Mathematics High School

Avery solves the equation below by first squaring both sides of the equation.
√z^2+8 = 1 -2z
What extraneous solution does Avery obtain?
z= ?

Avery Solves The Equation Below By First Squaring Both Sides Of The Equation.z^2+8 = 1 -2zWhat Extraneous

Answers

Answer 1

Answer:

z = -1 and 7/3

Step-by-step explanation:

after squaring each side you get:

z² + 8 = (1 - 2z)²

z² + 8 = 1 - 4z + 4z²

combine like terms to get this trinomial:

3z² - 4z - 7, which has factors of (3z - 7)(z + 1)

therefore, z = 7/3 and z = -1

Answer 2

The extraneous solutions for the Avery equation is [tex]z = \frac{7}{3}[/tex].

What is an equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Given equation

[tex]\sqrt{z^{2}+8 } =1-2z[/tex]

Squaring on both sides

[tex]z^{2} +8=(1-2z)^{2}[/tex]

[tex](1-2z)^{2}[/tex] is in the form of [tex](a-b)^{2} =a^{2} -2ab+b^{2}[/tex].

[tex]z^{2}+8=1-4z+4z^{2}[/tex]

[tex]4z^{2} -z^{2} -4z+1-8=0[/tex]

[tex]3z^{2} -4z-7=0[/tex]

[tex]3z^{2} +3z-7z-7=0[/tex]

[tex]3z(z+1)-7(z+1)=0[/tex]

[tex](3z-7)(z+1)=0[/tex]

[tex]z=\frac{7}{3}[/tex] or [tex]z=-1[/tex]

because [tex]\sqrt{z^{2}+8 } \ge 0[/tex] so [tex]1-2z \ge 0[/tex]

When [tex]z=\frac{7}{3}[/tex]          [tex]1-2 \times \frac{7}{3} =-\frac{11}{3} < 0[/tex](Abandon)

When z = -1          1 - 2 × (-1) = 1 + 2 = 3 > 0

So the extraneous solutions is [tex]z = \frac{7}{3}[/tex].

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Related Questions

WILL MARK BRAINLIEST IF GOTTEN RIGHT

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The diameter is the measure across the circle: the diameter is given

Solution: 20 ft

Answer:

20 ft.

Step-by-step explanation:

Diameter is length across the circle/ across the middle

GO GO GO

<3

A nickel has a mass of 5 grams. What is the mass of the nickel in milligrams?

Answers

Answer:

5,000 milligrams

Step-by-step explanation:

Know That One 1 gram equals = 1,000 milligrams

Hope this Helps!

What is the difference between a trapezoid and a rhombus?
A) A trapezoid is a parallelogram and a rhombus is not.
B) A rhombus always has 4 equal sides and a trapezoid does not.
C) A rhombus always has 4 right angles and a trapezoid does not have to.
Eliminate
D) A rhombus never has 2 sets of parallel sides and a trapezoid always does.

Answers

Your answer is C bro


[tex]x ^{2} + {x}^{2} + 8x + 4x = [/tex]
pls solve I couldn't finish this expression
​

Answers

2x^2 + 12x

(I think this is the answer, and if you want to simplify it, the simplified/factorised answer would be 2x(x+6)

Step-by-step explanation:

[tex] {x}^{2} + {x}^{2} + 8x + 4x = \\ 2 {x}^{2} + 12x[/tex]

twice the sum of a number and ten

Answers

Answer:

2(x+10)

Step-by-step explanation:

Well since sum is addition and the number and 10 are the sum, let’s make the “number“ (x) and add em up. 10+x.

Now we gotta double that sum which is basically

2(10+x)

Find the value of the x in the figure shown.

Answers

Answer:

22

Step-by-step explanation:

x + 90 + 68 = 180

x + 158 = 180

x = 22

your answer is 22°. 68+90=158; then, you subtract 158 from 180 and get the missing angle, X.

6TH GRADE MATH!

Which of these expressions are equivalent to p over 3?
​Select each correct answer.
A. 3 divided by p
B. 1/3p +1/3p +1/3p
C. p-2/3p
D. 1/3p
E. p-3
F. 3p over 9

Please hurry, i only have 20 minutes left :(

Answers

Answer:

D. 1/3p and F. 3p over 9

Step-by-step explanation:

1/3p and 3p over 9

6. MGSE7.RP.2: The points on the coordinate grid represent the costs for the different numbers
of peaches.
Cost of Peaches
(8,6)
Cost (dollars)
Woo
(4.3)
(1.0.75)
0 1 2 3 4 5 6 7 8 9 10
Number of Peaches
Select THREE statements that are true about the graph.
A. There is a proportional relationship between the number of peaches and the cost because a
line can be drawn passing through the origin and connecting all the points shown.
B. There is a proportional relationship between the number of peaches and the cost because the
X-value is always greater than the y-value.
C. The point (1, 0.75) can be used to represent the unit rate of 0.75 dollars per peach.
D. The point (1, 0.75) can be used to determine the total cost by subtracting 0.25 from the
number of peaches.
E. The point (4, 3) represents 4 peaches at a cost of $3.

