Explain why the initial value of any function of the form
f(x)= a(b) is equal to a.

Explain Why The Initial Value Of Any Function Of The Formf(x)= A(b) Is Equal To A.

Answers

Answer 1

Hello there!

Initial value is the y-intercept so x = 0. Then b⁰ = 1 because x⁰ = 1 if x ≠ 0. So the value of function is a * 1 which is equal to a.

Answer 2

Step-by-step explanation: The initial value of any function of the form f(x)= a(b) is equal to a because this type of function is a linear equation, which means that the rate of change (slope) is constant. This means that the output is always equal to the input multiplied by a constant, which is the coefficient a. Therefore, when the input (x) is equal to 0, the output (f(x)) is equal to 0 multiplied by a, which is equal to a.


Related Questions

which set of ordered pairs below is a function?

Answers

The first and the third set of order pairs is a function.

What is function?

A set of ordered pairs that contain only unique ordered pairs with unique x coordinates is referred to as a function. A function is defined by an equation that generates a set of ordered pairs.

Consider, the given set of order pairs,

I - {(3, 3), (6, 1), (2, 3)}

II - {(4, 7), (2, 8), (4, 2)}

III - {(9, 6), (3, 1), (7, 3)}

We have check which set of ordered pairs above is a function.

Since, a function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.

In the given order pairs the second order pair contain same x - coordinate.

So, the second order pair is not a function.

Hence, the first and the third set of order pairs is a function.

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-(-10x-6)-6=-9x
Solve for x

Answers

Answer:

x=0

Step-by-step explanation:

Solving the equation:

10x+6-6=-9

10x=-9x

19x=0

x=0

X would equal zero (see attached images)

Complete the equation of the line who’s y intercept is (0,-1) and slope is 4

Answers

Y=4x-1

The equation of a line is:

Y=mx+c

We are told that the slope is 4 which is also gradient, meaning that M=4

Now we are left with:

Y=4x+c

There are two ways to get C:

1. We know that C represents the y-intercept so immediately we can conclude that C=-1

2. You can work it out by substituting the coordinate for the X and Y value:

-1=4(0)+c

-1=C

So in conclusion, the equation of the line is:

Y=4x-1

The difference between ( -7×-7) + -(7×7) is
A)98. B)28
C)0. D)-28

Answers

To find the difference between (-7*-7) + -(7*7), we first need to calculate the values of each expression.

(-7*-7) = 77 = 49

-(77) = -49

The difference between these two values is 49 - (-49) = 49 + 49 = 98.

Therefore, the answer is A) 98.

The Correct answer is Option (A) = 98.

We need to determine the value of each part and calculate their difference. after that.

Here,    (-7*-7)= 49

and,     -(7*7) = -49

Now, their difference is to be calculated as follows:

          =49 - (-49)

          = 49+ 49

          = 98.

So, the answer is 98.

 

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What is irrational statement?

Answers

An irrational statement is a kind of genuine number that can't be addressed as a basic portion. It can't be communicated in that frame of mind of a proportion. If N is silly, N isn't equivalent to p/q where p and q are numbers and q isn't equivalent to 0. Model: √2, √3, √5, √11, √21, π(Pi) are nonsensical.

A number can't be communicated as a portion of any numbers and. . Unreasonable numbers have decimal developments that neither end nor become occasional. Each supernatural number is irrational.

If a square root is not an ideal square, then it is viewed as an unreasonable number. These numbers can't be composed as a portion because the decimal doesn't end (non-terminating) and doesn't rehash an example (non-repeating).

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Mason invested $65,000 in an account paying an interest rate of 4. 6% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $142,200?

Answers

It would take about 17.4 years, to the nearest year, for the value of the account to reach $142,200 if the interest rate is 4.6% and no deposits or withdrawals are made.

Therefore the answer is 17.4 years.

To find out how long it would take for the value of the account to reach $142,200, we need to use the formula for compound interest:

A = P(1 + r)^(t)

Where:

A = the future value of the account

P = the present value of the account ($65,000)

r = the annual interest rate (4.6%)

t = the number of years

We know the future value of the account (A) and the present value of the account (P), so we can substitute these values into the formula and solve for t:

142,200 = 65,000(1 + 0.046)^t

To solve for t, we can take the natural logarithm of both sides:

ln(142,200) = ln(65,000(1 + 0.046)^t)

ln(142,200) = ln(65,000) + t(ln(1 + 0.046))

Then we can divide both sides by ln(1+0.046) and take the power of e:

t = (ln(142,200) - ln(65,000)) / ln(1+0.046)

To the nearest year, this gives us t = 17.4 years.

