Determine the rule for translating ABC to A'B'C'

Answer:  3 1/4 Is the correct answer.

Firslty, we need to find the function, whcih we can do by substituting one into the other:

Now, for the domain we have more complicated approach.

We first have to find the domain for both f(x) and g(x).

The domain of f(x) is all real number, because it is a quadratic polynomial.

The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:

Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).

Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).

The domain of g(x), as we saw, is:

And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:

So, the correct alternative is:

Answer:

11

Step-by-step explanation:

[tex]3^{2}[/tex] + 2

9 + 2

11

The expansion of ( 2x - y⁵)² using algebraic identity, as a polynomial is  4x² - 4xy⁵+ y¹⁰

Algebraic identities are the identities which aids in solving products or powers of algebraic expressions. Most common identities are :

(a+ b)² = a² + 2ab + b²

(a- b)² = a² - 2ab + b²

a² -b² = (a+ b) (a- b), where a and b can be variable or constants or algebraic expressions.

For expanding (2x - y⁵)²

Use identity (a-b)² = a²-2ab+b², let a = 2x and b = y⁵

Then, ( 2x - y⁵)² = (2x)² - 2(2x)( y⁵) + (y⁵)²

⇒  ( 2x - y⁵)²  = 4x² - 4xy⁵+ y¹⁰

Therefore, the standard form of  ( 2x - y⁵)² as a polynomial is  4x² - 4xy⁵+ y¹⁰

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There are 4/5 of the fraction 5/8 in the fraction 1/2

The mathematical statement is given as

"how much of the 5/8 is in the 1/2"

The above means that

Dividend = 1/2

Divisor = 5/8

The number of fractions is then calculated as

Count = Dividend/Divisor

Substitute the known values in the above equation

So, we have the following equation

Count = (1/2)/(5/8)

Evaluate

Count = 4/5

Hence, the number of 5/8 in 1/2 is 4/5

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Answer:

y=2x+11

Step-by-step explanation:

Answer:

18 and 51

Step-by-step explanation:

the sum of the two other angles would be 69 degrees because there has to be 180 degrees in a triangle

given that we can create the equation 6x + 17x = 69 and solve for x

x = 3

so now we can plug in each part of that equation and find out the two angles

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

The question provides that ΔABC and ΔDEF are similar. By the definition of similar triangles, we have that:

Since congruent angles are equal, we have:

From the provided diagram, we have the measures of the following angles:

Comparing the congruent angles, we have that:

The sum of angles in a triangle is 180°. If we add up the angles of ΔDEF, we can get the value of z:

Given the value of z, we can get the measure of [tex]\begin{gathered} m\angle E=10z-5 \\ m\angle E=10(5)-5=50-5=45\degree \end{gathered}[/tex]By comparing the congruent angles, we have that:

ANSWER:

Angle B = 45 degrees.

The value of z is 5.

The point slope form for the line with slope 1/2 and passing through the point ​(-3​,-8​) is y + 8  = m(x + 3)

A linear equation can be represented in point slope form as follows:

y - y₁ = m(x - x₁)

where

Therefore, the point slope form is represented as follows;

m = 1 / 2

It passes through the points ​(-3​,-8​).

Hence,

y + 8  = m(x + 3)

Therefore, the point slope form of the line is y + 8  = m(x + 3)

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The graph of g(x) is the graph of f(x) translated 7 units right

According to the question; g(x)=f(x−7).

Given f(x) then f(x + a) represents a horizontal translation of f(x).

Thus, f(x - 7) represents a shift right of 7 units.

What is Graph ?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

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Answer: The graph of g(x) is the graph of ​f(x)​ translated 7 units right.

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

this is because it is going up if it is going down it’ll be negative and if it was zero it would be flat

a=2cm. b=50cm. x=?

x=b:a. x=50:2. x=25

The driving time in hours for the remaining of Guenther's trip would be = 9.5 hours.

The Speed of a moving object is defined as the change in distance divided by change in time.

The first distance covered by Guenther = 260 miles.

The time it took to cover the first distance= 5 hours.

The remaining distance = 494 miles

The time it will take to cover the remaining distance = X hours

But if , 260 miles = 5 hours

494 miles = X hours

Make X the subject of formula;

X hours= 494 × 5 / 260

X hours = 2,470 / 260

X hours = 9.5 hours.

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Answer:

he has 556 pages in his book

The number has been assigned to be number line and attached as a picture

A number line refers to a picture representing array of numbers arranged to suit the calculation intended to represent.

