A figure is translated 3 units to the right and down 2 units. Select the algebraic
expression that shows how the translation affects the coordinates of the preimage.

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:

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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The degree of the polynomial 3x^6 - 4x^4 + 5x - 6 degree of polynomial is 6

Definition of degree of polynomial

The degree of polynomials in one variable is the highest power of the variable in the algebraic expression.

Here the algebraic expression is 3x^6 - 4x^4 + 5x - 6

Polynomials appear in lots of regions of arithmetic and technological know-how. for instance, they're used to form polynomial equations, which encode a extensive variety of issues, from essential word issues to complex medical troubles;

they are used to outline polynomial features, which seem in settings ranging from fundamental chemistry and physics to economics and social technological know-how; they're utilized in calculus and numerical analysis to approximate other features.

In advanced mathematics, polynomials are used to assemble polynomial jewelry and algebraic sorts, which are imperative ideas in algebra and algebraic geometry.

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In linear equation, there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.

What are a definition and an example of a linear equation?

Let the number of 250g=0.25  kg jars be x and that of 500g=0.5 kg jams be y;

therefore:

total number of jars was

x+y=511

x=511-y..........i

total amount kg was:

0.25x+0.5y=186.5....ii

substituting i in ii

0.25(511-y)+0.5y=186.5

127.75-0.25y+0.5y=186.5

solving for y we get:

0.25y=186.5-127.75

0.25y=58.75

y=58.75/0.25

y=235 jars

and

x=511-x

=511-235

=276

hence , there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.

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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

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."

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:

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

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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The early pay will always be $60 no matter the number of days, the deposit plus will be $35, $50, $65, $80, and the daily pay would be $0, $30, $60 $90, $120.

Based on the information, if you choose the option early pay, you will pay only $60 and you can swim as many days as you want, due to this, the total paid will always be $60.

Day 0: $20 (deposit)

Day 5: $20 (deposit) + $15 = $35

Day 10: $20 (deposit) + $30 = $50

Day 15: $20 (deposit) + $45 = $65

Day 20: $20 (deposit) + $60 =$80

Day 0: $0

Day 5: $30 (6x5)

Day 10: $60 (6x10)

Day 15: $90 (6x15)

Day 20: $120 (6x20)

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Answer:

20

Step-by-step explanation:

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

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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The value of logarithmic expression log s√7/t² is log (7/t²)^1/s.

By considering the given  logarithmic expression

log s√7/t²

=log (7/t²)^1/s

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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The x-intercept of the function are (√2-1,0) and(-√2-1,0). and the y-intercept of the function is  (0,-1) and the inverse of the function is f⁻¹(x)=±√(x+2)-1.

The x and y intercepts of a function is defined as the points on the cartesian plane where the graph of the function intersects  the co-ordinate axes.

The intercepts are calculated by substituting the value of x and y to zero to calculate the corresponding variable.

The inverse of a function y=g(x) is calculated by finding the value of x from the equation.

At x=0 , we get the y intercept.

f(0)=(0+1)²-2

or, f(0)=-1

So the y-intercept is at (0,-1) .

At y=0 we get the x-intercept.

f(x)=0

or,(x+1)²-2=0

or,(x+1)²=2

or, x+1= ±√2

or, x=±√2-1

Therefore the x-intercepts are (√2-1,0) and(-√2-1,0).

Now let us calculate the inverse of the function.

y=(x+1)²-2

or,y+2=(x+1)²

or, x+1=±√(y+2)

or, x=±√(y+2)-1

Hence the inverse of the function is written as

f⁻¹(x)=±√(x+2)-1

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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!

[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]

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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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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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

The product or multiplication of the polynomials is given as

x² +11x + 24.

A result or product is produced by multiplication or a statement that lists the factors to be multiplied.

Given (x+8) (x+3)

let us find the product :

= x² + 8x + 3x + 24

= x² +11x + 24

Let us now test the equivalency .

(x+8) (x+3) = (1+8)(1+3) = (9)(4) = 36

x² +11x + 24 = (1)² + 11(1) + 24 = 36

Hence we can see that the product is same in both the cases.

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Answer:

The answer is (−1,−1)

Step-by-step explanation:

Hope this helps!

Sorry If I'm wrong

Answer:

l speak frenchjwhehdgdhehdhs

Answer:

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

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

Step-by-step explanation:

[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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Answer:

x= 7

Step-by-step explanation:

3x= 13+8

3x= 21

x= 21/3

x= 7