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How can you tell if a graph is linear or logarithmic?

Answers

A linear graph will have a straight line, whereas a logarithmic graph will have a curved line.

1. Look at the graph and identify the shape of the line.

2. If the line is straight, then the graph is linear.

3. If the line is curved, then the graph is logarithmic.

When looking at a graph, you can tell if it is linear or logarithmic by examining the shape of the line. A linear graph will have a straight line, whereas a logarithmic graph will have a curved line. This is due to the fact that a linear graph is plotted by plotting the points of a linear equation, whereas a logarithmic graph is plotted by plotting the points of a logarithmic equation. The linear equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The logarithmic equation is of the form y = logb(x), where b is the base of the logarithm. Thus, the shape of the line will depend on the form of the equation used to plot the graph. If the line is straight, then it is a linear graph, and if it is curved, then it is a logarithmic graph.

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Which variation is represented by this situation:
A building that is 6 stories tall has a shadow that is 22 meters long.
How many stories tall is a building with a shadow that is 40 meters
long? Is it inverse variation or direct variation?

Answers

When a building is 40 meters long in shadow cast by another building of the same height, there are 10 levels there.

what is direct variation ?

equation that can be used to explain the mathematical relationship between two variables, where one variable is equal to a constant multiplied by the other. A direct variation's (proportional relationship's) graph is a straight line that pierces the origin. On a graph of direct variation, the graph will always pass through (1, k), where k is the proportionality constant. Direct variation refers to a change in one quantity that directly affects the other. The complete opposite of this is inverse variation.

The equation that describes this variation is:

h =kx

1st Data                                                            2nd Data

s=22 m                                                                    s  = 40 m

h=6 stories                                                               h = find 2nd

k=find 1st                                                                  k = 0.27 story/m

Find k:                                                                       Find h :

h=kx                                                                           h = kx

6 stories=k(22 m)                                                 h = ( 0.27 story/m ) ( 40 m)                                                                                                                                                                                                

k=6 stories/22 m                                                           h = 10    stories

k=0.27 story/m

so its direct variation .

When a building is 40 meters long in shadow cast by another building of the same height, there are 10 levels there.

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What are the 7 degree of polynomial?

Answers

The degree of a constant polynomial (such as 7) is zero.

The variable's highest power in a polynomial expression is the polynomial's degree.

A polynomial is a mathematical expression made up of more than two algebraic terms, particularly the sum (or difference) of several terms that each contain a different power of a single or several variables (s).

It is a monomial combination that is linear. Since the polynomial can be conceived of as 7x0, the degree of a constant polynomial (such as 7) is zero.

Normally, the degree of the zero polynomial (zero) is regarded as being undefinable.

A polynomial function with a degree of 7 is known as a septic function (also known as a 7th degree polynomial). 

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. Find sin D , sin E , cos D , and cos E . Write each answer as a fraction in simplest form.

Answers

The trigonometric functions are sin D = 28/53, sin E = 45/53, cos D =45/53, and cos E = 28/53 as fractions.

What are Trigonometric functions?

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric functions are given in the question

Apply the sine ratio on the given right triangle

⇒ sin(θ) = Perpendicular/hypotenuse

sin D = EF/DE

sin D = 28/53

sin E = DF/DE ,

sin E = 45/53

Apply the cosine ratio on the given right triangle

⇒ cos(θ) = Base/hypotenuse

cos D = DF/DE

cos D =45/53

cos E = EF/DE

cos E = 28/53

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Please help due soon pleaseeee!!!!!! Help

Answers

Answer:

  see attached

Step-by-step explanation:

Given the pictorial equations, you want to know the single-digit values of each of the images.

Equations

There are 6 equations in 5 unknowns, but no numerical values are assigned. Solving the equations will only give ratios of values. From those, we need to determine the numerical values that will keep all numbers in the range 1–9.

