Avery solves the equation below by first squaring both sides of the equation.
Answers
Answer:
z = 7/3 is extraneous.
Step-by-step explanation:
√(z^2+8) = 1 - 2z
z^2 + 8 = (1 - 2z)^2
z^2 + 8 = 1 -4z + 4z^2
3z^2 - 4z - 7 = 0
3z^2 + 3z - 7z - 7 = 0
3z(z + 1) - 7(z + 1) = 0
(3z - 7)(z + 1) = 0
3z = 7, z = -1
z = 7/3, -1.
One of these might be extraneous.
Checking:
√(z^2+8) = 1 - 2z, if z = -1:
√(1 + 8) = 3, -3
1 - 2(-1) = 3. So its not z = -1
if z = 7/3
√((7/3)^2 + 8) = 13.44
1 - 2(7/3) = -3.66
So its z = 7/3
Answer:
[tex]z=\dfrac{7}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{z^2+8}=1-2z[/tex]
Square both sides:
[tex]\implies (\sqrt{z^2+8})^2=(1-2z)^2[/tex]
[tex]\implies z^2+8=1-4z+4z^2[/tex]
Subtract [tex]z^2[/tex] from both sides:
[tex]\implies 8=1-4z+3z^2[/tex]
Subtract 8 from both sides:
[tex]\implies 0=-7-4z+3z^2[/tex]
[tex]\implies 3z^2-4z-7=0[/tex]
Rewrite the middle term:
[tex]\implies 3z^2+3z-7z-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 3z(z+1)-7(z+1)=0[/tex]
Factor out the common term [tex](z+1)[/tex]:
[tex]\implies (3z-7)(z+1)=0[/tex]
Therefore:
[tex]\implies (z+1)=0 \implies z=-1[/tex]
[tex]\implies (3z-7)=0 \implies z=\dfrac{7}{3}[/tex]
To find the extraneous solution (the root that is not a root of the original equation), enter the two found values of z into the original equation:
[tex]\begin{aligned}z=-1\implies \sqrt{(-1)^2+8}&=1-2(-1)\\\implies 3&=3\implies \textsf{true}\\\end{aligned}[/tex]
[tex]\begin{aligned}z=\dfrac{7}{3} \implies \sqrt{\left(\frac{7}{3}\right)^2+8}&=1-2\left(\frac{7}{3}\right)\\\implies \dfrac{11}{3} &=-\dfrac{11}{3}\implies \textsf{false}\end{aligned}[/tex]
[tex]\textsf{As}\: \dfrac{11}{3} \neq -\dfrac{11}{3}\:\textsf{then}\: z=\dfrac{7}{3}\:\textsf{is the extraneous solution}[/tex]
Related Questions
Simplify the expression
Answers
Answer:
-1
Step-by-step explanation:
Use the Pythagorean Identity:
1 + tan^2(x)= sec^2(x)
Rearrange it. Substitute. Simplify.See image. It's been done two ways on the image. You don't need both. But they both use the process above. See image.
a 10 gallinas,un costal de alimentos les dura 30 dias .¿cuanto dias les durara el mismo costal de alimentos a un grupo de 15 gallinas y a otro de 25 gallinas?
Answers
Usando proporciones, hay que el mesmo costal dura 20 dias a un grupo de 15 gallinas y 12 dias a un grupo de 25 gallinas.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.
a 10 gallinas,un costal de alimentos les dura 30 dias. ¿cuanto dias les durara el mismo costal de alimentos a un grupo de 15 gallinas? La regla de três es dada por:
10 gallinas - 30 dias
15 gallinas - x dias
Las medidas son inversamente proporcionales, por eso, aplica-se multiplicación de linea:
15x = 300
x = 20
Para 25 gallinas:
10 gallinas - 30 dias
25 gallinas - x dias
25x = 300
x = 12
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A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is 6 feet tall casts a shadow that is 3 ft long. How tall is the flagpole?
Answers
The height of the flagpole is 100 feet.
What are shadows?Shadows are area devoid of light as a result of the obstruction of light by an opaque object.
Analysis:
The length of the shadow and the height of the flagpole are at right angles.
Similarly, the height of the woman and the length of her shadow are at right angles. Making both similar right-angled triangles.
The ratio of the height of the woman to that of pole is equal to ratio of the length of woman's shadow to that of the flagpole.
let length of flagpole be h.
height of woman = 6 feet
length of shadow of woman = 3 feet
length of shadow of pole = 50 feet.
[tex]\frac{6}{h}[/tex] = [tex]\frac{3}{50}[/tex]
3h = 300
h = 100 feet
In conclusion, the height of the flag pole is 100 feet.
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Leanne and her family plan to attend a symphony at an orchestra hall. Before booking the tickets, Leanne checked a website where visitors rated the view of the symphony's soloist from their seating section. The data from the website is summarized in the table.
Section Number of reviewers who sat in the section Number of reviewers who rated the view as "perfect"
L1 90 57
L2 52 33
L3 75 47
U1 84 55
U2 43 27
U3 35 22
According to the data from the website, in which seating section should Leanne's family book the tickets if they want to maximize their chances of having a "perfect" view of the symphony's soloist?
