What is the solution to this equation?
3d + 2) – 12 = d - 2
==
-
O d = 2
O d = 4
O d = 8
O d = 10
Answers
Answer:
D=4
Step-by-step explanation:
a. The solution of the equation x + 2 = √3x + 10 is x = -3 or x =2.
b. Extraneous solution is x= -3.
c. Extraneous solution does not satisfy original equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
As given in the question,
Given equation :
x + 2 = √3x + 10
a. Squaring both the sides
( x + 2 )² = ( √3x + 10 )²
⇒ x² + 4x + 4 = 3x + 10
⇒ x² + x - 6 =0
⇒ x² + 3x -2x -6 =0
⇒ ( x+ 3) ( x -2) =0
⇒ x= -3 or x = 2
b. Extraneous solution:
x = -3
-3 + 2 = √3(-3)+ 10
⇒ -1 ≠ 1 extraneous solution.
x= 2
2+ 2 =√3(2) +10
⇒4 = 4 not extraneous.
c. Extraneous solution does not satisfy original equation
Therefore, the solution of the equation is x = -3 or x=2and its extraneous solution is x =-3. Extraneous solution does not satisfy original equation.
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The complete question is :
Use the equation below to answer these questions.
x + 2 = √3x + 10
a) What is the solution to the equation?
b) What is the extraneous solution? Why?
c) In general, what is an extraneous solution?
Related Questions
A particle moves along the x-axis so that time t>0 the position is given by x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1. What is the velocity of the particle at the first instance the particle is at the origin?
Answers
The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.
To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.
Since the particle is at the origin when x(t) = 0, we have:
[tex]0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0[/tex]
Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.
Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).
Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):
v(t) = dx/dt
[tex]v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6[/tex]
Now, we can find the velocity at t ≈ 2.944:
[tex]v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6[/tex]
v(t ≈ 2.944) ≈ 16.885
So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.
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If K = F( A + B ) , find “ A ” if F = 2 , B = 3 , K = 10
Answers
Answer:
The value of A is 2
Step-by-step explanation:
F = 2 , B = 3 , K = 10
K = F( A + B )
10 = 2(A + 3)
10 = 2A + 6
Now, Subtract 6 from each side we get,
10 - 6 = 2A + 6 - 6
4 = 2A
2A = 4
Now, divide both side by 2 we get,
2A/2 = 4/2
A = 2
Thus, The value of A is 2
FOR VERIFICATION ONLY :-K = F( A + B )
10 = 2(2 + 3)
10 = 2(5)
10 = 10
L.H.S = R.H.S
Hence Proved!
-TheUnknownScientist 72
Which of the following represents 3 times the sum of 3
and 8?
Answers
Answer:
The expression would be (x + 3)(x - 8) and if we multiplied those together we would get x^2 - 5x - 24
Step-by-step explanation:
are 16/72 and 18/81 equivalent rational numbers
Answers
Answer:
yes
Step-by-step explanation:
[tex]\frac{16}{72}[/tex] ( divide numerator/ denominator by 8, the LCM of 16 and 72 )
= [tex]\frac{2}{9}[/tex]
[tex]\frac{18}{81}[/tex] (divide numerator/ denominator by 9 the LCM of 18 and 81 )
= [tex]\frac{2}{9}[/tex]
Both rational numbers simplify to [tex]\frac{2}{9}[/tex] and are equivalent
solutions: ( x = 2 & x = -2 )
Answers
hmmmmhmmmmmmmmmmmmmmmmmmmmmm
A house has increased in value by 3% each year. It was worth £150000 4 years ago. How much is it worth now? Give your answer to a sensible degree of accuracy. morto
Answers
Answer: 350000
Step-by-step explanation: Hope this helps :) (if wrong please make sure next time add answer that can be picked from it better or if theres no answers maybe give some more detail?)
Find the slope of a line parallel to the line whose equation is y-4=7(x+2).
