count by 5 from 6 to 51

[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]

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)

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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

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Answer:

Step-by-step explanation:

[tex](\frac{5}{2} -\frac{3}{4} )-\frac{1}{4} (1-x)=\frac{1}{2}[/tex]

[tex](\frac{10}{4} -\frac{3}{4}) -\frac{1}{4} -\frac{1}{4} x=\frac{1}{2}[/tex]

[tex]\frac{7}{4} -\frac{1}{4} -\frac{1}{4} x=\frac{1}{2}[/tex]

[tex]\frac{6}{4} -\frac{1}{4}x=\frac{1}{2}[/tex]

[tex]1=\frac{1}{4} x[/tex]

[tex]4=x[/tex]

[tex]x=4[/tex]

Hope this helped! Have a great day!

Answer:

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

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

Step-by-step explanation:

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."

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

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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:

$92

Step-by-step explanation:

32+4x where x is 15

32+(4*15)=?

32+60=92

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).

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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:

l speak frenchjwhehdgdhehdhs

Answer:

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

Step-by-step explanation:

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.

Answer:

  (x +3)² +(y -4)² = 9

Step-by-step explanation:

You want the equation of a circle with center (-3, 4) and radius 3.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

You have a circle with center (h, k) = (-3, 4) and radius r = 3. Using these values in the above equation, we find the circle equation to be ...

  (x -(-3))² +(y -4)² = 3²

  (x +3)² +(y -4)² = 9

[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.

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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.

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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

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.

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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.

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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:

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

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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.

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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]

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Answer:

The answer is (−1,−1)

Step-by-step explanation:

Hope this helps!

Sorry If I'm wrong

Answer:

20

Step-by-step explanation:

8x2=16 and 2/4 times 8 is 4 so 20