The picture shows a number line from -6 to 6

The division in the number line is showing two lines representing 1/3 and 2/3 before the next number.

This means that the point before point 6 counting from point 5 is 5 1/3, 5 2/3 then point 6

For the negative direction we have

-5, -5 1/3, -5 2/3, -6

The required answer to the questions attached

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Answer: es

Step-by-step explanation: I know Spanish

Answer:

look at the step by step

Step-by-step explanation:

I think -12 x-12 and something with the other number I think you have to mulitply it all

The amount of money that June has is $40 and Maria has $400. The total amount is $440.

From the information, John has $400 June has 1/10 of that and June has 0.1 of Maria’s money.

Therefore the amount that June has will be:

= 0.1 × John's money

= 0.1 × 400

= 40

June has 0.1 of Maria’s money. Let Maria's money be x. Therefore, 0.1 × x = 40

0.1x = 40

Divide

x = 40 / 0.1

x = 400

Maria's money = 400

Therefore, the total amount that they have will be:

= Amount that John has + Maria's amount

= 400 + 40.

= $440

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Answer:  The equation is written as:   " 7x  +  28  =   8  −  3x " .
  The value for x , when the equation is solved, is:  " -2 ."

Step-by-step explanation:

Let the "unknown number" be represented by the variable, x ;

7 (times) the [sum of: (x + 4)] ; (is the same as):  8 [decreased by]:

  3(times)x ;  
Rewrite:    " 7(x + 4) = 8 − 3x ".   This is the written expression.

____
Now, if we wish to "solve for x" ;
Let's examine the 'left-hand side' of the equation:
     7(x + 4)  ;

Note the 'distributive property' of multiplication:
  a(b + c) = ab + ac ;

____
 So:  7(x + 4) = 7*x + 7*4 =  7x + 28 ;

Now, let's write the entire equation:
  7x + 28 = 8 − 3x  ;
Let's add 3x , and subtract 8 ;  from Each Side of the equation:

 7x + 28 + 3x − 8 = 8  + 3x − 8 ;

→ 7x + 3x + 28 − 8 = 8 − 3x + 3x;

 to get:
 10x + 20  = 0 ;

Now:  Subtract 20 from Each Side of the equation:
  10x + 20 − 20 = 0 − 20 ;

to get:
   10x = -20 ;  Now, divide both sides of the equation by 10 ;

to isolate x on one side of the equation; & to solve for x :

    10x/10 = -20/10 ;
to get:  " x = - 2 " .
____
Alternate method:
 10x + 20 = 0 ;

Divide the Entire Equation by 10 ;

(10x + 20) / 10 = 0____ ;

 to get:  (10x/10) + (20/10) = 0 ;

  →  x + 2 = 0  ;

Now subtract 2 from each side of the equation;

 to isolate x on one side of the equation; & to solve for x :

     x + 2 − 2 = 0 − 2 ;

to get:  " x  =  -2 " .

____

Answer:
 The equation is written as:
 " 7x + 28 =  8 − 3x " .
The value for x, when the equation is solved, is  "-2".
____
Hope this is helpful to you!  Best wishes!
____

Answer:it’s (-1,8)

Step-by-step explanation:

The number of Quarter coins that she has is 8 and the number of Dimes is 16.

It is given in the question that the woman has twice as many Dimes as the quarters in her purse.

We know that the value of Dimes is 0.10$ and the value of Quarters is

0.25 $

Let the number of Quarter coins is y and the number of Dimes coin be u.

According to the question above,

u = 2y  equation (i)

The total value z = 0.25y + 0.10u

Putting here the value of u from equation (i) we have,

z = 0.25y + 0.10(2y)

⇒ z = 0.25y + 0.20y

⇒ z = 0.45y equation (ii)

Now it has been mentioned that if the Dimes were Quarters and the Quarters were the Dimes, she would have $ 1.20 greater than she has now.

So we have,

z + 1.2 = 0.25u + 0.10y

Putting the value of u from above eqation (i),

z + 1.2 = 0.25(2y) + 0.10y

⇒ z + 1.2 = 0.50y + 0.10 y

⇒ z + 1.2 = 0.60y

Putting the value of z from equation (ii)

⇒ 0.45y + 1.2 = 0.60y

⇒ 0.45y - 0.60y = - 1.2

⇒ -0.15y = - 1.2

⇒ y = [tex]\frac{-1.2}{-0.15}[/tex]

⇒ y = 8

Therefore u = 2y

⇒ u = 2 x 8 = 16

Hence the number of Quarter coins is 8 and the number of Dimes is 16

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16 dimes, 8 quarters

I checked RSM it's correct

The graph of the inequality (x + y >1),  will be:

{(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]} and we can shade right-side of the line.