Answers
Using proportions, it is found that Leanne's family should book their tickets at Section U1 to maximize their chances of having a "perfect" view.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the section with the highest proportion of perfect views should be chosen, hence:
pL1 = 57/90 = 0.633
pL2 = 33/52 = 0.635
pL3 = 47/75 = 0.623
PU1 = 55/84 = 0.655
pU2 = 27/43 = 0.628
pU3 = 22/35 = 0.629
Leanne's family should book their tickets at Section U1 to maximize their chances of having a "perfect" view.
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Answer:
answer in the picture have a nice day loves :)
Step-by-step explanation:
There are 14 animals in the barn. Some are geese and some are sheep. There are 48 legs in all.
How many of each animal are there?
Answers
Answer:
24
Step-by-step explanation:
48÷2 (because every birds has 2 legs(
A car used 12 gallons to travel 288 miles. How many gallons of gas will the car use to travel 192 miles?
Answers
12x + 288y = 0 -->(i) x + 192y = 0
=> 12(x + 192y) = 0 × 12
=> 12x + 2304y = 0 -->(ii)
By Elimination method,Equation (i) - (ii)(12x + 288y) - (12x + 2304y) = 0 - 0
=> 12x + 288y - 12x - 2304y = 0
=> - 2016y = 0
=> y = 2016
Putting the value of "y" in Equation (i)12x + 288y = 0
=> 12x + 288 × 2016 = 0
=> 12x + 580608 = 0
=> 12x = - 580608
=> x = 48384
Hope it helpsWhich math sentence can be used to determine if this triangle is a right triangle? A triangle has side lengths 12, 15, 18. 12 15 = 18 12 squared 15 squared = 18 squared 12 18 = 15 12 squared 18 squared = 15 squared.
Answers
Answer: its c
Step-by-step explanation:
Convert 20341 base 5 into decimal system (also verify )
Answers
[tex](20341)_5\\\\=(2 \times 5^4 + 0 \times 5^3 + 3 \times 5^2 +4 \times 5^1 +1\times 5^0)_{10}\\\\=(2 \times 625+0+3 \times 25 +20 +1)_{10}\\\\=(1250+75+21)_{10}\\\\=(1346)_{10}[/tex]
9 in
11 in
5 ft
19 in
12 in
Surface
Surface Area =
9)
3)
I need the surface area some please help
Answers
Answer:
730 in cubed
Step-by-step explanation:
hope this helps
have a good day
Solve 8 = 2x + 4
Ox=-4
OX= -1
Ox = 0
O x = 7
Answers
The equivalent value of x from the equation is x = 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.
Given data ,
Let the equation be represented as A
Now , the value of A is
8 = 2x + 4
On simplifying the equation , we gt
Subtracting 4 on both sides , we get
2x = 8 - 4
2x = 4
Divide by 2 on both sides , we get
x = 2
Therefore , the value of x is 2
Hence , the equation is solved and x = 2
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PLEASEEE I CAN'T DO ITT
Answers
Answer:
answer is cm² ok
Step-by-step explanation:
because it is saying area ,in area we have to put cm2
-1/3+(-7/4) in simplist form
Answers
Answer:
your answer will be [tex]-\frac{25}{12}[/tex]
Step-by-step explanation:
hope this helps have a nice day :)
[tex]-\dfrac 13 + \left( -\dfrac 74\right)\\\\\\=-\dfrac 13 - \dfrac 74\\\\\\=-\dfrac{4}{12}-\dfrac {21}{12}\\\\\\=-\left( \dfrac 4{12} + \dfrac{21}{12} \right)\\\\\\=-\left( \dfrac{4+21}{12}\right)\\\\\\=-\dfrac{25}{12}[/tex]
Which of the following is equal to the rational expression when x≠1 or -1 5(x-1)/(x+2)(x-1)
Answers
The solution to the given expression will be [tex]\dfrac{-15}{x+2}[/tex]
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The solution will be:-
[tex]= \dfrac{-15(x-1)}{(x+2)(x-1)}[/tex]
[tex]=\dfrac{-15}{x+2}[/tex]
Therefore the solution to the given expression will be [tex]\dfrac{-15}{x+2}[/tex]
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The integral in this exercise converges. Evaluate the integral without using a table 0e^0d0
Answers
The value of 0e^0d0 is -1 if the integral in this exercise converges after applying limit.
What is convergent of a series?A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We are assuming the:
[tex]=\int\limits^0_{-\infty} {\theta e^{\theta}} \, d\theta[/tex]
Applying limit;
[tex]=\lim_{n \to \infty} \int\limits^0_{-n} {\theta e^{\theta}} \, d\theta[/tex]
After solving the integral:
[tex]=\lim_{n \to \infty} (e^{\theta})|^0_-_p[/tex]
= -(1-0)
= -1
Thus, the value of 0e^0d0 is -1 if the integral in this exercise converges after applying limit.
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Which of these daily activities helps build a stronger body?
riding in the car to school
doing homework at your desk
watching TV on the couch
riding a bicycle to and from school each day
Answers
Answer:
riding a bicycle to and from school each day
Step-by-step explanation:
As this involves the constant application of force from the leg muscles, this will help to build a stronger body.
Answer: Riding a bicycle to and from school each day
Step-by-step explanation: Evey other action is to do with your mind.
Dolores is going to make a sandwich. She has 2 types of bread, 3 types of cheese, and 2 types of meat to choose from. How many different sandwiches can she make that have 1 bread, 1 cheese, and 1 meat?
Answers
I WILL GIVE Brainliest
WHAT IS 2 + 2=
a.4
b.3
c.69
d.420
Answers
Answer:
4
Step-by-step explanation:
2 + 2 = 4
Have a nice day:)
Step by step
2 + 2 equals 4
What is the greatest possible integer solution of the inequality 3.7x<12.3
Answers
Answer:
3 is the answer.
Step-by-step explanation:
You will have to divide both sides by 3.7, and you will get x<3.3. But because 3 is lesser than 3.3, it is the largest possible integer that satisfies the inequality.
Hey there!
EQUATION:
3.7x < 12.3
DIVIDE 3.7 to BOTH SIDES:
3.7x/3.7 < 12.3/3.7
SIMPLIFY IT!
x < 12.3/3.7
ANSWER:
x < 3.324324
Therefore, your answer is:
x < 3.324324
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Hunter just got hired for a new job and will make $31,000 in his first year.
Hunter was told that he can expect to get raises of $1,500 every year going
forward. How much money in salary would Hunter make in his 10th year
working at this job?
Answers
What is 1 + 1 im dying from sleep deprivation and I lost the grand math challenge bc of this bro help me pls you smart ppl
Answers
Answer:
1
Step-by-step explanation:
say you don't have a dog.. your parents get you one dog, and then get you another, you now have 2 :)
A. y= 1/2x-14
B. y=1/2x-5
C. y=2x-14
D. y=2x-5
Answers
Answer:
B. y=1/2x-5
Step-by-step explanation:
From the graph, we read the slope of line JK.
slope = rise/run = -3/-6 = 1/2
The equation we need has the same slope.
y = mx + b
y = (1/2)x + b
It passes through point P(6, -2). Now we find b.
-2 = (1/2)(6) + b
-2 = 3 + b
b = -5
The equation is
y = (1/2)x - 5
OMG GUYS HELP ME I GIVE 100 points what is 1+1 and what is 2-1 tell me!!! QUICK
Answers
Answer: 1 + 1 = 2
2-1 = 1
Step-by-step explanation:
basic math stuff
Using the diagram, determine which statements are true. Select all that apply. m∠1 = 50° m∠3 = (2x + x + 25)° m∠2 = (x + 25)° m∠1 + m∠2 + m∠3 = 180° 50 + 2x+ x + 25 = 180
Answers
Answer:
All of them are true except for the second one.
Step-by-step explanation:
Answers A, C, D, E
Simplify
3x+4.4-2(6.6+x)
Answers
A survey of students in the junior class at Avery's high school provided the following information:
Percentage of students who think there is too much homework
85%
Average number of hours per week spent on homework this year
8 hours
Average number of hours per week spent on homework last year
5 hours
Average number of students with afterschool jobs this year
215 students
Average number of students with afterschool jobs last year
135 students
In three to five complete sentences, write a statement that Avery can present to the school principal explaining why 85 percent of the students in the junior class think there is too much homework.
Answers
Avery can explain to her school principal that 85% of juniors think there is a lot of homework because several indicators have increased.
What is an indicator?An indicator is a datum that is taken as a reference to analyze the evolution or change of a fact over time. In this case, the indicators would be:
Weekly hours used to do homeworkNumber of students with work for after school.According to the information, it can be inferred that 85% of Junior students consider that there is an increase in homework because there were the following changes compared to last year:
Increase in hours spent on after school homework, last year the average was 5 hours, this year it is 8 hours.Increase in the number of students with after school jobs, last year it was 135 students, this year it is 215 students.From the foregoing, it can be inferred that the number of homework has increased in Junior students and that is why now 85% of them consider that homework has increased.
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QPR=7x-9
RPS=4x+22
Find QPR
Answers
QPR = 40
x = 7
Explanation: You would want to combine both the angles and equal them to 90 because they’re perpendicular to each other.
Problem 7
The figure shows a large rectangle with a small rectangle removed from one corner.
18
4
12
What is the area of the figure?
o A. 60 square units
o
B. 66 square units
OC. 72 square units
O D. 84 square units
Answers
Answer:
60
Step-by-step explanation:
add 18 and 12 to get 30 and divide that by 2 then you will get 15.
15 times 4 is 60
plssss i need helpp ASAP
Answers
Answer:
A.
1) 60
2) 27
B)
1.cm³
2.cm³
3.m³
Step-by-step explanation:
A)
5x3x4 =60cm³
3x3x3=27cm³
B)
1.cm³
2.cm³
3.m³
What power of ten do we need to multiply 3.15576 by in order to find an expression equivalent to 31,557,600
Answers
Answer:
3.15576 * 10 to the power of 7 will get you 31557600.
What are the solutions of the equation 2x^2=18
Answers
See the attached image for the work!