Describe the transformations necessary to transform the graph of f(x) into that of g(x).

Notice that

y² - 20y + 100 = y² - 2•10y + 10² = (y - 10)²

Then

√(y² - 20y + 100) = y - 10

is equivalent to

√((y - 10)²) = y - 10

|y - 10| = y - 10

If y ≥ 10, then |y - 10| = y - 10, and

y - 10 = y - 10   ⇒   0 = 0

so there are infinitely many solutions, y ≥ 10.

Otherwise, if y < 10, then |y - 10| = -(y - 10), and

-(y - 10) = y - 10   ⇒   10 = -10

which is false, so there are no solutions in this case.

[tex]\\ \tt\hookrightarrow \sqrt{y^2-20y+100}=y-10[/tex]

[tex]\\ \tt\hookrightarrow y^2-20y+100=(y-10)^2[/tex]

[tex]\\ \tt\hookrightarrow y^2-20y+100=y^2-20y+100[/tex]

Both sides are equal

Hence

Answer:

18 and 24.

Step-by-step explanation:

x + (x + 6) = 42

x + x + 6 - 6 = 42 - 6

x + x = 36

2x = 36

2x/2 = 36/2

x = 18

42 - 18 = 24 The numbers are 18 and 24.

The required two numbers are 18 and 24 and number is 6 more than the the smaller number.

Given, that one number is 6 more than other.

Let the number be x.

Let the other number be x + 6 .

Rewriting in form of equation, that sum of two numbers is 42.

x + (x + 6) = 42

Subtract 6 from both sides.

x + x + 6 - 6 = 42 - 6

Combine like terms,

x + x = 36

2x = 36

Divide by 2 on both sides,

2x/2 = 36/2

x = 18

Thus one number is 18.

The other number is 6 more than 18,

18 + 6 = 24

Thus the two numbers are 18 and 24.

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Answer:

Step-by-step explanation:

For this type of question, it helps to draw the rectangle and label its sides. Label the length x. We are given that the width is 5 miles less than the length, which can be represented algebraically as x-5. So, if y = width, then we have y = x-5.

We are also given that the area is 84 square miles, so how do we find the area of a rectangle? The formula is Area = length * width. Substituting in what we know, we get 84 = x(x-5). We distribute on the right hand side to get 84 = x^2-5x, which is equivalent to x^2-5x-84=0. This can be factored as (x-12)(x+7)=84. The solutions are x=12 or x=-7, but we ignore x=-7 because we cannot have negative length. Thus, the length of the rectangle is 12 miles and the width is 12-5=7 miles.

Answer and Step-by-step explanation:

Alright, so when creating any type of math problem, it is important to identify the parts of the problem and where they go. First, we need to start by putting the problem together. We will use one of the most common forms of equations of math, also known as the linear equation of y=mx+b.

So we have: S(w)=__x + __. S(w) is also equal to f(x), which is also equal to y. So: y= __x + __.

Let's start filling this equation in. So, because it says that she will add 25 dollars each week, The problem is addition. Also, the 25 dollars each week will represent the mx in this situation. Here's why:

The x in this can stand for the amount of week she added this 25 dollars to her account. So:

y= 25x + __.

Now, we can add the 150 to the problem because that is what she started with for this one-time deal. So now we have:

y= 25x + 150.

You can now where everything is represented, but we are not done. Let's change y and x back into S(w) and w like the question asks us to have. So:

S(w)= 25w + 150.

If you want to solve this question, just replace the number of weeks in place of all w's in the equation, like this: S(2)= 25(2) + 150.

I hope that this helps.

Answer:

Check the attachment.

If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of 6.

Step-by-step explanation:

The objects that have the same shape are known as similar figures. Since they are similar in shape it doesn't necessary for those objects to have the same size.

Dilation is the process that enlarges or shrinks the size of an object to its similar figure without changing its size. The Dilation is based on a factor that makes the object to enlarge or shrink.

Since its size has changed so as the perimeter will be changed for both of the figures. The perimeter of an object remains same as the scale factor used to dilate the object.

Consider a square with its side as 2 cm initially and dilated with factor 3.

Perimeter of the square = 4 a. where a is the side.

Then the perimeter of the square will be 8 cm initially.

After dilation the side of the square will be changed as 6.

Then the perimeter will change as 24 cm.

