f(x)=4x+1 and g(x)=2x2+1, find (f∘g)(x) and (g∘f)(x)

Answer:

Step-by-step explanation:

9. D

10.D

11.E

12.D

Answer:

9.

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

10.

[tex]x^2-25\\(x-5)(x+5)[/tex]

11.

[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]

12.

[tex]x^2+100\\[/tex]

This polynomial cannot be factored by using the difference of squares method

Answer:

See below

Step-by-step explanation:

[tex]A = \{2, 4, 6\}[/tex]

[tex]A^c =\{1, 3, 5\}\\B = \{4, 5, 6\}\\B^c = \{ 1,2, 3\}[/tex]

To prove 1 we have

[tex](A \bigcup B) = \{2, 4, 6\} \bigcup \{4, 5, 6\} = \{2, 4, 5, 6\}\\(A \bigcup B) ^c =\bold{\{1,3\}}\\A^c \bigcap B^c = {\{1, 3, 5\} \bigcap \{1, 2, 3\} =\bold{\{1,3\}}\\[/tex]

Hence proved

To prove 2

[tex](A \bigcap B) = \{2, 4, 6\} \bigcap \{4, 5, 6\} = \{4, 6\}\\\\(A \bigcap B)^c = \bold{\{1,2, 3, 5\}}\\A^c \bigcup B^c = \{1, 3, 5\} \bigcup \{1, 2, 3\} = \bold{\{1,2,3,5\}}\[/tex]

Hence proved

Notes

The complement of a set is the set of all elements not in the set

Here the set of all outcomes is {1, 2, 3,4,5, 6}

So if A = {2, 4, 6} then the complement of A s=is the set of outcomes not in A ie the set {1, 3, 5} which is the set of odd numbers on a die throw

The union of two sets is the set of all elements in both sets without duplication

The intersection of two sets is the set of all elements common to both sets

Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.

The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.

Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:

Side CD equals side DB.

Side CD = 5x - 17

Side DB = 3x + 1

Make both segments equal to each other. Therefore, we would have the equation:

5x - 17 = 3x + 1

Solve for x

Add both sides by 17

5x - 17 + 17 = 3x + 1 + 17

5x = 3x + 18

Subtract 3x from both sides

5x - 3x = 3x + 18 - 3x

2x = 18

Divide both sides by 2

2x/2 = 18/2

x = 9

CD = 5x - 17

Plug in the value of x

CD = 5(9) - 17

CD = 45 - 17

CD = 28 units.

DB = 3x + 1

Plug in the value of x

DB = 3(9) + 1

DB = 27 + 1

DB = 28 units.

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Answer:

  H

Step-by-step explanation:

Plane K is shown with two lines. Points on one of them are A, B, G. Points on the other one are G, M, N.

The point in plane K that is not shown on any line is point H.

the inequality gives the 'y' value as -4

An inequality is a mathematical tool that compares two values, expressing when one is less than, greater than, or not equal to the other value.

For instance,

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

From the information given, that 3y+1 is less than -11 . It can be expressed as;

3y + 1 ∠ -11

Let's collect like terms

3y ∠ -11 - 1

add like terms

3y ∠ -12

make 'y' the subject of formula

y ∠ -12/3

y ∠ -4

The inequality gives the 'y' value as -4

Thus, the inequality gives the 'y' value as -4

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Hello and Good Morning/Afternoon!

Let's take this problem step by step:

Let's consider some facts:

 ⇒ angles are opposite each other

    ⇒ by the Vertical Angle Theorem

        ⇒ angles opposite each other are equal in measure

So:

 [tex]\hookrightarrow 4x + 12 = 64[/tex]

Let's solve

  [tex]4x + 12 = 64\\4x = 52\\x = 13[/tex]

x's value is 13

Answer: 13

Hope that helps!

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The value of the probability P(A and D) is 0.30

Using the probabilities on the tree diagram, we have the following parameters

P(A) = 0.5

P(D/A) = 0.6

The probability P(A and D) is then calculated using the following formula

P(A and D) = P(A) * P(D/A)

Substitute the known values in the above equation

P(A and D) = 0.5 * 0.6

Evaluate the product

P(A and D) = 0.30

Hence, the value of the probability P(A and D) is 0.30

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Answer:

2.8 metres each

Step-by-step explanation:

14/5

2.8

(a) The result of the long division is a - b + c.

(b) The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).

Long division is an algebraic procedure with which we can find the result of a division of two polynomials. Now we proceed to present the entire procedure explained:

(a) a² - b² + 2 · b · c - c² divided by a + b - c.