As per the question statement, we are supposed to graph the inequality

x + y >1. So, first we solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For x = 0, y = 1 or (0,1)

For y = 0, x = 1 or (1,0)

So now we can graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

The boundary line would be solid because the inequality contains "or equal to" clause.

Graph: {(x^2+(y-1)^2-0.05)((x-1)^2+y^2-0.05)(x+y-1)=0 [-10, 10, -5, 5]}

We can shade right-side of the line.

Because the inequality operator lacks a "or equal to" phrase, the boundary line will be altered to a dashed line.

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 x = 41/6 is value of x in transversal lines.

What are transversal lines?

 ( 12x + 1)° = 2

 2 = 83°

 ( 12x + 1)° = 83°

  12x° + 1° = 83°

12x = 83 - 1

12x = 82

 x = 82/12

 x = 41/6

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The Domain and the range of the function are given as

x ≥ 0, y ≥ 3000

This is the complete set of values that is used to represent the independent variable in the function. The independent variable that we have here is represented by x and it is 0.

This is the set of the possible values that the dependent variable in the function is to have. The dependent variable is given by y.

The range of x would have to start from 0 for the range of all values of x. Hence x ≥ 0, while y is seen to be in  the form of y ≥ 3000 because this is the value of trout that was stocked.

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Answer:

AB = 32

Step-by-step explanation:

Since line l bisects AB at point M, we have AM = MB.

[tex]4x = 5x - 4[/tex]

[tex]4x + 4 = 5x[/tex]

[tex]x = 4[/tex]

AM = 4(4) = 16, MB = 5(4) - 4 = 16.

So AB = AM + MB = 16 + 16 = 32.

Answer:

The answer is 35:19

Step-by-step explanation:

First what is a ratio?

A relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4. A ratio can also be expressed as a decimal or percentage.

So as a result

= There are 35 mangoes and 19 strawberries

And since we are comparing mangoes to strawberries

The answer would be

= 35:19

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Answer:

x = 25 when y = 8

Step-by-step explanation:

If y is inversely proportional to square root of x we write it as
[tex]y \propto \dfrac{1}{\sqrt{x}}[/tex]

This is also equivalent to
[tex]y = k \dfrac{1}{\sqrt{x}} \;\;\;\;\ \text{ [1]}[/tex]

where k is a constant known as the constant of proportionality

Given y = 10 when x = 16 we can find k by substituting for y and x in [1]

[tex]\rightarrow 10 = k\dfrac{1}{\sqrt{16}}\\\\\rightarrow 10 = k \dfrac{1}{4}\\\\\drightarrow 40 = k \:\:\:\: \text{by multiplying both sides by 4}\\\\\text{which can be written as }\\\\k = 40\\[/tex]

So constant of proportionality k = 40

To find x when y = 8, substitute y and k in [1] to get
[tex]y = k \dfrac{1}{\sqrt{x}}\\\text{Multiply both sides by \sqrt{x} and divide by y at the same time to get}\\\\\sqrt{x} = \dfrac{k}{y}[/tex]

Dividing both sides by y and multiplying by √x gives us
[tex]\sqrt{x} = \dfrac{k}{y}\\\\\text{Substituting k = 40, y = 8}:\\\\\sqrt{x} = \dfrac{40}{8}\\\\\sqrt{x}= 5\\\\\text{Squaring both sides: }\\\\(\sqrt{x})^2 = 5^2\\\\x = 25 \;\;\;\text{since $(\sqrt{x})^2$ = x}[/tex]

The answer is

x = 20

Formulate y=k/x based on the following criteria.

Replace: 10= k/16

Change the sides so that k/16 = 10.

Subtract the coefficient of the variable from both sides of the equation: k = 10×16

Determine the quotient or product: k = 160

Replace with y = 160/x.

Replace with: 8 = 160/x

The denominator cannot be zero if the fraction is defined: as x ≠ 0

As the domain, append the inequality: 8= 160/x, x≠0

Divide the common denominator by both sides of the equation: 8x = 160x/x, x≠0

8x=160x/x, where x ≠ 0. Reduce the fraction.

By the variable's coefficient, multiply both sides of the equation (x=160÷8, x ≠ 0).

Calculate the quotients or product: x = 20,x ≠ 0

Find the junction at x=20.

Answer : x = 20

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A. -234

B. -62

C. [tex]-72+151=79[/tex]

D. [tex]612+144=756[/tex]