what is the solution to the equation(3/m+3)-(m/3-m)=(m^2+9/m^2-9)
Answers
1) Subtract fractions correctly as a cross product.
2) Rewrite the second degree polynomials correctly.
3) Cancel terms that have the same exponent.
4) Make algebraic sums correctly.
Answer:
m = 3
See attached image.
it has no solution , yw
Related Questions
Tough one!
For what values of a and b is the following equation true?
limx->0 ((sin2x)/x^3)+a+(b/x^2)) = 0
@Calculus1,
Answers
= > limx->0 (2a*sinx*cosx - (b /cosx)*sinx)/ 4x3 = 1/2 => limx->0 (a*sin2x - b*tanx)/ 4x3 = 1/2 [0/0 form],
applying L'Hospital rule again ,we get,
= > limx->0 (2a*cos2x - b*sec2x) / 12x2 = 1/2
For above limit to exist,Numerator must be zero so that we get [0/0 form] & we can further proceed.
Hence 2a - b =0 => 2a = b ------(A)
limx->0 (b*cos2x - b*sec2x) / 12x2 = 1/2 [0/0 form], applying L'Hospital rule again ,we get,
= > limx->0 b*(-2sin2x - 2secx*secx.tanx) / 24x = 1/2 => limx->0 2b*[-sin2x - (1+tan2x)tanx] / 24x = 1/2
[0/0 form], applying L'Hospital rule again ,we get,
limx->0 2b*[-2cos2x - (sec2x+3tan2x*sec2x)] / 24 = 1/2 = > 2b[-2 -1] / 24 = 1/2 => -6b/24 = 1/2 => b = -2
from (A), we have , 2a = b => 2a = -2 => a = -1
Hence a =-1 & b = -2
Simplify using the distributive property.
8(y + 12)
8y + 12
20y
20 + y
8y + 96
Answers
= 8y + 96 (Answer D)
The expression 8(y + 12) simplifies to 8y + 96 using the distributive property, which involves multiplying 8 by both y and 12.
The question asks us to simplify the expression using the distributive property. The expression given is 8(y + 12). To simplify, we apply the distributive property by multiplying 8 with both y and 12.
So, we have:
8(y) + 8(12) = 8y + 96.
Therefore, the simplified form of the expression 8(y + 12) is 8y + 96.
4. find the real number roots. sqrt-0.25
Answers
Given is square root of a negative real number, i.e. [tex] \sqrt{-0.25} [/tex]
When we find square root of positive real numbers, we get Real answers.
But when we find square root of negative real numbers, we get Imaginary answers. To solve them, we can split the given negative number into product of -1 and the number itself but with positive sign. e.g. -4 = -1 x 4.
For square root of -1, we use english letter 'i' called Imaginary unit i.e. [tex] \sqrt{-1} = i [/tex]
Now we can use -0.25 = -1 x 0.25
[tex] \sqrt{-0.25} =\sqrt{-1*0.25} \\\\
\sqrt{-0.25} =\sqrt{-1}*\sqrt{0.25} \\\\
\sqrt{-0.25} =i*0.5 \\\\
\sqrt{-0.25} =0.5i [/tex]
Hence, "0.5i" is the final answer.
The square root of -0.25 is not a real number because the square root of a negative number is not defined within the set of real numbers.
The square root of a negative number is not a real number. In the case of √(-0.25), the expression is undefined within the set of real numbers because taking the square root of a negative number results in a complex number. The square root of a negative number is typically represented using the imaginary unit "i" in the complex number system. Therefore, √(-0.25) is not a real number.
To know more about square root, refer here:
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two line segments ab and cd, have end points at A ( -5,11) , B( 3,5) , C (9,3) and D (2,10) which of the two lines segments is longer ?
Answers
segment AB is longer than segment CD
Line segment AB is longer than segment CD.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Two line segments AB and CD have endpoints at A (-5, 11), B(3, 5), C (9, 3) and D (2, 10).