Answers

Answer:

C i think if wrong im so sorry

Step-by-step explanation:

Can someone please help
1 answer choices are
A 122.2
B 68.115

2nd drop down menu answer choices are
A dollars
B square feet
C dollars per square foot
D square feet per dollar

3rd answer choices are
A increase
B decrease

4 are
A 122.20
B 68.115​

Answers

Answer:

A 122.2B square feet A increaseB 68.115

Ancient slingshots were made form straps of leather that cradled a rock until it was released. One would spin the slingshot
in a circle, and the initial path of the released rock would be a straight line tangent to the circle at the point of release.
The rock will travel the greatest distance if it is release when the angle between the normal to the path and the horizontal
is -450. The center of the circular path is the origin and the radius of the circle measure 1.25 feet.
Write and equation of the initial path of the rock in standard form.

Answers

Answer:

Step-by-step explanation:∠ MON= -45°→→ angle lies in fourth quadrant.

Where, MN represents the path of rock, which is a straight line.

Taking the Horizontal and vertical component of OM,to get the coordinate of point M

The coordinate of point M will be [1.25 cos (-45°), 1.25 sin(-45°)]=

Taking O as center and Coordinates of O as (0,0) and Coordinates of M as () we get the equation of line OM as

y= tan (315°)× x

As general form of equation of line passing through the origin will be,

y= m x, where m is angle made by line with positive direction of x axis.

m= (360-45)°= 315°

→→y=-x

→→  y +  x=0

equation of line perpendicular to OM will be

→→ x -  y + k=0

Since it passes through .

→→

So, equation of initial path of stone will be:

One equation in a system of equations is y=2x+4. Which of the following would be the second equation so that the system has (1,6) as its only solution

1. y=-2(x+2)
2. y=2x+8
3. y=5x+1
4. y=4x-7

Answers

Answer:

1. y = 2(x + 2)

Step-by-step explanation:

if we substitute the values,

we get 6 = 2*1 + 4

6 = 6

therefore, it is correct.

The system of equations has no solution. hence option d is correct.

What is Equation?

Equation is described as the state of being equal, and it is commonly represented as a math expression with equal values on both sides, or it refers to a problem involving numerous variables.

here, we have,

to find solution to the system:

The given equation is

y=2x+8  ..(1)

3(-2x + y) = 12  ...(2)

Substitute the y value in equation 2 from equation (1)

3(-2x + 2x+8) = 12

               3(8)=12

                24≠12

Hence the system of equations has no solution.

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complete question:

What is the solution to the system of equations

below?

y=2x+8

3(-2x + y) = 12

1) no solution

2) infinite solutions

3) (-1,6)

4) (1/2,9)

A spinner has 6 numbers on it, from 1-6, all with equally spaced area. Find the probability of spinning a
Prime number, P(Prime)
Select the correct response.
1
2

5
6

2
3

1
3.

Answers

Answer:

first option 1/2

Step-by-step explanation:

2,3,5 are the prime numbers from that set

each individual number has a 1 in 6 chance of landing on it and we have 3 so...

3 of 6 possibilities would be prime numbers. Simplify to...

1 in 2

Can someone plz help me with this Math problem and plz explain how you got your answers

Answers

21 cause of x and y on its axis to atoms and protons and electrons

What is the solution to the equation?

√2x+10−6=2


*Picture of the Problem Below*

Answers

Answer:

x = 27

Step-by-step explanation:

Given

[tex]\sqrt{2x+10}[/tex] - 6 = 2 ( add 6 to both sides )

[tex]\sqrt{2x+10}[/tex] = 8 ( square both sides )

2x + 10 = 8² = 64 ( subtract 10 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

find the value of two numbers if their sum is 12 and difference is 8

Answers

Let’s consider these two numbers to be ‘x’. If the sum of these numbers is 12, then we must determine what numbers can be added to equal 12. 1+11,2+10,3+9,4+8,5+7, and 6+6. From these numbers we can decide that 10-2=8 are the only 2 values that equal 8 when subtracted.

(3x^2+7)+(2x^2-5x+10)

Answers

Answer:

5x² - 5x + 17

Step-by-step explanation:

(3x² + 7) + (2x² - 5x + 10)

Combine the like terms.