Let the icons be represented by letter variables as follows:

hat  = hboot = bsock = stennis shoe = tmitten = m

Rewriting the equations to standard form, we have ...

  h +b -m -s = 0 . . . . . [eq1]

  h -b +t = 0 . . . . . . . . [eq2]

  b -3s = 0 . . . . . . . . . [eq3]

  h -s -t +m = 0 . . . . .  [eq4]

  h +2s -m = 0 . . . . . . [eq5]

  h +b +s -2t = 0 . . . . . [eq6]

Solution

We can add [eq4] to [eq1] and [eq5] to eliminate the m variable.

  (h +b -m -s) +(h -s -t +m) = 0   ⇒   2h +b -2s -t = 0 . . . . [eq7]

  (h +2s -m) +(h -s -t +m) = 0   ⇒   2h +s -t = 0 . . . . . . . . . [eq8]

Adding [eq2] to [eq6], and [eq7] will eliminate the b variable.

  (h +b +s -2t) +(h -b +t) = 0   ⇒   2h +s -t = 0 . . . . same as [eq8]; no help

  (2h +b -2s -t) +(h -b +t) = 0   ⇒   3h -2s = 0 . . . . . [eq9]

Now, we have 3 equations in 4 unknowns:

  b -3s = 0 . . . . . . . [eq3]

  3h -2s = 0 . . . . . . [eq9]

  2h +s -t = 0 . . . . . [eq8]

The smallest positive integer values that will satisfy [eq9] are ...

  h = 2, s = 3

Using these in the remaining equations gives ...

  b -3·3 = 0   ⇒   b = 9

  2·2 +3 -t = 0   ⇒   t = 7

And we can find m using [eq5]:

  m = h +2s = 2 +2·3 = 8

Then the solution is ...

hat = 2boot = 9sock = 3tennis shoe = 7mitten = 8

Which expression is equivalent

Answers

Answer:

10^14

Step-by-step explanation:

The expression (10^2)^7 uses an exponent rule known as power raised to a power.

The rule states that when you multiply a base and its exponent to a power, you multiply the inner exponent and the outer exponent:

[tex](a^m)^n\\a^m^n[/tex]

Thus, we have

[tex](10^2)^7\\10^2^*^7\\10^1^4[/tex]

What is the coefficient of y2 in the expression 3y² 4x?

Answers

The coeficient of y² in the expression is the number 3

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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please help if you know the answer i need to get my grade up

Answers

Work hard to get all your work done and still have time to study.

How can you request a grade increase?

Highlight your drive to improve. It is critical that your lecturer recognizes your desire to enhance your course performance. During your meeting, ask the professor for advice on how to enhance future assignments. “I’m really committed to improving my grade in this course,” try stating.

Say what you feel is wrong with your grade calmly and professionally. Present additional examinations and assignments that indicate your abilities, and provide a solution that you believe is feasible. Be persuading and confident, but don’t think you know more or better than your teacher.

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Does anyone know how to do this

Answers

The experimental probability of spinning a number less than 3.

7/25.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The total number of spuns.

= 8 + 6 + 9 + 11 + 9 + 7

= 50

Total number of spuns of the spinner less than 3.

= 8 + 6

= 14

The probability of spinning a number less than 3.

= 14/50

= 7/25

Thus,

The probability is 7/25.

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PLS HELP DO TOMORROW!!!

Answers

Answer: 3 grams

Step-by-step explanation:

I just looked up the answer lol- I tried though, (Also I can't guarantee if it's right... But it probably is).

What are the top 5 formulas in math?

Answers

According to the use and the fundamental knowledge behind these formulas, The top 5 formulas in mathematics are quadratic, Pythagorean , slope-intercept , exponential and Euler's Formula.

What is mathematics?

Mathematics is the study of numbers, shapes, and patterns. It is the science of studying the properties and relationships of quantities and shapes using logic, symbols and mathematical operations. It is a way of understanding the world and solving problems using quantitative reasoning.

What do you mean by formula?

A mathematical formula is a set of symbols, numbers and mathematical operations that express a relationship or equation. These formulas are used to model, describe and explain phenomena in the natural and physical world, as well as in abstract mathematical theories. Formulas can take many forms, including equations, identities, and inequalities. They allow us to make predictions and calculations, and can be used in various fields of science, engineering and other fields to solve problems.

