1. The equation is of the form , where a, b, and c are all positive integers and . Using this equation as a model, create your own equation that has extraneous solutions. (a) Using trial and error with numbers for a, b, and c, create an equation of the form , where a, b, and c are all positive integers and such that 7 is a solution. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (b) Solve the equation you created in Part 2a. (c) If your solution in Part 2b did not have an extraneous solution, revise your equation so that 7 is one solution and there is an extraneous solution. If your solution in Part 2b did have an extraneous solution, create another equation with different values of a, b, and c that also has 7 as one solution and an extraneous solution.

Answers

Answer 1

Answer:

[tex]7 + a = \sqrt{7b + c}[/tex] --- equation

[tex]a = 3; b =5\ and\ c = 65[/tex] --- the equation is true for these values

[tex]a = 4; b=5\ and\ c = 10[/tex] --- the equation is extraneous for these values

Step-by-step explanation:

Given

[tex]x +2 = \sqrt{3x + 10[/tex]

[tex]x + a = \sqrt{bx + c}[/tex]

Solving (a): Equation to solve for a, b and c, using trial by error where [tex]x = 7[/tex]

We have:

[tex]x + a = \sqrt{bx + c}[/tex]

Substitute 7 for x

[tex]7 + a = \sqrt{7b + c}[/tex] --- This is the equation

Solving (b): Solve for a, b and c --- to make the equation true

[tex]7 + a = \sqrt{7b + c}[/tex]

Let a = 3 ----- Here, we choose a value for a

[tex]7 + 3 = \sqrt{7b + c}[/tex]

[tex]10 = \sqrt{7b + c}[/tex]

Square both sides

[tex]100 = 7b + c[/tex]

Let b = 5 --------- Here, we choose a value for b

[tex]100 = 7*5 + c[/tex]

[tex]100 = 35 + c[/tex]

Subtract 35 from both sides

[tex]c = 65[/tex]

So, [tex]x + a = \sqrt{bx + c}[/tex] is true for

[tex]a = 3; b =5\ and\ c = 65[/tex]

Solving (b): Solve for a, b and c --- to make the equation false

[tex]7 + a = \sqrt{7b + c}[/tex]

Substitute [tex]a = 4; b=5\ and\ c = 10[/tex]

So, we have:

[tex]7 + 4 = \sqrt{7*5 + 10}[/tex]

[tex]11 = \sqrt{35 + 10}[/tex]

Square both sides

[tex]121 = 45[/tex] --- This is false

i.e.

[tex]121 \ne 45[/tex]


Related Questions

Which ordered pair is a solution to the following linear system?

y= x + 1

y = -2x + 1

A) (-1,-2)
B) (2,1)
C) (0,1)
D) (0,0)

Answers

Answer:

C. (0,1)

Step-by-step explanation:

x + 1 = -2x + 1

3x = 0

x = 0

y = (0) + 1

y = 1

Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.

6 x = negative 2 x minus 4.5

What errors did Emma make? Select two options.
She should have used division to represent the quotient of six and x.
She should not have included an equal sign.
She should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5).
She should have subtracted the difference (x minus 4.5) from Negative 2.
She should have used parentheses to show that Negative 2 is multiplied by (4.5 minus x).

Answers

The errors Emma made from her translation are;

She should have used division to represent the quotient of six and x.

She should have used parentheses to show that Negative 2 is multiplied by (4.5 minus x).

The correct answer choice is option A and E

What errors did Emma make?

quotient of six and a number, x, is the same as negative two times the difference of x and 4.5

6/x = -2 × (4.5 - x)

6/x = -2(4.5 - x)

Ultimately, Emma should have translated the statement in the form 6/x = -2(4.5 - x).

Read more on algebra:

https://brainly.com/question/4344214

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Answer: A and C

Step-by-step explanation:

A car was traveling at a rate of x miles per
hour for 3 hours. How far did the car travel?

Answers

Is there more information? All what I got from this was m=3x (“m” means slope!)

2+4 = 8 and ½ + ½ = 1 is an example of which type of statement?

Answers

Answer:

it is an example of conditional statement.

hope it helps

I need help please!!!

Answers

Answer:

answer is line m........

At a grocery​ store, you want to buy lb of 2 1/2cheese What decimal should the digital scale​ show

Answers

Answer:

The tenths place.

Step-by-step explanation:

If you want to buy 2 1/2 lb of cheese, you want to buy 2.5lbs. The tenths place is the first place after the decimal, and the place the scale needs to show to show you 2.5lbs.

