Ms. Moya has received 13 Starbucks cards from students and generally gets 2 more
each year she teaches. Ms. Powers has only ever been given 1 Starbucks gift card but
plans to get 5 more each year she teaches. Which equation models the situation to find
the number of years before they have the same number of Starbucks cards?

The value of the function f(x) + 1 is 3x + 3

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The functions are given as

f(x) = 3x + 2

g(x) =x^2 - x

To calculate the value of the function f(x) + 1, we use the following definitions:

New function = f(x) + 1

Substitute f(x) = 3x + 2 in New function = f(x) + 1

So, we have

New function = 3x + 2 + 1

Evaluate the sum

So, we have

New function = 3x + 3

Rewrite as

So, we have

f(x) + 1 = 3x + 3

Hence, the value of the function f(x) + 1 is 3x + 3

Read more about functions at

https://brainly.com/question/1415456

#SPJ1

Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 8}{log \\3}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

[tex]log_38[/tex]

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

[tex]log_38[/tex] =  [tex]\frac{log \ 8}{log \ 3}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 8}{log \\3}[/tex]

To know more about logarithms, visit :

brainly.com/question/5956809

#SPJ4

After evaluating the logarithm log₂ 2⁵, we get the result as 5.

The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.

For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output.  The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.

For example, the natural logarithm of 78 is written as ln 78. The natural logarithm determines how much we need to multiply "e" to get the required output.

We need to evaluate log₂ 2⁵Using the property logₐ (mⁿ) = n logₐ m log₂ 2⁵ can be written as

log₂ 2⁵ = 5 log₂ 2

We know that logₐ a = 15 log₂ 2= 5

Therefore, after evaluating the logarithm log₂ 2⁵, we get the result as 5.

Learn more about logarithms here:

brainly.com/question/25710806

#SPJ4

Answer:

#9 has 8 vertices

# 10 has 5 vertices

Step-by-step explanation:

A vertex is is a point where two or more curves, lines, or edges meet.  The word "vertices" is the plural of the word "vertex."

Answer:

see explanation

Step-by-step explanation:

substitute the values of x, situated inside the parenthesis into f(x)

f(- 1) = - 1 - 5 = - 6

f(0) = 0 - 5 = - 5

f(1) = 1 - 5 = - 4

f(2) = 2 - 5 = - 3

f(5) = 5 - 5 = 0

f(8) = 8 - 5 = 3

1) Substitute x = -1 into f(x) = x - 5

2) Substitute x = 0 into f(x) = x - 5

3) Substitute x = 1 into f(x) = x - 5

4) Substitute x = 2 into f(x) = x - 5

5) Substitute x = 5 into f(x) = x - 5

6) Substitute x = 8 into f(x) = x - 5

Answer:

The answer is (−1,−1)

Step-by-step explanation:

Hope this helps!

Sorry If I'm wrong

Answer: 13.89 in ==> B

Step-by-step explanation:

A=area of rectangle, l=length, w=width

A=l*w

108.35=7.8*w

108.35/7.8=7.8w/7.8

w=108.35/7.8

w=13.891 ==> w=13.89 in==> B

Answer: 21

Step-by-step explanation:

When it comes to finding the range, you must take the biggest number and subtract it from the smaller number, therefore in your question the answer is

25 - 4 = 21

Hope it helped :D

The solution for the given logarithmic expression log₂4+3 log₂9 as a single logarithm is log₂ (2916).

A logarithmic equation is one that includes a logarithm in the variable x.

An exponential formula is one where the variable is represented by an exponent. To answer exponential equations, first determine whether both sides of the equation can be written as powers of the exact number. If you can't, take the common logarithm from both of the equation's sides and use property 7 to solve the problem.

Now, as per the stated condition in question;

The expressed equation is;

= log₂4+3 log₂9

Using the Power Rule in the second term.

= log₂4+log₂9³

=  log₂4+log₂729

As, the base of each log term is 2. We can use product rule to simplify the equation.

= log₂(4×729)

= log₂ (2916) [As a single log function]

Therefore, the simplification of the given logarithmic expression as the single logarithm is log₂ (2916).