Answers
Answer:
m'=7
Step-by-step explanation:
they are parallel to each other so if slope of 1st line be "m" and 2nd line as "m' ", then we have:
m = m'
y-4=7x+14
y=7x+18
y=mx+h
So m = 7
& m' = 7
Simplify (12+3i)−(−5+2i)
Answers
Answer:
17+5i
Step-by-step explanation:
add the like terms
double negative equals positive
;)
Answer:
17+i
Step-by-step explanation:
What is the diameter of a circular swimming pool with the radius of 8 feet
Answers
PLEASE HELP WILL GIVE FULL PONITS! 3. Using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer. (2 points)
Known side: ____________________
Unknown side: ___________________________
4. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? Identify your choice, and then calculate the distance. (4 points: 1 point for the ratio, 2 points for shown work, 1 point for the answer)
Trigonometric ratio (name): ___________________________
Calculation (Show your work):
5. While you're at the top of the tower, you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? Use the ratio to find the measurement. (4 points: 1 point for the method, 2 points for shown work, 1 point for the answer)
6. Confirm that your answer to question 5 is correct using the Pythagorean Theorem instead of trig ratios. (3 points)
Answers
Answer:
The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.
Step-by-step explanation:
You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x
=> x = 50 m / tan(86°)
x = 50 m / 14.30 = 0.98 m
Select the correct answer.
What is ?
A.
B.
C.
D.
Answers
Answer:
B. 7 1/2
Step-by-step explanation:
1. To solve this problem, we have to multiply 2 1/2 by the reciprocal of 1/3.
In other words, multiply 2 1/2 by the inverse of 1/3, which is 3.2. (Solving)
[tex]2\frac{1}{2} *3[/tex] [tex]\frac{5}{2} *3[/tex] [tex]\frac{15}{2}[/tex] [tex]7\frac{1}{2}[/tex]Therefore, the answer is B. 7 1/2.
Answer:
its B mark branli.est pls
Step-by-step explanation:
7. answer correct for brainliest
Answers
Answer:
4 7/20
Step-by-step explanation:
8 1/4 - 3 9/10
get a common denominator of 20
8 1/4 *5/5 - 3 9/10 *2/2
8 5/20 - 3 18/20
borrow 1 from the 8 in the form of 20/20
7 +20/20 + 5/20 - 3 18/20
7 25/20 - 3 18/20
4 7/20
Answer: 4.35
Step-by-step explanation: 8 1/4 as a decimal is 8.25. 3 9/10 as a decimal is 3.9. 8.25 - 3.9 = 4.35.
HELP ME PLZ
Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 3.25 ⋅ 103 seconds?
Part B: Which is the more reasonable measurement of the distance between the tracks on a railroad:
1.435 ⋅ 10−3 mm or 1.435 ⋅ 103 mm? Justify your answer.
Answers
Answer:
salamat po sa
points.
pa
Step-by-step explanation:
branlest
answer
po
!!will mark BRAINLIEST if all are anwsered!!
Answers
Answer:
8) 31.4 ft
9) Scalene Triangle , and a right Triangle
10) 36 [tex]ft^{2}[/tex]
11) 2
12) 4/5
Step-by-step explanation:
8) Find last length
12^2+6^2=x^2
x=[tex]\sqrt{180}[/tex]
13.4
Perimeter = 13.4+12+6 = 31.4 ft
9)
10) area = 1/2 b*h = 1/2*12*6 = 36 [tex]ft^{2}[/tex]
11) slope = rise /run = 2/1 = 2
12) 80% will be girls, therefore 80/100 = 4/5
Find the measurement of the two angles
Please !
Answers
Answer:
1 -9 09u and than add
Step-by-step explanation:
What is the slope of this graph?
A-4
B 1/4
C-1/4
D 4
Answers
Answer:
The answer is D
Step-by-step explanation:
The line has 2 points: (-1;0) and (0;-4)
=> x1 = -1; x2 = 0 => x1 - x2 = -1 - 0 = -1
y1 = 0; y2 = -4 => y1 - y2 = 0 - 4 = -4
=> slope = (y1 - y2)/(x1 - x2) = [tex]\frac{-4}{-1}[/tex] = 4 => D
What is 2x-3y=12 on a graph?
Answers
if a/3=b/2, what are the following ratios?
a+b/b
Answers
Answer:
1
a+1
es posible q hayan doble respuesta
Step-by-step explanation:
Pasos
a+b/b
Divide b entre b para obtener 1.
da
d
(a+1)
La derivada de un polinomio es la suma de las derivadas de sus términos. La derivada de cualquier término constante es 0. La derivada de ax
n
es nax
n−1
.
a
1−1
Resta 1 de 1.
a
0
Para cualquier término t excepto 0, t
0
=1.