To find the distance:
The distance of two points
= √ {(x₂-x₁)² + (y₂-y₁)²}
The distance of segment AB
= √ {(3+5)² + (5-11)²}
= √ {(8)² + (-7)²}
= √(64 + 49)
= √(64 + 49)
= √113
= 10.63 unit.
The distance of segment CD
= √ {(2-9)² + (10-3)²}
= √ {(-7)² + (7)²}
= √(49 + 49)
= √98
= 9.9 unit.
Clearly, distance of AB > distance of CD
Therefore, distance of AB > distance of CD.
To learn more about the distance between two points;
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 190 grams of a radioactive isotope, how much will be left after 4 half-lives?
Answers
Polynomials Multiply. −3y(5y3+11y2−y+8) Express the answer in standard form. Enter your answer in the box.
Answers
Factored: 3y (-5y³-11y²+y-8)
The given expression is 3y (-5y³-11y²+y-8)
We use distributive rule to distribute 3y to the terms -5y³-11y²+y-8.
The distributive rule states :To multiply a sum by a number, multiply each term of the sum.
This can be applied to multiply a monomial and polynomial.
The Distributive Property is an algebra property which is used to multiply a single term and two or more terms.In multiplication exponents are added.
3y (-5y³-11y²+y-8) =[tex] -15y^{4} -33y^{3} +3y^{2} -24y [/tex]
Which rational number represents a decrease in water level from 8 feet to 6 feet?
Answers
Tell me if it is right or not
What is the explicit rule for the sequence?
34,26,18,10, …
an = 26 − 8n
an = 42 − 8n
an = 34n − 26
an = 34n + 42
Answers
the explicit formula for the sequence is:
an=a+(n-1)d
where
a=first term
n=index
d=common difference
from the sequence
a=34
d=26-34=-8
thus the explicit formula will be:
an=34-8(n-1)
an=34-8n+8
an=42-8n
Answer:
OPTION B
Step-by-step explanation:
Write an exponential function that passes through the points (0, 3) and (-1, 6)
Answers
when x=0, y=3, 3=ab^0, so you can figure out that a=3
when x=-1, y=6, 6=3b^(-1), b^(-1)=2, b=1/2
so the equation is y=3(1/2)^x
please help me !!!!!!!
Answers
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t – 16t2. how long after launch does the projectile return to the ground? 2 seconds4 seconds14 seconds16 seconds
Answers
v = 32 - 32t
at Max hight speed is 0m/s
therefore
0 = 32 - 32t
t = 32/32 = 1 s
so it goes up to Max hieght in 1 s
and it takes another 1s to come back
thus time after launch to return to ground is 2s!
Answer:
The correct option is A. 2 seconds
Step-by-step explanation:
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32·t – 16·t²
Now, we need too find the time after which the fired projectile touches the ground.
So, The fired projectile when touches the ground, The height of the projectile will become 0
⇒ Find the required time t when h = 0
⇒ 0 = 32·t - 16·t²
⇒ 0 = t × (32 - 16·t)
⇒ t = 0 or 32 - 16t = 0
⇒ 16t = 32
⇒ t = 2
So, t = 0 or t = 2
t cannot be 0 because initially the projectile is in the air as it has been already fired
⇒ t = 2 seconds
Therefore, The correct option is A. 2 seconds
Express the fractions 3/4, 7/16, and 5/8with the LCD.
A. 24/32, 14/32, 24/32 B. 12/16, 7/16, 10/16 C. 9/16, 49/16, 36/16 D. 3/4, 2/4, 3/4
Answers
12/16
7/16
10/16
Find the measure of each angle please?