Thus the perimeter of the square initially has increased 3 times after dilation.

Answer:

A

Step-by-step explanation:

9*27=243. If 1cm=9yd, then 27 cm would have to be multiplied by 9 too.

Answer:

Make an eqaution from here.
Let’s make evening 2 “x”

So the first evening has 9 less then the secon evening so…
x-9
Of course theres the second evening (x).

X-9+x
Then the third evening has 4 times as much as the second meeting so…
x-9+x+4x

And when solved, it has to equal 105.

So solve from here.
Combine like terms.

6x-9=105
Isolate

6x=114
x= 19

First evening is 9 less then 19, so 10.

The second evening was 19 calls.
The third evening was 4 times the second evening so, 19*4= 76

1st night = 10

2nd night= 19 calls
Thrid night= 76 calls

Answer:

So the answer would be no, because the length of the rope is needs to be 46 and 35 is not long enough

Step-by-step explanation:

A flagpole, rope and the length of secure point from the flagpole are forming the right triangle, where the rope is a hypotenuse. Let a = 45 and b = 10ft. Use Pythagorean Formula to find length of the rope c

a² + b² = c²

Since we are going to solve for c, we set up the equation like this:

c² = 45² + 10²  (Substitute into formula)

c² = 2,025 + 100 (Add)

c² = 2,125 (Simplify)

√c² = √2,125 (Take the square root from both sides)

c = 46.09772228646444 (Round to the nearest whole number)

c = 46

So the answer would be no, since the length of the rope needs to be 46ft long and a 35 foot piece of rope is not long enough.

Answer:

300 miles/hour

Step-by-step explanation:

The average speed = 1500 / 5

Take 2points

Slope:-

[tex]\\ \rm\hookrightarrow m=\dfrac{1500-0}{13-8}[/tex]

[tex]\\ \rm\hookrightarrow m=\dfrac{1500}{5}[/tex]

[tex]\\ \rm\hookrightarrow m=300[/tex]

Answer:There would be 1 chocolate bar left over

Step-by-step explanation: 2 people can eat 1 bar.

Answer:

1 chocolate bar

Step-by-step explanation:

Since they want to eat 1/2 a bar, 2 people can eat 1 bar. 6 total children / 2 that eat 1 bar = 3 chocolate bars eaten

4 original chocolate bars - 3 already eaten = 1 remaining chocolate bar

A=9

B=11

C=12

D=15

THE LENGTH OF THE LARGEST POSSIBLE SIDE IS

or,9+11+12+15

or,47 answer

Answer:

x = 0.7

y = 4.2

Coordinate form : (0.7, 4.2)

Step-by-step explanation:

Solve:

Plug in in 6x for y in 4x + y = 7

Plug in 0.7 for x in y = 6x

x = 0.7
y = 4.2

Coordinate form : (0.7, 4.2)

-Chetan K

Answer:

x = 7/10 (fraction)

Step-by-step explanation:

Given that y = 6x, we can substitute it for y

That makes your equation:

4x + 6x = 7

Now, all we need to do is solve for x:

Step 1: Add similar elements:

4x+6x=10x, which gives you 10x=7

Divide next:

10x/10=7/10 (10/10 = 0 and 7/10 = 7/10)

x= 7/10

Answer:

308

Step-by-step explanation:

Answer: 30&90

Step-by-step explanation:

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{5}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{13^2-5^2}=b\implies \sqrt{144}=b\implies 12=b[/tex]

Answer:

none

Step-by-step explanation:

there's only ten cubes

Answer:

5 hope this helps

Step-by-step explanation:

Answer:

I thino the awnser is 103.5

Step-by-step explanation:

Answer:

16,12,10,8

Step-by-step explanation:

a+(n-1)d

20-22=18-2=-2

Answer:

B. Of the students who pack lunch, the probability a student is interested in gluten free food is greater than the possibility a student isn’t

Step-by-step explanation:

Answer:

1000 dollars

Step-by-step explanation:

2000-1000 = 1000

Answer:

24 [tex]in^{3}[/tex]

Step-by-step explanation:

volume formula= l x w x h

Box A:

4 x 3  x 4 = 48

Box B: 48/2 = 24

Answer:

1) x = 3 and y = -2

2) x = 2 and y = 1

3) x = -2 and y = -1

4) x = 3 and y = 2

5) x = 2

6) x = 2 and y = -3

7) x = 4 and y = 3

8) x = -3 and y = -6

Step-by-step explanation:

1. Answer :

y = -2

4x - 3y = 18 ----(1)

Substitute y = -2 in (1).