1) Multiply a + b - c by a and subtract it from a² - b² + 2 · b · c - c²: Result: a / Remainder: - b² - a · b + 2 · b · c + a · c - c²

2) Multiply a + b - c by - b and subtract it from the result of 1): Result: a - b / Remainder: b · c + a · c - c²

3) Multiply a + b - c by c and subtract it from the result of 2): Result: a - b + c / Remainder: 0

The result of the long division is a - b + c.

(b) 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4 divided by m⁴ - 3 · m² + 4.

1) Multiply m⁴ - 3 · m² + 4 by 3 · m³ and subtract it from 3 · m⁷ - 11 · m⁵ + m⁴ + 18 · m³ - 8 · m + 3 · m² + 4: Result: 3 · m³ / Remainder: 2 · m⁵ + m⁴ + 6 · m³ - 8 · m + 3 · m² + 4.

2) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 1): Result: 3 · m³ + 2 · m / Remainder: m⁴ + 12 · m³ - 16 · m + 3 · m² + 4.

3) Multiply m⁴ - 3 · m² + 4 by 2 · m and subtract it from the result of 2): Result: 3 · m² + 2 · m + 1 / Remainder: 12 · m³ - 16 · m + 6 · m².

The result of the long division is 3 · m² + 2 · m + 1 + (12 · m³ - 16 · m + 6 · m²) / (m⁴ - 3 · m² + 4).

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Answer:

Step-by-step explanation:

Here's the solution

f^(-1)(x)=(\sqrt(5(x-10)))/(5), -(\sqrt(5(x-10)))/(5)

Answer:

Hola disculpa no me acuerdo

Step-by-step explanation:

De verdad que me encantaria ayudar pero no me acuerdo :(

Answer:

6

Step-by-step explanation:

Answer:

(4,8)

Step-by-step explanation:

hihihihihihihihohihih

Answer:

A

Step-by-step explanation:

If digits can be repeated, that means there are 10 options for each place in the pin code. 10*10*10*10 = 10,000

If digits can not be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit. 10*9*8*7 = 5040

The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].

Given a function f(x)=4-2x+6[tex]x^{2}[/tex].

We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.

Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.

f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).

f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]

=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])

=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]

=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]

[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h

=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]

=[tex](6h^{2} -2h+12ah)/h[/tex]

=6h+12a-2.

Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].

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Answer:

m = 3/2

Step-by-step explanation:

-7(m-1)= -(3m-1)

-7m + 7 = -3m + 1

-4m = -6

m = 3/2

Check.
-7(m-1)= -(3m-1)

-7(3/2 - 1) = -(3*3/2 - 1)

-7(1/2) = -(4.5 - 1)

-3.5 = -3.5

Use the distributive property to multiply −7 by m−1.

To find the opposite of 3m−1, find the opposite of each term.

The opposite of −1 is 1.

Add 3m to both sides.

Combine −7m and 3m to get −4m.

Subtract 7 from both sides.

Subtract 7 from 1 to get −6.

Divide both sides by −4.

Reduce the fraction -6/-4 to its lowest expression by extracting and canceling −2.

Answer: m=3/4 ✅

To estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T = R

825 + 0.06x = 1350 + 0.02x

Simplifying the equation, we get

x = 13125

We require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

For this case, we can assume that the total salary for Teresa T is given by T = 825 + 0.06x

Where x represents the number of sales. And similarly the total salary of Ramon we have:

R = 1350 + 0.02x

We want to estimate the amount of sales, x, will result in each of them earning the same amount for the week and we can set up the following equation:

T= R

825 + 0.06x = 1350 + 0.02x

Multiply both sides by 100

[tex]$825 \cdot 100+0.06 x \cdot 100=1350 \cdot 100+0.02 x \cdot 100$[/tex]

82500 + 6x = 135000 + 2 x

Subtract 82500 from both sides

82500 + 6x - 82500 = 135000 + 2x - 82500

6x = 2x + 52500

Subtract 2x from both sides

6x - 2x = 2x + 52500 - 2x

4x = 52500

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{52500}{4}$[/tex]

x = 13125

So then we require a total of 13125 for the number of sales to maintain the same amount for Ramon and Teresa at the end of the week.

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The missing length of the right triangle is 13.41 inches.

A right angle triangle has one of its angles as 90 degrees.

The side length of a right triangle can be found using Pythagoras theorem.