1. root of [tex]ax^2+bx+c[/tex] is [tex]x= \frac {-b+- \sqrt{b^2-4ac}}{2a}[/tex].

2.[tex]h^2 = p^2 +b^2[/tex]

3. [tex]y =mx+c[/tex]

4.[tex]e^x[/tex]

5.[tex]e^{ix} = cosx+isinx[/tex]

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In a survey of 170 girls, it was found that 18 girls
can neither dance nor can sing, 96 can dance and
69 can sing. By representing these information in
a Venn-diagram, find the number of girls who
both dance and sing.
Ans: 13

Answers

Answer:9

Step-by-step explanation:beacuse if you take 6 by 9 and 10 it will make 2 of 69

If the length of the American flag is 1.8 yards, find the hight

Answers

The flag uses a scale of
L:H=3:2
L=1.8
1.8/3
0.6=1 unit
2 units make up the height so
0.6 * 2 = 1.2
height =1.2 yards

What is an example of a no solution equation?

Answers

The equation 5x + 5 = 5x - 5 has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

No solution equation:

5x + 5 = 5x - 5

To solve this equation, we must first isolate the variable. To do this, we can subtract 5x from both sides of the equation.

5x + 5 = 5x - 5

Subtract 5x from both sides:

5 + 5 = - 5

Simplify:

10 = -5

At this point, we can see that this equation has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

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What is the use of if __ name __ == '__ main __' in Python?

Answers

The use of if__name__ == '__main__' in python is to check whether the current script is being run on its own or being imported somewhere else by combining it with if statement.

Here we need to find the use of if __ name __ == '__ main __' in Python.

Basically, in python the term Allows You to Execute Code When the File Runs as a Script, but Not When It’s Imported as a Module

Here for most practical purposes, this is known as the conditional block that you open with if __name__ == "__main__" as a way to store code that should only run when your file is executed as a script.

Therefore, the function is used as  a variable defined for each script that defines whether the script is being run as the main module or it is being run as an imported module.

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What is the least common multiple of 51, 68 and 85?

Answers

Answer:

1020

Step-by-step explanation:

I need some help with the problem from my math class (-4w - 7)5

Answers

-20w-35

I used the distributive property to distribute terms, and then simplified

Construction A construction company is building a new parking garage and is

charging the following rates: $5000 a month for the first 2 months; $8000 a month

for the next 4 months; $6000 in total for the last 4 months, when the garage will be

completed. This amount will be paid in a lump sum at the end of the 6th month.

Express the cost C (in thousands of dollars) as a function of

the time t (in months) that the construction company works

on the parking garage.

Answers

Answer:

C(t) = 5t for 0 < t ≤ 3

C(t) = (8t-9) for 3 < t ≤ 6

C(t) = 44 for 6 < t ≤ 10

C is given in thousands of dollars and t is given in months.

Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000

Step-by-step explanation:

We will do a piecewise analysis for this cost function.

How to obtain the total cost changes with each time interval.

In the first 3 months,

C(t) = 5t for 0 < t ≤ 3

Note that C is given in thousands of dollars

In the next 3 months,

C(t) = (8t-9) for 3 < t ≤ 6

- Here, it gets a little complex, we use the upper limit of the previous interval and the lower limit of this new interval to get the constant to be subtracted from the normal 8t that characterizes this interval.

8(3) = 24

5(3) = 15

constant = 24 - 15 = 9

In the last 4 months,

C(t) = 44 for 6 < t ≤ 10

- For the last four months, it is a single sum of $5000 plus the [8(6) - 9] from the previous inteval

C = [8(6) - 9] + 5 = 39 + 5 = 44

So, the cost of parking, tracked month after month gives

T | Cost (in thousands of dollars)

1 | 5

2 | 10

3 | 15

4 | 23

5 | 31

6 | 39

7 | 44

8 | 44

9 | 44

10 | 44

Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000

Hope this Helps!!!

This is not my answer yet is a stollen verrified one.

Consider the division of 8y2 - 12y + 4 by 4y.

What are the values of a and b?

=a+b++

O a = 2y and b = 3

O a= { and b = -3y

O a= 2y and b = -3

O a = ? and b = 3y

Mark this and return

Save and Exit

Next

Sub

Answers

By solving the given Algebraic expression, the correct answer is Option (C) ,a = 2y and b = –.