Answers
.. x +150 +(2x -50) +(x +40) +80 +(x +20) = 720
.. 5x +240 = 720 . . . . . . . . simplify
.. 5x = 480 . . . . . . . . . . . . . subtract 240
.. x = 96 . . . . . . . . . . . . . . . .divide by 5
The angles (clockwise from lower left) are
.. 96°
.. 150°
.. 142°
.. 136°
.. 80°
.. 116°
Factor completely. 12x^4+18x^3+45x^2
Answers
3x² ( 4x² + 6x + 15)
Answer: so is the answer 3^2 or the other?
Step-by-step explanation:
well anyway but what I know the answer should be the second thing because you want the numbers to be the LCM which for this it would be (4x^2 + 6x + 15) but not 100% bout this
Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Check all that apply.
A. The triangle pre-image is closer to the point of dilation than the image.
B. The triangle image is closer to the point of dilation than the pre-image.
C. The value of the scale factor, , is between 0 and 1.
D. The value of the scale factor, 6, is greater than 1.
E. The vertices of the pre-image are collinear with the vertices of the image.
Answers
although E I have no idea what those words mean (XD)
However B and C are completely wrong.
" S " is the "pre-image" and " S' " is the "Image"
the pre-image is closer to the dilation point P in distance 2 units, whilst the other is 12 units away.
Pleas help !!!!!
The table below shows some values of f(x) and g(x) for different values of x: x f(x) = 2x + 24 g(x) = 5(0.5)x −2 20 −1 0 5 1 2.5 2 28 Complete the chart and determine the solution of the equation f(x) = g(x). x = −2 x = −1 x = 1 x = 20
Answers
f (x) = 2x + 24
g (x) = 5 (0.5) ^ x
We write the table now correctly completing the missing values:
x f(x) = 2x + 24 g(x) = 5(0.5)^x
−2 20 20
−1 22 10
0 24 5
1 26 2.5
2 28 1.25
We observe that according to the table:
f (x) = g (x) for x = -2
Answer:
x = -2
Javier has a savings account with an interest rate of 3.3%. he deposited $1200.00 into the account. write an equation, then graph it. how much money would he have after 6 years?
Answers
Total = 1,200.00 * (1.033)^6
Total = 1,200.00 * ( 1.2150717649 )
Total = 1,458.09
Let f(x)=4x^2+x+1 and g(x)=x^2-2. Find g(f(x)). Show each step of your work.
Answers
Today we are dealing with composite functions. I am going to introduce you to a new way of thinking about any function and this will help you in your understanding of composite functions.
So I want you to think of a function like a machine. Let's take a function and call it the f machine. If you take the input value 'x' and insert it into the f machine, you get f(x) as an output.
Now, for composite functions, the process is very similar BUT slightly more complicated. If we wanted to find g(f(x)), we would plug in 'x' to the f machine to get the output f(x). After that, we would plug the output into the g machine to get g(f(x)).
Let's try an example. Let's say f(x)=4x²+x+1 and g(x)=x²-2 and we want to find g(f(x)).
Well it looks like they already gave us the output for plugging x into the the f machine. The output is 4x²+x+1. Now we have to plug this into the g machine. Since the output that plugging x into the g machine is x²+2, and we want to find g(4x²+x+1), plug in 4x²+x+1 for x in the g machine. (This also means that g(4x²+x+1)=g(f(x)).)
Look...
g(4x²+x+1)=(4x²+x+1)²+2
which means...
g(f(x))=(4x²+x+1)²+2
Now simplify this...
(4x²+x+1)(4x²+x+1)+2
16x⁴+4x³+4x²+4x³+x²+x+4x²+x+1
16x⁴+8x³+9x²+2x+1
I really hope this helps!
Best wishes :)
You bought jeans last week for $55. Today you see that the jeans are on sale for $40. What is the percent decrease of the price? (Explain please!)
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I need help with how to solve this geometry question! PLEASE! DESPERATELY NEEDED!!
Answers
To find the missing side, you have to write a proportion because the sides are proportional.
When an angle is bisected like this, you can write:
28/x = 12/(30 - x)
Cross multiplying will give you:
12x = 840 - 28x
40x = 840
x = 21
You could plug the 21 back in and you will see that the sides are proportional.
Good luck!
If arc SQ = 92° and arc QR = 86°, what is the measure percent of ∠RPS
Answers
Since it's a triangle the sum of all angles is 180. So 180-86-92=2
The answer is 45°. First combine arc SQ and QR: 178°. Then subtract that from the whole circle (360°) and that will give us 182°. Now subtract arc SQ from it and divide the difference (90°) by two.
Find the volume of the sphere with a radius of 9. Express your answer in terms of π.
Answers
On this exercise is given the radius of the sphere and is asked to find its volume in terms of π. The first step would be substitute the values into the previous mention formula.
V=4/3πr^3
V=4/3π(9)^3
V=4/3π(729)
V=972π
The volume of the sphere in terms of pi is 972π.
Matias and Hannah are responsible for the centerpieces on the buffet tables at the school dance.they have 6 dozen carnations,80 lilies,and 64 rosebuds. all the centerpieces must be identical.determine the greatest number of centerpieces Matias and Hannah can make if they use all the flowers.then describe the centerpiece
Answers
There are 2 ways you can find the gcf:
1. List all factors
72-1,2,3,4,6,8,9,12,24, 36, 72
80-1,2,4,5,8,10,16,20,40,80
68-1,2,4,17, 34, 68
The greatest common factor is 4.
2. List prime factorization and match all prime numbers from all 3 lists.
72=2x2x2x3x3
80=2x2x2x2x5
68=2x2x17
2x2=4 flower arrangements
Each of the 4 center pieces will have 18 carnations, 20 lilies, and 17 rosebuds.
Matias and Hannah can make 8 identical centerpieces using all the flowers, with each centerpiece composed of 9 carnations, 10 lilies, and 8 rosebuds, arranged harmoniously.
Explanation:Matias and Hannah can make the greatest number of identical centerpieces by finding the largest number that can divide into the quantities of all three types of flowers without remainder. They have 6 dozen carnations (72 carnations), 80 lilies, and 64 rosebuds. The highest common factor that divides into 72, 80, and 64 is 8. This means they can make 8 centerpieces, with each centerpiece containing 9 carnations, 10 lilies, and 8 rosebuds.
Describing the centerpiece based on the description in the hypothetical art reference: The centerpiece would feature a balanced and harmonious arrangement of flowers with the carnations drawing the viewer's attention at the center. Similar to the composition in Chittenden's paintings, the various flower types, such as lilies and the delicate rosebuds, would be distributed to complement each other in the arrangement, creating an aesthetically pleasing and symmetrical display for the school dance buffet tables.
Four times the larger of two numbers is equal to seven times the smaller. the sum of the numbers is 22. what are the numbers?
Answers
The larger is 14 the smaller is 8
Explanation:Let the larger number be L and the smaller be S
So we know that
1) L+S=22
And
2)4L=7S
From equation 1) we get L=22-S
Substitute this into equation 2) to get 4(22-S)=7S
88-4S=7S
88=11S
S=8. The smaller number is 8
As they total 22 the larger number is 14.
Check: 4x14=7x8. Yes
Solution 2:
Let x= larger number
And let y= smaller. umber
Now we are told that:
4x=7y--------eq1
We are also told that:
x + y=22-----eq2
Substitution method looks easier.
From eq1 x=(7/4)y. Substitute this into eq2
(7 /4)y +y=22
(7/4)y+(4/4)y=22
(11/4)y=22 multiply each side by 4
11y=88
y=8
From eq2, x+8=22
x=14
Hope this helps
Final answer:
To find the two numbers where four times the larger is equal to seven times the smaller, and the sum is 22, we set up a system of equations and solve them. We find that the larger number is 14 and the smaller number is 8.