To know more about the logarithmic expression, here

https://brainly.com/question/23268551

#SPJ4

According to the box-and-whisker plot,

5)The 25th quartile = 60

6)The 75th quartile = 100

7)The range = 40

Box-and-whisker plot allows us to determine the mean, the largest or the lowest number in the data set as well as the quartiles in the data.

In this case, from the given figure,

Median is equal to = 80,

The range is equal to = 110-40

We can subtract the value,

So we can write,

The range is equal to = 70.

The 25th quartile is equal to = 60

The 75th quartile is equal to = 100.

The range is equal to = 100-60

We can subtract the value,

So we can write,

The range is equal to = 40. 

So,

Then,

The median=80

The range=70

Therefore,

According to the box-and-whisker plot,

5)The 25th quartile = 60

6)The 75th quartile = 100

7)The range = 40.

To learn more about quartile visit : brainly.com/question/4204333

#SPJ9

The number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.

We are given that;

a represents the number of drinks purchased.

y represents the number of tacos purchased

He must buy a minimum of 11 drinks and tacos altogether. Thus, the inequality that describes this is;

2a + 4y ≤ 40

a + y ≥ 11

The inequality graph that represent the given system of inequalities is as shown in the atatched file.

From the given inequality graph, we can tell that one possible solution is; (a, y) = (2, 9)

Thus, the number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.

Read more about Inequality Graph at; https://brainly.com/question/11234618

#SPJ1

Answer: Option D is correct.

Step-by-step explanation:

Given: 7 and 11

We need to find the geometric mean of 7 and 11.

Geometric series whose common ratio is equal.

The geometric mean of two numbers is the square root of the product of two numbers.

If a, b and c are in GP then the geometric mean is b

The geometric mean of any two numbers a and b is

The given numbers are 7 and 11

Geometric mean is [tex]\sqrt 7x11\\[/tex]

Geometric mean: [tex]\sqrt{x} 77[/tex]

Answer:

Typically when solving an equation with one variable, your objective is to isolate the variable on one side of the equation. This can be done adding/subtracting number to cancel them out on one side. You can also multiply/divide coefficients in order to isolate a variable.

Example:

Add -4 to both sides to isolate the variable.

Simplify.

Divide both sides by 2 to isolate the variable on one side.

Step-by-step explanation:

[tex]\large\bf\implies{infinitely \:many\: solutions}[/tex]

Alternate forms :

[tex] \large \bf \implies{x \in ( - \infty \: , \infty)}[/tex]

[tex] \bf \longrightarrow{3(2x - 2) = 6(x - 1)}[/tex]

[tex] \bf \longrightarrow{6x - 6 = 6x - 6}[/tex]

[tex] \bf \longrightarrow{6x - 6x = - 6 + 6}[/tex]

[tex] \bf \longrightarrow{0 = 0}[/tex]

[tex]\bf \longrightarrow{infinitely \:many\: solutions}[/tex]

Answer:

The answer is around 50,000,000,000 years so its E

Step-by-step explanation:

Answer:

l speak frenchjwhehdgdhehdhs

The simplified form of the expression is 6⁶

From the question, we are to simplify the given expression

The given expression is

6^5 * 2^3 * 6^4 / 12^3

That is,

6⁵ × 2³ × 6⁴ / 12³

Simplifying

6⁵ × 2³ × 6⁴ / 12³

6⁵ × 6⁴ × 2³ / 12³

Applying the exponents rule

6⁵ ⁺ ⁴ × 2³ / 12³

6⁹ × 2³ / 12³

Expanding 12³, we get

6⁹ × 2³ / 6³ × 2³

= 6⁹ / 6³

= 6⁹ ⁻ ³

= 6⁶

Hence, the simplified form of the expression is 6⁶

Learn more on Simplifying an expression here: https://brainly.com/question/19284077

#SPJ1

Answer:

x = 2 + [tex]\sqrt{3}[/tex] i

x = 2 - [tex]\sqrt{3}[/tex] i

Step-by-step explanation:

we get f(-4)= -52 and f(3)=4

suppose f(x)= -2x^2+6x+4

we have to compute f( -4)  and  f(3)