What is an Algebraic Expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.

Assume that  8y2 - 12y + 4  has  terms with a=8y² , b=-12y, c=4

Now, to divide 8y2 - 12y + 4  by the monomial (single term) 4y,

The easy way is divide each term of the dividend by the monomial:

8y2 - 12y + 4  /4y

=(8y²-12y+4)/4y

=(8y²/4y)-(12y/4y)+(4/4y)

=2y-3+1/y

After performing the division we get that now a = 2y and  b = –3

We can conclude that the correct answer is a = 2y and b = –3

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Given: PS bisects angle RST, 2SP=3SQ, 2ST=3SR

Prove: Triangle STP ~ triangle SRQ

Answers

The Triangle STP is similar to Triangle SRQ.

We can prove that triangle STP is similar to triangle SRQ using the Angle Bisector Theorem and the ratios of the sides of the triangles.

The Angle Bisector Theorem states that if point P bisects angle RST, then the ratio of the length of the side ST to the length of the side SR is equal to the ratio of the length of the side PT to the length of the side PQ.

In this case, we are given that 2SP = 3SQ and 2ST = 3SR.

Dividing both sides of the equation 2SP = 3SQ by 2 and both sides of the equation 2ST = 3SR by 2, we get:

SP/PQ = 3/2 and ST/SR = 3/2

As the ratio of the length of the side ST to the length of the side SR is equal to the ratio of the length of the side PT to the length of the side PQ.

Therefore, triangle STP is similar to triangle SRQ.

It can also be proven using the fact that PS bisects angle RST which means that the angle PST = PSR. And if two angles of two triangles are equal and the sides are in proportion then the two triangles are similar.

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25 less than the sum of a number and 5 results in 15 what is the number

Answers

The number is 35.

What is an equation?

An equation is a statement of equality between two expressions. It uses the equal sign (=) to show that the expressions on either side of the sign have the same value.

For example 2x+3=5y-7z, and x+y=5 are examples of equations.

In solving your problem,

25 less than the sum of a number and 5 results in 15, can be written as an equation like this:

let x be the number we want to find.

x + 5 =15+25 (25 less than the sum of x+5)

x + 5 = 40

then

x=40-5

x=35

So the number is 35.

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Does 3 4 5 make a right triangle?

Answers

Answer:

Yes

Step-by-step explanation:

The side lengths are a Pythagorean triple.

Write the expression. Then, check all that apply. twice the difference of a number and six A 2-column table with 4 rows. Column 1 is labeled Key Words with entries twice, the difference of, a number, six. Column 2 is labeled Replace with entries 2 times, (minus), n, 6. Replace “a number” with the variable, n. The two operations are multiplication and addition. The two operations are multiplication and subtraction. The constants are 2 and 6. The expression is written as 2(n – 6). The expression is written as 2 × 6 – n.


PLS HELP ME!

Answers

The expression for the sentence that is twice the difference of a number and six is given as follows:

2(n - 6).

How to write the expression?

The sentence for this problem is defined as follows:

"Twice the difference of a number and six."

The number is unknown, hence the variable that represents the number is given as follows:

n.

The difference between the number and six is given by the subtraction of n by 6, as follows:

n - 6.

(the - symbol represents the subtraction).

The expression twice is equivalent to a multiplication of the expression n - 6 by 2, as follows:

2(n - 6).

(the multiplication symbol is implicit before the parenthesis, meaning that the distributive property is applied).

Which is the expression that represents the sentence given at the beginning of the answer.

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Homework Progress
28/37 Marks
a) Complete the prime factor trees for 16 and 40:
16
b)
2
2

2
4
2
2
40
2
What is the lowest Common Multiple of 16 and 40?
2
1
5

Answers

The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and and the common multiple of 16 and 40 could be 2 .

What is prime factor ?

prime factor can be defined as the number which is divisible by that number and the number should be prime.

The prime factor tree for 16 as follows

16 = 2*8 = 2* 2 * 4 = 2*2*2*2

                16

            2         8

                     2    4

                         2     2

The prime factor tree for 40 as follows

40 = 2*20 = 2*2*10 = 2*2*2*5

                40

           2            20

                      2        10

                              2      5

Hence, The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and the common multiple of 16 and 40 could be 2 .

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