i need help please

A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.

Therefore, the answers for the given composite functions are:

f(g(7)) = 814

g(f(4)) = 151

f(g(8)) = 898

f(f(2)) = -4

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depended on another quantity.

Here,

To evaluate function compositions, we substitute the inner function into the outer function and simplify.

(a) To evaluate f(g(7)), we first find g(7):

g(7) = 7(7)^2 + 9(7) + 3 = 343 + 63 + 3 = 409

Now we can substitute g(7) into f(x):

f(g(7)) = f(409) = 2(409) - 4 = 814

(b) To evaluate g(f(4)), we first find f(4):

f(4) = 2(4) - 4 = 4

Now we can substitute f(4) into g(x):

g(f(4)) = g(4) = 7(4)^2 + 9(4) + 3 = 112 + 36 + 3 = 151

(c) To evaluate f(g(8)), we first find g(8):

g(8) = 7(8)^2 + 9(8) + 3 = 7(64) + 72 + 3 = 451

Now we can substitute g(8) into f(x):

f(g(8)) = f(451) = 2(451) - 4 = 898

(d) To evaluate f(f(2)), we first find f(2):

f(2) = 2(2) - 4 = 0

Now we can substitute f(2) into f(x):

f(f(2)) = f(0) = 2(0) - 4 = -4

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Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

Yes

Step-by-step explanation:

Yes, it's a function.

If It have one more y to the same x, it's not a function.

I hope I've helped you.

Answer:

A to C and B to D

Step-by-step explanation:

Thats how it works dude/Bro

Answer:

The geometric mean of 6 and 30 is 13.416407864999

Answer:

11 1/2 years old

Step-by-step explanation:

Let Amanda's age be a.

Let the company's age be c.

The company is 24 years older than Amanda. This means that:

c = 24 + a ______(1)

The sum of Amanda's age and the company's age is 121 years. This means that:

c + a = 121 ________(2)

Put (1) in (2):

24 + a + a = 121

2a = 121 - 24

2a = 97

a = 97 / 2 = 48 1/2 years

She has been there for 37 years, therefore, her age when she started working there is:

48 1/2 - 37 = 11 1/2 years old

NOTE: This age doesn't seem right but I worked based on the parameters given.

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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Answer:

13 hours

Step-by-step explanation:

We just divide the total distance (52 miles) by the distance that the person can cover at that constant speed (4 miles) so we'll get something like: 52 / 4 = 13 so 13 hours.

The quotient is found to be 4/5. The correct option is (B).

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0. The number a is called as the numerator and b is the denominator. In order to divide two fractions take the reciprocal of the other fraction and change the sign as multiplication. It can be shown as a/b ÷ c/d = a/b × d/c.

The given expression is -3/5 ÷ (-3/4).

It can be simplified as follows,

Take the reciprocal of the fraction (-3/4) as -4/3.

And, change the sign of division to multiplication to obtain,

-3/5 ÷ (-3/4)

⇒ -3/5 × -4/3 = 4/5

Which the value of the quotient.

Hence, the quotient for the given arithmetic operation is 4/5.

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Answer:

5 and 12

Step-by-step explanation:

Answer:

12 and 5

Step-by-step explanation:

12 + 5 = 17 and 12 * 5 = 60

Answer: 7 cm

Step-by-step explanation: Divide by two to find the radius

Answer:

B

Step-by-step explanation:

To answer this question, we can just pick a couple of points and see which table gives the correct values.

Test Value 1)

Let's let m be 0.5.

So, our output will be:

\(-(T(0.5)+G(0.5))\)

From our original tables, we know that T(0.5) is 1.25 and G(0.5) is 4.9. So:

\(=-(1.25+4.9)\)

Add:

\(=-6.15\)

So, when m is 0.5, our output should be -6.15.

The only choice that does this is B. So, B is our correct answer!

However, let's do another test point just to confirm.

Test Value 2)

Let's let m be 1.2.

So, our output will be:

\(-(T(1.2)+G(1.2))\)

From our original table, we know that T(1.2) is 3 and G(1.2) is 11.76. So:

\(=-(3+11.76)\)

Add:

\(=-14.76\)

The only choice that does this is B. So, we are confident that B is our answer.

And we're done!

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

For the Cranberry Scones you all add 14 with it so 14+28=42 42+14=56 56+14=70 70+14=84. So, the answers on Cranberry scones are

28    42      56      70      84  

Orange scones you add 11 to all of them so 11+16=27 27+11=38 38+11=49 49+11=60.So the answer on Orange Scones is

16      27      38      49      60

Answer: question 1) 20% decrease.

question 2) 20% increase.

Step-by-step explanation:

use the percent change formula.

The approximate area of the shaded sector is 97 cm^2

What is area of circle ?

area of circle can be defined as the product of pi and square of radius ,the value of pi is 22/7 or 3.14 .

