answer:

false

Step-by-step explanation:

so D(2) is equal to how much money he has after 2 years while D(7) is after 7 years. since he earns 3% interest each year he will have more money after 7 years than 2 years

Answer:

8/15

Step-by-step explanation:

For right triangles tan p = opposite leg / adjacent leg

tan p = 24 /45   =   8/15

Answer: I dont really understand your questions

Step-by-step explanation: find the solution to your problem

Answer:

3) r = 1.5

7) y = 18

11) x = -10

Step-by-step explanation:

3) Isolate the variable by dividing each side by factors that don't contain the variable.

7) Solve for y by simplifying both sides of the equation, then isolating the variable.

11) Move all terms that don't contain x to the right side and solve.

The choice is tangent rule and the distance from the base to the tower is 3. 98 meters

The trigonometric ratio to use is

tan α = opposite side/ adjacent side

This is so because the angle 86° is facing the side of the distance from the top to the base

The choice is tangent rule

adjacent  = x

Angle = 86°

Opposite side = 57

We have

tan 86° = 57/x

14. 300= 57/x

x = 57 ÷ 14.300

x = 3.98meters

Thus, the choice is tangent rule and the distance from the base to the tower is 3. 98 meters

Learn more about trigonometry here:

https://brainly.com/question/7331447

#SPJ1

Answer:

(3(3) × 3(4) ) ÷ 3(2)

(9 × 12) ÷ 6

108 ÷ 6

18

The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ1

Answer:

40, 10, 30
see picture

Step-by-step explanation:

Answer:

X = 92 degrees

Step-by-step explanation:

the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88

180-88= 92 so X = 92

In the given diagram, the length of OQ is 11

From the question, we are to determine the length of OQ

From the given information,

OP = 17

QP = 6

In the diagram, we can observe that

OQ + QP = OP

∴ OQ + 6 = 17

Subtract 6 from both sides

OQ + 6 - 6 = 17 - 6

OQ = 11

Hence, the length of OQ is 11

Learn more on Calculating the length of a line here: https://brainly.com/question/11795570

#SPJ1

[tex]\huge \boxed{\sf 11}\\\\\\\displaystyle \sf OP=OQ+QP\\\\OQ=OP-QP\\\\OQ=17-6\\\\OQ=11[/tex]

The total number of sugar will be 9/4.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

A Baker Had 1/3 Cups Of Sugar.

he Added 1/9 Cups To It

Let the number of sugar be x

x (1/3)  + 1/9x = 1

3x + 1x = 9

4x = 9

x = 9/4

Hence, the total number of sugar will be 9/4.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ1

Answer:

$0.16

Step-by-step explanation:

unit price = price of carton / number of eggs

unit price = $1.92/12

unit price = $0.16

The average rate of the change from x = 2 to x = 5 is about 20 , The domain is constrained at x =0

A function is a mathematical statement used to derive a relation between a dependent variable and an independent variable.

A) The vertical axis of the graph shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company , i.e is the x axis .

So the x-intercepts represent prices of the pencil at which the profit is 0

and The maximum value of the graph represents the maximum profit that can be obtained for any price of the pencil.

The Profit is increasing from (x = 0 to 5) and starts decreasing from x =5 to 10

B) From the graph

(f(5) -f(2))/(5 -2) = (160-100)/3  = 20

The average rate of the change from x = 2 to x = 5 is about 20.

This indicates that the profit will increase at a an average rate of $20 for each $1 increase in price in that interval.

(C)The domain is constrained at x =0 as there it cannot be concluded that if the price is 0 , the profit will be 0 , and we are obligated to sell the pencil at x =6 , as the maximum profits are booked at that point.

To know more about Function

https://brainly.com/question/12431044

#SPJ1

Answer:

Step-by-step explanation:

Comment

There is only 1 number under probability that is greater than or equal to 5. That number is 15

There are 4 possible answers. Only 1 is successful.

Answer: P(y≥5) = 1/4 or 0.25

Answer:

A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations).

Step-by-step explanation:

A parallelepiped focuses on three-dimensional figures formed by six parallelograms.

A parallelepiped shape has the following features

Think of a cube or a cuboid.

Notice that they contain squares and rectangles

A parallelepiped is to a parallelogram as a square is to a cube and a rectangle to a cuboid

Read more about parallelepiped at:

https://brainly.com/question/3050890

#SPJ11

a)

We know that a 4-sided polygon's angles add up to 360 degrees

so to find x:

360-(69+118+84)=89 degrees

b)

For a 4-sided polygon we also know that the outside angles add up to 360 degree.

so to find p:

360-(100+62+106)=92 degrees

Hope it helps!

Answer:

The second statement is true.

Step-by-step explanation:

Draw the corresponding parabola and use it to verify  all statements.

Answer:

The function is negative for all real values of x where

x < –3 and where x > 1.

Step-by-step explanation:

The answer above is correct.

Triangle JKL was rotated 90 degrees about the origin and translated 2 units left to form triangle J"K"L"

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Triangle JKL was rotated 90 degrees about the origin and translated 2 units left to form triangle J"K"L"

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

Answer:

Step-by-step explanation:

Answer:

70 is the right answer....

Answer:

70 ways

Step-by-step explanation:

8 C 4 =   8 ! / ( 4! * 4!) = 70 ways

Answer:

x² - 10x + 25

Step-by-step explanation:

The formula for squaring any binomial (an expression with two terms) is:

(a ± b)² = a² ± 2ab + b²

Let a = x and b = 5.

∴ Substituting:

   (x - 5)² = x² - 2(x)(5) + (-5)²

               = x² - 10x + 25

Answer:

answer is option C

Step-by-step explanation:

just take 6n as common and divine each value by it

The factored form of expression 6n⁴ - 24n³ + 18n is

6n (n² - 2n + 1) (n² - 2n + 3).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can factor out the greatest common factor of the expression, which is 6n:

6n(n³ - 4n² + 3n)

Next, we can factor the expression inside the parentheses by grouping:

n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)

Substituting this back into the original expression.

6n (n² + 3) (n - 4)

However, we can further simplify by noticing that the expressions

(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.

Thus,

The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

Hey there!

2(2y - 12) = 0
2(2y) + 2(-12) = 0

4y - 24 = 0

ADD 24 to BOTH SIDES

4y - 24 + 24 = 0 + 24

SIMPLIFY IT!

4y = 0 + 24

4y = 24

4y/4 = 24/4

SIMPLIFY IT!

y = 24/4

y = 6

Therefore, your answer should be:

y = 06 (Option B.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

y=6 (06) should be your answer

Step-by-step explanation:

4y-24=0

After you simply the first equation in the parenthesis, you then move the 24 to the 0,

4y=24

The answer becomes positive 24 because when you move things across the equal sign you switch the sign

y=6

Then divide 24 by 4 to isolate y, which then gives you the answer 6.

Teniendo en cuenta la regla de tres simple, el cartero reparte 64.200 cartas en un semestre.

La regla de tres es una forma de resolver problemas de proporcionalidad entre tres valores conocidos y un valor desconocido, estableciendo una relación de proporcionalidad entre todos ellos.

Es decir, lo que se pretende con ella es encontrar el cuarto término de una proporción conociendo los otros tres.

Si la relación entre las magnitudes es directa, es decir, cuando una magnitud aumenta, la otra también (o cuando una magnitud disminuye, la otra también), se debe aplicar la regla de tres directa.

Para resolver una regla de tres directa se debe seguir la siguiente fórmula, siendo a, b y c datos conocidos y x la variable a calcular:

a ⇒ b

c ⇒ x

Entonces: [tex]x=\frac{cxb}{a}[/tex]

En este caso, se puede aplicar la regla de tres de la siguiente manera: Entonces, si el cartero en un mes reparte 10.700 cartas, ¿en 6 meses (un semestre) reparte cuántas cartas?

1 mes ⇒ 10.700 cartas

6 meses ⇒ ×

Entonces: [tex]cantidad de cartas=\frac{6 mesesx10.700 cartas}{1 mes}[/tex]

Resolviendo:

cantidad de cartas= 64.200 cartas

En resumen, el cartero reparte 64.200 cartas en un semestre.

Aprende más con estos ejemplos:

https://brainly.com/question/21685920

https://brainly.com/question/24786153

#SPJ1

It should be noted that a reflection is known as a flip and it's a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.

In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.

The reflection is attached.

Learn more about reflection on:

https://brainly.com/question/1908648

#SPJ1

Answer:

[tex]n {}^{2} + 3[/tex]

Answer:

[tex]\frac{x-22}{(x+2)(x-4)}[/tex]

Step-by-step explanation:

multiply the numerator/denominator of the first fraction by (x - 4)

multiply the numerator/denominator of the second fraction by (x + 2)

this ensures that the fractions have a common denominator

[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]

= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator

= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]

=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]