3x² + 2x² = 5x²

-5x does not have a like term, so there is no change.

7 + 10 = 17

Combine them, and the final equation is

5x² - 5x + 17.

Answer: 5x² - 5x + 17

Step-by-step explanation:

(3x^2+7)+(2x^2-5x+10)

3x^2 + 2x^2

-5x

7 + 10

5x^2 - 5x + 17

- If I've understood correctly

A principal wanted to survey students who took a standardized college entry exam about how prepared they felt for
the exam. The principal put together a bag of marbles. There was 1 marble for each student, and 20 of the marbles
were red. Each student chose a marble, and those who chose the red marbles took the survey. Which sampling
method was used?
O cluster sampling
simple random sampling
O stratified random sampling
O systematic random sampling

Answers

Answer:

B. Simple Random Sampling

Step-by-step explanation:

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected

A North Dakota license plate has six characters: 3 digits followed by 3 letters (e.g. 123AAA). Any number from 0 to 9 can be used as a digit. Any of the 26 letters from A to Z can be used as a letter.

How many different North Dakota license plates can be issued?

Answers

Answer:

17,576,000

Step-by-step explanation:

Since, there is 3 digits, 0-9, you would have 10 numbers total to choose from. As well as the 26 letters. Since you need three of each, you multiply.

10*10*10*26*26*26

=

17576000

HELPP ME PLEASE ILL GIVE BRAINLIST :)

Answers

Answer:

C 7ft/yr

Step-by-step explanation:

Five years ago today, Artie was four times as old as his sister Carrie. In five years time, Artie will be twice as old as Carrie. Find their current ages using a system of linear equations.

Answers

Answer: 25 , 10 years

Step-by-step explanation:

Suppose the present age of Artie and Carrie is x and y

According to the question, 5 years ago

[tex]\Rightarrow x-5=4(y-5)\\\Rightarrow x-4y=-15\quad \ldots(i)\\[/tex]

In five year time

[tex]\Rightarrow x+5=2(y+5)\\\Rightarrow x-2y=5\quad \ldots(ii)[/tex]

Solving (i) and (ii) we get

[tex]x=25,y=10[/tex]

The current age of Artie and Carrie is 25 and 10 years

The large stones of Stonehenge are arranged in a circle about 30 meters in diameter. What
is the radius?

Answers

Answer:

The radius is just the diameter split in half, so r = 15 meters.

Explanation:

D = 30

30/2 = 15

r = 15

The answer is r=15

D=30/2 =15=r

PLEASE HELP ASAPPP!!!

Answers

Step-by-step explanation:

hope it helps you......

Your answer is 50


A triangles angles add up to 180 degrees.
52+78=130
180-130=50
Angle m = 50 degrees

what is the inequality for more than 100,000

Answers

Answer:

>100,000

Step-by-step explanation:

Pop smoke I’m the one they wanna meet 1

1
Factorise 2x2 + 11x + 12. You can use the grid to help.
2x
3x
8x
1
12
2x2 + 11x + 12 =

Answers

Answer:

(2x+3)(x+4)

Step-by-step explanation:

hope the picture helps.

The table represents some points on the graph of an exponential function Which function represents the Same relationship? ​

Answers

Answer:

the answer is a b and d

Step-by-step explanation:

I took the quiz

Can someone help me please

Answers

Answer:

The answer is D

Step-by-step explanation:

1/8 is the equivalent to 0.12

square root of 0.02 is 0.14

18% is equal to 0.18

Answer:

d. [tex]\sqrt{0.02}[/tex]

Step-by-step explanation:

1/8 = 0.125

18% = 0.18

1/5 = 0.2

1.6

0.09

[tex]\sqrt{0.02}[/tex] = 1.141

How much commission would a salesperson ear for selling a car that costs $29,389? He receives 16% commission on each sale.

Answers

Answer:

Commission on car = $4,702.24

Step-by-step explanation:

Given:

Sales price of car = $29,389

Commission on sale of car = 16% = 0.16

Find:

Commission on car

Computation:

Commission on car = Sales price of car x Commission on sale of car

Commission on car = 29,389 x 16%

Commission on car = 29,389 X 0.16

Commission on car = $4,702.24

Free to whoever gets it​

Answers

LolAnswer:

Step-by-step explanation:

Wanna be in a hangouts gc?

Order the numbers from least to greatest.
LEAST
1
8
= 0.13
= 0.12222...
12.7%

Answers

0.122, 0.13, 12.7%, 1, 8

PLEASE HELP I WILL GIVE BRAINIEST. What is the range?

Answers

Answer:

range= 8

Step-by-step explanation:

to find range> subtract highest number to the lowest

so 10- 2= 8

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