Given , diameter = 12

We need to convert diameter to r

d =2r

d/2 =r

12/2=r

6 =r

The radius is 6

A= pi *6^2

A = 36 *(3.14)

A = 113.04 cm^2

Now the fraction of the circle that is shaded is 301degrees out of 360

(A circle is 360 degrees)

=310/360 * area of a circle

=310/360 * 113.04

= 97.34

Hence , The approximate area of the shaded sector is 97 cm^2 .

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A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of her goal. The variable in the equation is

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem.

Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

In the context of the problem, the boutique owner wants to make $1,200 in clothing each week. This amount in made by the number of items sold as this is added to get to the amount the boutique owner is targeting

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Answer:

D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Answer:

43.667 years

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)ⁿ

Step 1: Define variables

A = 10,000

P = 5,000

r = 0.016

n = unknown

Step 2: Substitute variables

10,000 = 5,000(1 + 0.016)ⁿ

Step 3: Solve for n time

2 = (1.016)ⁿ

\(\log_{1.016}2\)

43.667 years

Answer:

\(y = - \frac{3}{2} x + 3\)

slope is -3/2, y-intercept is 3.

Step-by-step explanation:

\(m = \frac{ - 3 - 6}{4 - ( - 2)} = \frac{ - 9}{6} = - \frac{3}{2} \)

\(6 = - \frac{3}{2} ( - 2) + b\)

\(6 = 3 + b\)

\(b = 3\)

\(y = - \frac{3}{2} x + 3\)

Answer:

c = 12.5903 as it is more accurate

Step-by-step explanation:

tan65 = 27/d , value of tan65 is 2.1445

2.1445 = 27/d

d = 27/2.1445

d = 12.5903

so answer would be c as it is more accurate than others.

Answer:

3.5

Step-by-step explanation:

10.5 divided by 3= 3.5

Answer:

Niczego nie dołączyłeś. Więc nie mogę ci pomóc.

Answer:

f(1)=10

f(n)=nf(n-1)+5

f(2)=2f(1)+5=2*10+5=25

f(3)=3f(2)+5=3*25+5=75+5=80

f(4)=4f(3)+5=4*80+5=320+5=325

f(5)=5f(4)+5=5*325+5=1625+5=1630

The value for the function for given conditions is f(5) = 6440

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

One function

for which, f(1)=10

f(n) = -5 f(n-1)-n

f(5) =?

So, by putting n = 2 in given condition

f(2) = -5f(1) -2

f(2) = -52

Similarly, we solve it till n= 5

f(5) = 6440

Hence, the value of f(5) is 6440

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Step-by-step explanation:

The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.

The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.

To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:

For y = sin(x):

x = 0, y = 0

x = π/2, y = 1

x = π, y = 0

x = 3π/2, y = -1

x = 2π, y = 0

For y = sin(2x):

x = 0, y = 0

x = π/2, y = 0

x = π, y = 0

x = 3π/2, y = 0

x = 2π, y = 0

As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).

Therefore, the correct statement is: It is compressed horizontally.

Answer:

Y = 5.5x

The constant is 5.5

since no matter what y and x are there will always be a 5.5 difference

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The required constant of proportionality is 5.5 in the given expression.

Given that,
The equation y = 5.5x represents a proportional relationship. What is the constant of proportionality is to be determined.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
The given proportion equation is,?
y = 5.5x
Where y is the dependent variable and x is the independent variable,
And 5.5 is contant.

Thus, the required constant of proportionality is 5.5 in the given expression.

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Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ \(\frac{2}{x+2}\) and remainder is 2

A mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.

Here,

Given : synthetic division for

x³ + 3x² + 8x + 14

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

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

         -2 -2  

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

     1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

           -2 -2

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

         1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

        -2 - 2

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

     1    1   6

=> We get:

As

x² +x+6+ \(\frac{2}{x+2}\)

and remainder is 2

Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ \(\frac{2}{x+2}\) and remainder is 2.

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Answer:

The main flaw of this  proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp  and a 3 cent postage  must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

Step-by-step explanation:

From the question we are told that

   The  proof is

Every postage stamp of three cents or more can be formed using just 3 cent and 4 cent stamps.  

 Basic Step : We can form postage of 3 cents with a single 3 cent stamp and we can form postage of 4 cents using a single four cents tamp

Inductive Step: Assume that we can form postage of j cents for all non negative integers j with j <= k using just 3 cent and 4-cent stamps. We can then form postage of k+1 cents by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps

  FLAW IDENTIFICATION

Looking the inductive step, the statement ''by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps '' means that it is possible to use a 3-cent stamp for postage that requires a 4 -cent stamp  and this is not correct according the statement in the basic step

Generally the main flaw of this  proof is that it did not take into  consideration the fact a 4 cent postage must be made with a 4 cent stamp  and a 3 cent postage  must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage