How many extraneous solutions does the equation below have? StartFraction 9 Over n squared 1 EndFraction = StartFraction n 3 Over 4 EndFraction.
Answers
The equation has one extraneous solution which is n ≈ 2.38450287.
Given that,
The equation;
[tex]\dfrac{9}{n^2+1} =\dfrac{n+3}{4}[/tex]
We have to find,
How many extraneous solutions does the equation?
According to the question,
An extraneous solution is a solution value of the variable in the equations, that is found by solving the given equation algebraically but it is not a solution of the given equation.
To solve the equation cross multiplication process is applied following all the steps given below.
[tex]\rm \dfrac{9}{n^2+1} =\dfrac{n+3}{4}\\\\9 (4) = (n+3) (n^2+1)\\\\36 = n(n^2+1) + 3 (n^2+1)\\\\36 = n^3+ n + 3n^2+3\\\\n^3+ n + 3n^2+3 - 36=0\\\\n^3+ 3n^2+n -33=0\\[/tex]
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y
with 0 and solve for x. The graph of the equation is attached.
n ≈ 2.38450287
Hence, The equation has one extraneous solution which is n ≈ 2.38450287
For more information refer to the link.
https://brainly.com/question/15070282
Related Questions
PLEASE HELP!
Question 3 (Essay Worth 10 points)
(03.04 MC)The youth group is going on a trip to the state fair. The trip costs $62. Included in that price is $14 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answers
Answer:
One pass is $24
Step-by-step explanation:
14+2x=62
-14
2x=48\2
X=24
Answer: The person above's answer
Step-by-step explanation:
I did the test and it was right
i need help with this!!
Answers
Answer:
[tex]x<-4[/tex]
Step-by-step explanation:
[tex]8x-4<-36\\\Add\:}4\mathrm{\:to\:both\:sides}\\8x-4+4<-36+4\\\mathrm{Simplify}\\8x<-32\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8x}{8}<\frac{-32}{8}\\Simplify\\\frac{8x}{8}<\frac{-32}{8}\\Simplify\\\frac{8x}{x}:x\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{8}=1\\=x\\Simplify\\\frac{-32}{8} \\[/tex]
Apply the fraction rule
[tex]=-\frac{32}{8}\\Divide\\ \frac{32}{8} = x=-4\\x<-4[/tex]
How do you graph x less than -3 1/2
Answers
Answer:
Graph attached
Step-by-step explanation:
Rewrite the expression as only multiplication and evaluate.
2
1 -
Answers
Answer:
72
Step-by-step explanation:
1 * 3/2 * (-8) * 3 * (-2)
3/2 * (-8) * 3 * (-2)
(-24/2) * 3 * (-2)
(-12) * 3 * (-2)
24 * 3
72
What is the domain of the function
y = √x
Answers
Answer:
[tex]0\leq x<\infty[/tex]
Step-by-step explanation:
The function [tex]y=\sqrt{x}[/tex] is not defined for negative numbers in the domain as they produce non-real results. Therefore, all positive numbers including 0 are included in the domain, so the domain of the function would be [tex]0\leq x<\infty[/tex].
I've attached a diagram to help you visualize the domain.
Mr. Bannon sells roses at a commission rate of 25%. What is his commission for selling 235 dozen roses, priced at $15.50 a dozen? NEED HELP IMMEDIATELY
Answers
Step-by-step explanation:
that means he gets 25% of the sales.
he sold 235 dozen roses for $15.50 per dozen.
so, the total sales was
235 × 15.5 = $3,642.50
100% = $3,642.50
25% = 100%/4 = $3,642.50/4 = $910.63 (rounded to cents)
5. PRACTICE E Use Math Tools There were 242 fish in 22 fish
tanks at the pet store. If there were an equal number of fish in
each fish tank, how many fish were in each tank? Draw models
to find the quotient.
Answers
Answer:
There is 11 fish in each fish tank
Step-by-step explanation:
242 total fish
divided into 22 fish tanks
242÷22=11
Draw 11 fish in each of the 22 fish tanks
solve -(-7x+9)+(3x-1)=0
Answers
Answer: x = 1
Step-by-step explanation:
Find the 60th term of the following sequence.
4, 8, 12,
Answers
Answer:
240
Step-by-step explanation:
Fill in the blank for this graph.
Answers
Answer:
2.22
Step-by-step explanation:
Help for 100 points if correct
Answers
Saved:-
[tex]\\ \sf\Rrightarrow 2\dfrac{1}{4}-\dfrac{3}{8}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{9}{4}-\dfrac{3}{8}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{18-3}{8}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{15}{8}[/tex]
[tex]\\ \sf\Rrightarrow 1\dfrac{7}{8}[/tex]
Answer:
[tex]\textsf{D)} \quad 1 \dfrac{7}{8}[/tex]
Step-by-step explanation:
Subtract the used volume of punch from the starting volume of punch.
Convert the mixed number to an improper fraction:
[tex]\begin{aligned} \implies 2\frac{1}{4}-\frac{3}{8} & = \dfrac{2 \times 4+1}{4}-\dfrac{3}{8}\\\\ & = \dfrac{9}{4}-\dfrac{3}{8}\end{aligned}[/tex]
Make the denominators of both fractions the same by multiplying the numerator and the denominator of 9/4 by 2:
[tex]\implies \dfrac{9 \times 2}{4 \times 2}-\dfrac{3}{8} = \dfrac{18}{8}-\dfrac{3}{8}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\begin{aligned} \implies \dfrac{18}{8}-\dfrac{3}{8} & = \dfrac{18-3}{8}\\\\ & = \dfrac{15}{8}\end{aligned}[/tex]
Convert back into a mixed number:
[tex]\begin{aligned}\implies \dfrac{15}{8} & = \dfrac{8+7}{8}\\\\ & = \dfrac{8}{8}+\dfrac{7}{8}\\\\ & = 1\dfrac{7}{8}\end{aligned}[/tex]
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answers
Answer:
This is essentially a rule in the unit of radicals, where n✔️X^m = X^m/n. If the value of m is equal to n, as in 2✔️3^2 it would simply be 3^2/2 which is nothing but 3^1 = 3. Basically, the m value can be greater than n and or less than n, but if it is equal the m and n values cancel out. Hope this helped <3
If January 20 falls on a Tuesday, then February 15 of that same year falls on which day of the week? (January has 31 days)
Answers
Answer: Sunday
Step-by-step explanation:
The 27th would be tuesday
The 3rd would be tuesday
The 10th would be tuesday
The 15th would be sunday
Solve for x in the triangle. Round your answer to the nearest tenth.
Answers
Answer:
x=4.225
Step-by-step explanation:
You can use your trigonometric ratios to help you solve this problem. We have the hypotenuse and the angle that the triangle makes with the adjacent side. X is the adjacent side of this problem, therefore we need to take the cosine of this angle (remember SOHCATOA, Sine: Opposite/Hyp, Cosine: Adjacent/Hyp, and Tan: Opp/Adj) using this, we can model an equation where Cos(62)=(x/9), in order to solve for x, simply multiply both sides by 9 to get a final answer of 4.225...
write y= - 4x on a graph
Answers
12 in. to 36 in. increase in percent or decrease?
Answers
Answer:
33.3333%
Step-by-step explanation:
Answer:
12/36=0.333+
it decrease
NO LINKS PLEASE. 18 POINTS! WHAT IS THE ANSWER TO 5 and 6 IN THE SCREENSHOT? PLEASE HURRY! P.S. BRAINLIEST
Answers
Answer:
#5 -1.75, 2.5, -0.2
#6 3 1/2, 2 1/4, -1/2
Step-by-step explanation:
Well when the opposite they mean if the number is positive it becomes negative, and if is negative it becomes positive. very simple happy to help :)
Only like 5 or 6 more questions for the last question I’m doing 100 points
Answers
Answer:
700 foundations is the answer
Answer:
500 foundations
Step-by-step explanation:
what is 36×82×58+38?
Answers
Answer:
171,254
Step-by-step explanation:
calculate it
------------------------
A line has slope 56 and y–intercept −3.
Which answer is the equation of the line?
y=56x+3
y=−3x+56
y=56x−3
y=3x+56
Answers
Answer:
c
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
m=56
b=-3
y=56x-3
f(x)=x^3+6x^2+x^1/2 and g(x)=x^1/2 Find f(x)/g(x)
A).x&5/2+6x&3/2-1
B).(x^5+6x^3+1)^1/2
C).x^5/2+6x^3/2+1
D).x^3/2+6x+x^1/4
E).x^3/2-6x+x^1/4
Answers
Answer:
C) x^5/2 +6x^3/2 +1
Step-by-step explanation:
The relevant rule of exponents is ...
a^b/a^c = a^(b-c)
__
[tex]\dfrac{x^3+6x^2+x^{1/2}}{x^{1/2}}=x^{3-1/2}+6x^{2-1/2}+x^{1/2-1/2}=\boxed{x^{5/2}+6x^{3/2}+1}[/tex]
Find the component form of a vector.
Answers
Answer:
b
Step-by-step explanation:
Help
Activity:
2x²2+2x-312=0
Answers
Answer:
Step-by-step explanation:
0.326
In word form and stranded form please help!!?! I am taking things that are from 4th grade ahh I can't even remember anything from then. please help me word form and stranded form.
Answers
Answer:
three hundred twenty six thousandths
The bottom of a rectangular swimming pool has a perimeter of 62 meters. Its area is 220 square meters. What are the dimensions of the pool?
_____meters by ____ meters
PLEASEE HELPP MEE PLEASEEEE!
Answers
Half the perimeter is the length + the width
62/2 = 31
Area = length x width
16 + 15 = 31, 15 x 16 = 240
17 + 14 = 31, 17 x 14 = 238
20 + 11 = 31, 20 x 11 = 220
Answer: 20 meters x 11 meters
Solve the equation 3x + 2 = x + 4(x +2)
Answers
Answer:
x = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityDistributive Property
Terms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
3x + 2 = x + 4(x + 2)
Step 2: Solve for x
[Subtraction Property of Equality] Subtract x on both sides: 2x + 2 = 4(x + 2)[Distributive Property] Distribute 4: 2x + 2 = 4x + 8[Subtraction Property of Equality] Subtract 4x on both sides: -2x + 2 = 8[Subtraction Property of Equality] Subtract 2 on both sides: -2x = 6[Division Property of Equality] Divide -2 on both sides: x = -3Answer:
x=-3
Step-by-step explanation:
3x+2=x+4(x+2)
3x+2=x+4x+8
3x=5x+6
3x-6=5x
-6=2x
x=-3
Nachelle is 1.45 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 23.05 meters. She stands 18.9 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answers
Step-by-step explanation:
this creates 2 similar triangles.
that means all angles are the same. and all the side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.
her shadow is 23.05 - 18.9 = 4.15 m long.
the factor between the shadow lengths is then
4.15 × f = 23.05
f = 23.05 / 4.15 = 5.554216867...
the same factor now applies to the relation of the heights :
1.45 × 5.554216867... = 8.053614458... m
rounded the tree is 8.05 m tall.
what would the equation be?
Answers
Answer:
y = -2x + 30
Step-by-step explanation:
Firstly, choose 2 coordinates ( I chose [1,28] and [2,,26] ) next use y2-y1/x2-x1 to find your slope, in this case it is -2. Next, take two points and plug them into your equation with your slope to find your b, for this case the b is 30. Put it all together and you get y = -2x + 30
Brainliest would be appreciated. :-)
PLEASE HELP ME I BEG IMMA FAILLLLLLLLLLLLLLLL
Identify the missing angle measure in a right triangle where one angle measures 12°.
168°
78°
Cannot be determined
88°
Answers
Answer:
78
Step-by-step explanation:
180-90-12=78
102 + missing angle = 180
Missing angle = 180 - 102
Missing angle = 78
Hope this helps!
Brainliest is much appreciated!
HELPPP I NEED HELP
plzzz
Answers
1) 23
That's all I know lol