4x - 3(-2) = 18

4x + 6 = 18

Subtract 6 from both sides.

4x = 12

Divide both sides by 4.

x = 3

So,

x = 3 and y = -2

2. Answer :

y = 6x - 11 ----(1)

2x + 3y = 7 ----(2)

Substitute y = 6x - 11 in (2).

2x + 3(6x - 11) = 7

2x + 18x - 33 = 7

20x - 33 = 7

Add 33 to both sides.

20x = 40

Divide both sides by 20.

x = 2

Substitute x = 2 in (1).

y = 6(2) - 11

= 12 - 11

= 1

So,

x = 2 and y = 1

3. Answer :

x = -3y - 5 ----(1)

4x - 5y = -3 ----(2)

Substitute x = -3y + 5 in (2).

4(-3y - 5) - 5y = -3

-12y - 20 - 5y = -3

-17y - 20 = -3

Add 20 to both sides.

17y = -17

Divide both sides by 17.

y = -1

Substitute y = -1 in (1).

x = -3(-1) - 5

= 3 - 5

= -2

So,

x = -2 and y = -1

4. Answer :

x = 5y - 7 ----(1)

-2x - 3y = -12 ----(2)

Substitute x = 5y - 7 in (2).

-2(5y - 7) - 3y = -12

-10y + 14 - 3y = -12

-13y + 14 = -12

Subtract 14 from both sides.

-13y = -26

Divide both sides by -13.

y = 2

Substitute y = 2 in (1).

x = 5(2) - 7

= 10 - 7

= 3

So,

x = 3 and y = 2

5. Answer :

5x + 3y - 8 = 0 ----(1)

2x - 3y - 6 = 0 ----(2)

Solve for 3y in (1).

5x + 3y - 8 = 0

Subtract 5x from both sides.

3y - 8 = -5x

Add 8 to both sides.

3y = -5x + 8

Substitute 3y = -5x + 8 in (2).

2x - (-5x + 8) - 6 = 0

2x + 5x - 8 - 6 = 0

7x - 14 = 0

Add 14 to both sides.

7x = 14

Divide both sides by 7.

x = 2

6. Answer :

x - 3y - 11 = 0 ----(1)

5x + y - 7 = 0 ----(2)

Solve for x in (1).

x - 3y - 11 = 0

Subtract 3y and 11 to both sides.

x = 3y + 11 ----(3)

Substitute x = 3y + 11 in (2).

5(3y + 11) + y - 7 = 0

15y + 55 + y - 7 = 0

16y + 48 = 0

Subtract 48 from both sides.

16y = -48

Divide both sides by 16.

y = -3

Substitute y = -3 in (3).

x = 3(-3) + 11

= -9 + 11

= 2

So,

x = 2 and y = -3

7. Answer :

2x - 3y = -1 ----(1)

y = x - 1 ----(2)

Substitute y = x - 1 in (1).

2x - 3(x - 1) = -1

2x - 3x + 3 = -1

-x + 3 = -1

Subtract 3 from both sides.

-x = -4

Multiply both sides by -1.

x = 4

Substitute x = x in (3).

y = 4 - 1

= 3

So,

x = 4 and y = 3

8. Answer :

-4x + y = 6 ----(1)

-5x - y = 21 ----(2)

Solve for y in (1).

-4x + y = 6

Add 4x to both sides.

y = 4x + 6 ----(3)

Substitute y = 4x + 6 in (2).

-5x - (4x + 6) = 21

-5x - 4x - 6 = 21

-9x - 6 = 21

Add 6 to both sides.

-9x = 27

Divide both sides by -9.

x = -3

Substitute x = -3 in (3).

y = 4(-3) + 6

= -12 + 6

= -6

So,

x = -3 and y = -6

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Thank You!