The value of f(-4) is found by substituting -4 into the equation per variable, solving and simplifying as needed, to get the answer.

f(x)= -2x^2+6x+4

we have to compute f( -4)  

then f( -4)= -2(-4)^2+6(-4) +4

               = -32-24+4

               = -52

similarly ,The value of f(3) is found by substituting 3 into the equation per variable, solving and simplifying as needed, to get the answer.

f(x)= -2x^2+6x+4

we have to compute f( 3)  

then f( 3)= -2(3)^2+6(3) +4

               = -18+18+4

               =4

Hence we get f(-4)= -52 and f(3)=4

learn more about of substitution here

https://brainly.com/question/20261270

#SPJ9

The result of simplifying each number 64²/₃ 64²/₃  using the exponent rules is 256

To solve this exercise we have to resolve algebraic operations following the exponent rules.

64²/₃ * 64²/₃

The base number 64 is the same that: 4³, then we get:

(4)³ ⁽²/₃⁾ * (4)³ ⁽²/₃⁾

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

4⁽³*²/³⁾ * 4⁽³*²/³⁾

4⁽⁶/³⁾ * 4⁽⁶/³⁾

(4)² * (4)²

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

4⁽²⁺²⁾

4⁴

4*4*4*4

256

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

Learn more about exponent at: brainly.com/question/847241

#SPJ4

[tex]81^{\frac{1}{4} }[/tex] can be simplified into 3.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 81 = 3 x 3 x 3 x 3 = [tex]3^{4}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e., [tex](x^{m})^{n} = x^{mn}[/tex]

According to the given condition,

∴ [tex]81^{\frac{1}{4} }[/tex] = [tex](3^{4} )^{\frac{1}{4} }[/tex]

Applying the law of indices mentioned above,

[tex](3^{m})^{n} = 3^{4 X\frac{1}{4} }[/tex]

= 3.

Thus, the

[tex]81^{\frac{1}{4} }[/tex] can be simplified into 3.

To learn more about laws of indices, refer to this link:

brainly.com/question/27432311

#SPJ4

2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.

Given: 2 log (x + 1) = 5

=> log (x + 1) = [tex]\frac{5}{2}[/tex]

Raising both sides by 10, in order to remove the logarithm:

=> [tex]10^{log_{10}(x+1)} = 10^{2.5}[/tex]

=> x + 1 = 316.22 ( as [tex]a^{log_a(x)} = x[/tex])

=> x = 315.22

Hence, 2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

The situation in which a function behaves differently over different parts of its domain is modeled by considering it to be a piecewise function.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable

Such a situation can be explained through an example:

f(x) =   { x, for x > 0

        {     1, for x = 0

        { -x, for x < 0

now, when we take x value less than 0, say x= -1

   thus, f(x)= f(-1)= -(-1) = 1 , here we used f(x) given x<0

now, when we take x value more than 0, say x= 1

   thus, f(x)= f(1)= (1) = 1, here we used f(x) given x>0

now, when we take x =  0,

   thus, f(x)= f(0)= 1, here we used f(x) given x=0

this is how we model piecewise function, we  use f(x) as per the value of x. Following image shows plotted answer for this example.

Since inequalities given are exclusive of 0, we leave the dot at the origin unfilled. Now, for x = 0. Since the value is constant at f(x) =1, we pointed a point at (0,1)

more questions on piecewise functions

brainly.com/question/12089993

#SPJ1

Answer:

$92

Step-by-step explanation:

32+4x where x is 15

32+(4*15)=?

32+60=92

Answer:

undefined

Step-by-step explanation:

4x-32=4x+2

-4x

-32=2

undefined

Step-by-step explanation:

Reread the underlined sentence on page 4.

What does the figurative language in this

sentence suggest about the narrator?

He feels that people should have used better tools

to help them detect advanced life forms on other

planets.

He sympathizes with people for not apprehending

that there was advanced life on other planets.

He is unable to believe that there could be any

form of life more advanced than humans.

He blames people's exaggerated idea of their

superiority for their failure to imagine life more

advanced than themselves.