Therefore,

c² = a² + b²

where

Therefore,

x² = 18² - 12²

x² = 324 - 144

x² = 180

x = √180

x = 13.416407865

x = 13.41 inches

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Answer:x>1

Step-by-step explanation:

Subract 11 from both sides

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The total number of students is given by:

26 + 3 + 9 + 10 + 6 + 5 + 7 = 66

Of those, 26 play only football, hence the probability is:

p = 26/66 = 13/33

Which means that option c is correct for question 19.

Of those same 66 students, 9 + 7 = 16 play baseball but not football, hence the probability is:

p = 16/66 = 8/33

Which means that option d is correct for question 20.

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Answer + Step-by-step explanation:

the correct question:

For r ≠ 1 ,Prove using the mathematical induction method that :

[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]

………………………………………………………………………………………………………………

for n = 0 :

1⁰ = 1  and  (1 - r⁰⁺¹)/(1 - r) = (1 - r)/(1 - r) = 1

Then the property is true for n = 0.

For n ≥ 0 :

Suppose

[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]

And prove that

[tex]1+\cdots+r^{n+1} =\frac{1-r^{n+2}}{1-r}[/tex]

Since :

[tex]1+\cdots+r^{n+1} =(1+\cdots+r^n)+r^{n+1}[/tex]

Then

[tex]1+\cdots+r^n+r^{n+1} =\frac{1-r^{n+1}}{1-r}+r^{n+1}[/tex]

[tex]= \frac{1-r^{n+1}+r^{n+1}(1-r)}{1-r}[/tex]

[tex]= \frac{1-r^{n+2}}{1-r}[/tex]

Then according to the mathematical induction method

[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]

Where n is a natural number and r ≠ 1.

Using the permutation formula, there are 157,410 ways for the medals to be distributed.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:

P(55,3) = 55!/52! = 157,410

157,410 ways for the medals to be distributed.

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If the Hansens want to reduce their expected estate tax liability prior to the death of either of the spouses, they could initiate a Marital Transfer.

A Marital transfer simply means that the Hansens should bequest their assets to each each other in case either of them die.

If this happens, the surviving spouse will not be charged any estate taxes because bequests to spouses are not subject to taxation.

To do this, the Hansens should put it into both of their wills that they plan to gift/ bequest their assets to their spouse if they die.

The big disadvantage of using a marital transfer however, is that the estate will still be subject to taxes when the surviving spouse dies. All the estate taxes that had been avoided would then be incurred by the estate but only after the death of both spouses.

In conclusion, they should use a marital transfer.

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Answer:

69500

Step-by-step explanation:

695 x 100 = 69500

to check answer divided 69500 by 100

which is equals to 695

695 is a hundred times smaller than 69500

multiplication is a method of finding the product of two or more numbers.

We need to find the number which 695 is a hundred times smaller than

Six hundred ninety five times smaller than

Let us consider the number to be x.

Let us multiply 695 with 100 to  get the value or answer of the above question.

Six hundred ninety five into hundred is sixty nine thousand five hundred

695 x 100 = 69500

To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct

69500/100=695

Hence 695 is a hundred times smaller than 69500

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Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

A linear function is modeled by:

y = mx + b

In which:

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

0.25 = 10 - 0.75t

0.75t = 9.75

t = 9.75/0.75

t = 13 hours.

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Answer: 55

Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.

Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.

Thus, we could label the points A, B, and C, and set up an algebraic expression.

Let A = 27, B = 98, and C = x.

A + B + C = 180°.

Substituting A, B, and C we get:

27 + 98 + x = 180°.

Adding, we get:

125 + x = 180°

Subtracting 125 by 180, we get:

x = 55°

Thus, the angle X is 55°.

We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.

Based on the amount that Steve Weatherspoon wants to withdraw every year beginning in June 30, 2024, and the interest rate, the balance on June 30th 2023 should be $45,203.

The fact that Steve Weatherspoon wants to be able to withdraw a particular amount every year, this makes this amount an annuity.

The value in 2023 would therefore be the present value of the annuity that will then accrue to the required amounts as the years go by.

The present value of an annuity is:

= Annuity amount per year  x Present value interest factor of an annuity, 11%, 3 years between 2024 and 2027

Solving gives:

= 13,126.25 x 3.44371

= $45,203

In conclusion, the balance on the fund in 2023 should be $45,203 in order for Steve Weatherspoon to achieve his objectives.

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Answer:

421/6 degrees

Step-by-step explanation:

The acute angles of a right triangle are complementary, so

[tex]10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}[/tex]

So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.