Answer:

tenths place

Step-by-step explanation:

y=−x+4
y=x−2

What is the solution for the system of equations?

Answers

Step-by-step explanation:

y=-x+4

y=x-2

adding both the equations we get

2y=2

:. y=1

and putting the value of y in equation first we get

x=3

The owner of a produce stand is selling baskets of peaches, priced by the kilogram. She rounded each measurements to the nearest 2 1 ​ start fraction, 1, divided by, 2, end fraction of a kilogram.How much heavier is the heaviest basket than the second heaviest basket?

Answers

Answer:

[tex]1\frac{1}{2}kg[/tex]

Step-by-step explanation:

Given

[tex]a = 6\frac{1}{2}[/tex] --- heaviest

[tex]b = 5[/tex] --- second heaviest

Required

The difference (d)

This is calculated as:

[tex]d = 6\frac{1}{2} - 5[/tex]

[tex]d = 1\frac{1}{2}[/tex]

CAN SOMEONE PLEASE HELP?!

Answers

Answer:

70in.

Step-by-step explanation:

Since the given formula for perimeter is [tex]2l + 2w[/tex], all that's needed is to fill in the blanks with the numbers they give us.

[tex]2l + 2w[/tex]                  (Fill in for given length and width)

[tex]2(20)+2(15)[/tex]         (Multiply)

[tex]40 + 30[/tex]                  (Add)

[tex]70[/tex]

It tells us that length ([tex]l[/tex]) is 20 and that width ([tex]w[/tex]) is 15. So all that we have to do is use the equation it gave us to solve the equation.

I hope this helped :)

Step-by-step explanation:

Hey there!

Here;

Length (l) = 20 in

Width (w) = 15 in

Perimeter(p) = ?

We have;

Perimeter of rectangle (p) = 2l + 2w

= 2(l+w)

= 2(20+15)

= 2*35

= 70 inches

Therefore, perimeter of rectangular picture is 70 inches.

Hope it helps!

Choose the correct simplification of the expression (x?y)?
Ох^4у^3
Ox^6y^6
Ох^4у^2
Oxy^4

Answers

C, multiply the powers in the parentheses by 2

What is 3/5 divided by -1/5

Answers

Answer:

-0.12

Step-by-step explanation:

(3/5) / (-1/5) = -0.12

-0.12 i think............

20% of a number is 30. What is 60% of the number?

Answers

Answer:

90

Step-by-step explanation:

30 / 0.2 = 150

150 x 0.60 = 90

Step-by-step explanation:

Well, if 20% = 30, then 40% = 60, and 60% = 90

Edgar has a business painting Lines on the Highway. His workers can pay online 1/6 of my along every 10 minutes. At the end of an eight-hour workday, how many miles of wine will his workers have painted.

Answers

Answer:

8 miles

Step-by-step explanation:

In every 10 minutes, the workers paint 1/6 miles

Total number of minutes in 8 hours = 8 *60 = 480

Number of ten minutes in 480 minutes = 48

total miles of wine painted = 1/6 * 48 = 8 miles

The box plots show the basketball scores for two teams.

Answers

It’s c trust me I’m a goat at basketball

Answer:

C

Step-by-step explanation: A.P.E.X

The sum of a number and 3:

Answers

Answer:

x+3?

Step-by-step explanation:

honestly, there is not alot of information present here. so when a hear "a number" i think variable.... which would be set up as x+3

What is the direct variation between x and y when x=7 and y=3 1/2?

Answers

Answer:

[tex]{ \tt{y \: \alpha \: x }} \\ { \tt{y = kx}} \\ \\ { \bf{3 \frac{1}{2} = k \times 7 }} \\ { \bf{k = \frac{1}{2} }} \\ \\ { \tt{y = \frac{1}{2}x }} \\ \\ { \tt{y = 0.5x}}[/tex]

a. a perpendicular to z
b. a ll b
c. x ll z
d. x perpendicular to a

Answers

D) x is perpendicular to a

What is the slope of the line represented by the equation y = -2/3 - 5x

Answers

Answer:

-5

Step-by-step explanation:

equation of a line is y=m*x+b

m is the slope of that line

so for y= -5x -2/3 m would be -5

Answer:

The slope intercept form of a line takes the Form

y= mx + c

where M is the gradient and as you can see... Its the coefficient of "x"

From the equation given

y= -2/3 - 5x

The Slope(gradient) is -5.