Answered by: ms115

Answer:

See below for all answers and explanations

Step-by-step explanation:

Problem 1

4x - 3y = 18

4x - 3(-2) = 18 <-- Substituting y = -2

4x + 6 = 18

4x = 12

x = 3

Problem 2

2x + 3y = 7

2x + 3(6x-11) = 7 <-- Substituting y = 6x - 11

2x + 18x - 33 = 7

20x - 33 = 7

20x = 40

x = 2

y = 6x - 11 <-- Substituting x=2 to solve for y

y = 6(2) - 11

y = 12 - 11

y = 1

Problem 3

4x - 5y = -3

4(-3y-5) - 5y = -3 <-- Substituting x = -3y - 5

-12y - 20 - 5y = -3

-17y - 20 = -3

-17y = 17

y = -1

x = -3y - 5 <-- Substituting y = -1 to solve for x

x = -3(-1) - 5

x = 3 - 5

x = -2

Problem 4

-2x - 3y = -12

-2(5y-7) - 3y = -12 <-- Substituting x = 5y - 7

-10y + 14 - 3y = -12

-13y + 14 = -12

-13y = -26

y = 2

x = 5y - 7 <-- Substituting y=2 to solve for x

x = 5(2) - 7

x = 10 - 7

x = 3

Problem 5

5x - 3y - 8 = 2x - 3y - 6 <-- Setting equations equal to each other

5x - 8 = 2x - 6 <-- Eliminating y-variable to solve for x

3x - 8 = -6

3x = 2

x = 2/3

5x - 3y - 8 = 0 <-- Substituting x = 2/3 into first equation

5(2/3) - 3y - 8 = 0

10/3 - 3y - 8 = 0

10/3 - 3y - 24/3 = 0

-14/3 - 3y = 0

-3y = 14/3

y = -14/9

Problem 6

x - 3y - 11 = 0 <-- Solve for x

x - 3y = 11

x = 11 + 3y

5x + y - 7 = 0

5(11+3y) + y - 7 = 0 <-- Substituting x = 11 + 3y

55 + 15y + y - 7 = 0

55 + 16y - 7 = 0

48 + 16y = 0

16y = -48

y = -3

x = 11 + 3y <-- Substitute y=-3 into first equation to solve for x

x = 11 + 3(-3)

x = 11 - 9

x = 2

Problem 7

2x - 3y = - 1

2x - 3(x-1) = -1 <-- Substituting y = x - 1

2x - 3x + 3 = -1

-x + 3 = -1

-x = -4

x = 4

y = x - 1 <-- Substitute x=4 to solve for y

y = 4 - 1

y = 3

Problem 8

-4x + y = 6 <-- Solve for y in first equation

y = 6 + 4x

-5x - y = 21

-5x - (6+4x) = 21 <-- Substituting y = 6 + 4x

-5x - 6 - 4x = 21

-9x - 6 = 21

-9x = 27

x = -3

y = 6 + 4x <-- Substitute x = -3 to solve for y

y = 6 + 4(-3)

y = 6 - 12

y = -6

Answer:

6, 12, 24, 48, 96.

All the terms are multiples of 6.

Step-by-step explanation:

The given rule is to multiply by 2.

To find the next 4 numbers, we need to multiply 6, and the products that we've obtained after.

First number:

[tex]6 \times 2 = 12[/tex]

12 is our first number.

Second Number:

[tex]12 \times 2 = 24[/tex]

24 is our second number.

Third Number:

[tex]24 \times 2 = 48[/tex]

48 is our third number.

Last Number:

[tex]48 \times 2 = 96[/tex]

96 is our last number.

All the terms are multiples of 6.

Proof:

option b would be the correct one

Answer:

[tex]\huge\boxed{\sf 34}[/tex]

Step-by-step explanation:

P = Parenthesis

E = Exponents

D = Division

M = Multiplication

A = Addition

S = Subtraction

In that order:

= 3 × 9 + 7

Multiplying first

= 27 + 7

Adding after

= 34

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

34

Step-by-step explanation:

3 x 9 + 7

Using PEMDAS M is first and M is multiplication so you multiply first.

27 + 7

You then add because that’s what is left.

34

Your answer is : 34

Hope it helps! Stay safe!

Answer:

5 sec

Step-by-step explanation:

Hit the water, means h = 0

Solve -16t^2 + 68t +60 =0

4t^2 - 17t - 15 = 0

(4t + 3)(t - 5) = 0

so t = 5 sec

Answer:

the theorem states that the length of the hypotenuse when squared is equal to the addition of the adjacent and opposite when squared

Answer:

BD=ALTITUDES

CD=MEDIANS

AD=ANGLE BISECTORS