1
a+b/b
Divide b entre b para obtener 1.
a+1
Answer ASAP please<3
Answers
Step-by-step explanation:
So if you multiply both the numerator and denominator by the same number, you get the initial number. Your goal here is to get the same denominator so that you can solve the problem easily! hope it helped!
-2x -3 for x = -3
( Evaluate the following algebraic expression )
Answers
Answer:
well its -2*-3-3 so
-2*-3 is 6-3 is 3
Step-by-step explanation:
Write an equation in slope-intercept form for the line that has a slope of 5 and passes through the point (2, 30).
A. Determine the y-intercept
B. Write the equation of the line
Answers
Answer:
y-intercept = 20
y = 5x + 20
Step-by-step explanation:
Slope: 5
Point: (2,30)
y-intercept: 30 - (5)(2) = 30 - 10 = 20
solve for y: 1/2(4y+6)=4-2(y-6)/3
Answers
Answer:
y = 7/8
Step-by-step explanation:
12y+18=-4y+32
12y+18-18=-4y+32-18
12y=-4y+14
12y+4y=-4y+14+4y
16y=14
16y/16=14/16
y = 7/8
#3 A Firefighter needs to reach window that is 35 feet up. If the fire
department has a 37 foot ladder how far away from the building should
they put the bottom of the ladder?
Answers
Answer:
2 feet away from the building
Step-by-step explanation:
Hope this helps!
Look at attached link
Answers
Have a great day/night !
Answer:
[tex]-1\frac{13}{16}[/tex]
Step-by-step explanation:
Hello There!First let's put our equation to get started
[tex]-3\frac{5}{8}\cdot\frac{1}{2}[/tex]
We can make this an improper fraction by multiplying the integer with the denominator.
Then you would add the total you got with multiplying the total that you got from the whole number and the denominator
DefinitionAn integer is colloquially defined as a number that can be written without a fractional component[tex]-\frac{29}{8} \cdot\frac{1}{2}[/tex]
Now we can solve it
[tex]-29\cdot1=-29[/tex]
[tex]8\cdot2=16[/tex]
Now our equation is
[tex]-\frac{29}{16}[/tex]
ReduceDefinition - reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible
Once we've reduced we will have our equation being
[tex]-1\frac{13}{16}[/tex]
Have a good day :) !Felicia wants to keep her bill under $55. A cell phone provider charges Felicia $50 per month for her plan plus $0.05 per minute of long-distance calls. Which graph correctly shows the number of long-distance minutes Felicia can use this month?
Answers
Answer:
.05x+50=55
100 minutes
Step-by-step explanation:
simplify
.05x=5 (subtract 50 on both sides)
5/.05=x
100=x
she can call for 100 minutes
80% of __ is 16 help
Answers
Answer:
80% of 20 is 16.
Step-by-step explanation:
Hello darling, the answer is 20 ^^
Please solve with explanation
Answers
9514 1404 393
Answer:
4 : 1
Step-by-step explanation:
Each segment joining midpoints is called a "midline." It is parallel to the segment not being joined, and is half its length. All the dimensions of the smaller triangle are half those of the larger triangle. (They are similar triangles.) The ratio of areas is the square of the ratio of side lengths:
2² : 1² = 4 : 1 . . . . . . ratio of triangle areas
What is the value of l 3 l?
Answers
Answer:
3
Step-by-step explanation:
-3
I’m pretty sure this is correct because isn’t absolute value the opposite
(13x2+9x-4)-(12x2-2x+6)
add or subtract the polynomials
Answers
Answer:
[tex]x^{2} +11x-10[/tex]
Step-by-step explanation:
[tex](13x^{2} +9x-4)-(12x^{2} -2x+6)[/tex]
Remove the brackets and multiply the minus sign through all the numbers in the second polynomial
[tex]13x^{2} +9x-4-12x^{2} +2x-6[/tex]
Rearrange in the highest order
[tex]13x^{2} -12x^{2} +9x+2x-4-6[/tex]
Simplify
[tex]x^{2} +11x-10[/tex]
If the length of the line segment CD is 65% of the length of the line segment AB, what is the length of line segment CD? (AB is 13in)
Answers
Answer:
8.45
Step-by-step explanation
Convert 65% in decimal form
0.65 x 13 = 8.45