OPTION A IS CORRECT

PLZ ANSWER AND EXPLAIN IN DETAIL !!!!​

Answers

Answer:

720 liters

Step-by-step explanation:

In 2019 (a non-leap year)

January has 31 days

February has 28 days

March has    31 days

The Total number of days is 90 days

Each day shows a consumption rate of 8 liters / day

Total consumption = 8 * 90 = 720

help help help help help​

Answers

Step-by-step explanation:

press the picture to see the answer I swear it has a solution too

What’s the answer to this ?

Answers

Answer:

a

Step-by-step explanation:

Answer:

I am pretty sure its B

Step-by-step explanation: not sure though

Please help me I really need help

Answers

hi! the first one is -2+6 i & the second one is parallelogram!

Answer:

-2 + 6i

Parallelogram

Step-by-step explanation:

( 5 - 2i ) + ( - 7 + 8i )

remove parenthesis

5 - 2i + ( -7 ) + 8i

combine like terms

5 + (-7) = -2

-2i + 8i = 6i

-2 + 6i

The arrows on the opposite sides indicate that the sides are parallel

A shape with two sets of parallel sides is known as a parallelogram

Find the image of NPQ under the translation of (x, y) + (x + 8, y + 1).

АВС

DEF

KLM

GHJ

Answers

Answer:

Triangle KLM

Step-by-step explanation:

Firstly, we need to write the coordinates of triangle NPQ

We have this as;

(-7,-6) for N

(-4,-3) for P

(-4,-6) for Q

Now, we are going to use the given translation formula;

(x + 8, y + 1)

N’ will be (-7+ 8, -6 + 1) = (1,-5)

P’ will be (-4+ 8, -3+1) = (4,-2)

Q’ will be (-4+ 8, -6+1) = (4,-5)

Now, we need to find the triangle with the exact given transformation coordinates calculated above;

We have the triangle as;

KLM

With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)

Which of the following is the correct definition of payment shock??

Answers

Answer:

payment shock refers to a dramatic increase in an individual's debts and liabilities that may cause them to default on their financial obligations. Put simply, payment shock occurs when, rather suddenly, someone is obligated to pay more in monthly debt than they can afford from their income

Answer: The new payment after the initial fixed-rate period is much higher

than the homeowner expected.

Step-by-step explanation: took the quiz.

Line A (y=4x+2) is transformed into Line B (y=x+5). Which best describes the new slope and y-intercept?

Answers

Answer:

The new slope is 1 and the line is shifted flatter.

Step-by-step explanation:

Line A slope is 4.

Line B slope is 1.

The y-intercept rose up 3

As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.  

in one day a store sells 254 gallons of milk for a profit of -$0.17 each they also sell 51 half gallons of orange juice for a profit of 0.34 each what was the store's net profit for the day for these two items total

Answers

Answer:

-$25.84

Step-by-step explanation:

254* -0.17 = -$43.18 profit from milk

51 * .34 = $17.34 profit from OJ

-43.18 + 17.34 = -$25.84 profit total

3a + b - 2 = b thank you

Answers

Answer:

Get rid of b:

3a+b-2=b

3a-2=0

3a=2

A=2/3

in what ratio we increase 900 to get 1200​​

Answers

Answer:

4:3

Step-by-step explanation:

Let's say that the number we multiply to get to 1200 from 900 is x.

900x=1200

Now, we divide both sides by 900:

x=1200/900

x=4/3

The number is 4/3. In ratio form, this is 4:3

Answer:

3 : 4

Step-by-step explanation:

      900  : 1200

= 30 x 30 : 30 x 40

=         30 : 40

=    3 x 10 : 4 x 10

=           3 : 4


Find the equation of a line with a slope of -9, passing through the point (1, -3). Enter
this equation in slope/y-intercept form in the blank

Answers

Answer:

y=-9x+6

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=-9(x-1)

y+3=-9(x-1)

y=-9x+9-3

y=-9x+6

Car price $118,191
Percent for car loan: 2.49%
36 months

Find monthly payment show work

Answers

Answer:

3410.64

Step-by-step explanation:

Gonna assume that the 2.49 is the APR

present value of the loan= present value of the payments

effective rate: .0249/12= .002075

x= payment

[tex]118191=x\frac{1-(1+.002075)^{-36}}{.002075}\\118191=34.6536494355x\\x=3410.63645317[/tex]

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