Explanation:
To solve the question "Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. What are the numbers?", we use a system of equations. First, we assign variables to the unknowns: let x be the larger number and y be the smaller number. According to the problem, we have two equations:
4x = 7y (because four times the larger number is equal to seven times the smaller)
x + y = 22 (because the sum of the numbers is 22)
Now, we can solve for one of the variables. Let's isolate y in the second equation:
y = 22 - x
Substitute this expression for y into the first equation:
4x = 7(22 - x)
Expand and solve for x:
4x = 154 - 7x
11x = 154
x = 14
Then we find y by substituting x back into the equation y = 22 - x:
y = 22 - 14
y = 8
Therefore, the larger number is 14 and the smaller number is 8.
SOMEONE HELP ME PLEASE MY LAST DAY TO TURN THIS IN!
Solving Systems of Equations by Elimination
1) 5x + 2y= 21
-x - y= -9
2) 3x + 2y= -13
3x+4y= 1
3) 7x + 3y= 22
4y= 20
4) -2x + y= 10
4x - y= -14
Answers
I'll solve the first two systems.
1)
[tex] \left \{ {{5x+2y=21} \atop {-x-y=-9}} \right. [/tex]
Multiply the second equation in the system by 2 to be able to cancel out y-terms:
[tex]-x-y=-9[/tex]
[tex]2(-x-y=-9)[/tex]
[tex]-2x-2y=-18[/tex]
Now, add the equations together:
[tex] \left \ {{5x+2y=21} \atop {-2x-2y=-18}} \right. [/tex]
_____________
[tex]3x-0=3[/tex]
[tex]3x=3[/tex]
[tex]x=1[/tex]
Plug 1 for x into one of the original equations to find y:
[tex]5x+2y=21[/tex]
[tex]5(1)+2y=21[/tex]
[tex]5+2y = 21[/tex]
[tex]2y=16[/tex]
[tex]y =8[/tex]
Check work by plugging your values for x and y back into both original equations:
[tex] \left \ {{5x+2y=21} \atop {-x-y=-9}} \right. [/tex]
[tex] \left \ {{5(1)+2(8)=21} \atop {-(1)-(8)=-9}} \right. [/tex]
[tex] \left \ {{5+16=21} \atop {-1-8=-9}} \right. [/tex]
Both are true; x = 1 and y = 8.
2)
[tex] \left \ {{3x+2y=13} \atop {3x+4y=1}} \right. [/tex]
For this system, to be able to cancel out x-terms, you can multiply either equation by -1; I'll use the bottom equation:
[tex]-1(3x+4y=1)[/tex]
[tex]-3x-4y=-1[/tex]
Now add the equations together:
[tex] \left \ {{3x+2y=-13} \atop {-3x-4y=-1}} \right. [/tex]
_____________
[tex]0-2y=-14[/tex]
[tex]-2y = -14[/tex]
[tex]y=7[/tex]
Plug 7 for y into either of the original equation to solve for x:
[tex]3x+2(7)=-13[/tex]
[tex]3x+14=-13[/tex]
[tex]3x = -27[/tex]
[tex]x=-9[/tex]
Plug -9 for x and 7 for y into each original equation to check work:
[tex] \left \ {{3(-9)+2(7)=-13} \atop {3(-9)+4(7)=1}} \right. [/tex]
[tex] \left \ {{-27+14=-13} \atop {-27+28=1}} \right. [/tex]
Both are correct; x = -9 and y = 7.
Apply these steps to the last two systems and you're good to go. (:
Which of the following functions has a maximum at x=3? SELECT ALL THAT APLLY.
A. f(x)= (x-3)^2
B. f(x)= (x-2)(4-x)
C. f(x)= -x^2+6x-5
D. f(x)= 1-(x-3)^2
E. f(x)= (x+3)^2-9
F. f(x)= x^2-4x+3
Answers
https://brainly.com/question/9370444
Which expression can be used to find the value of X?
Answers
b / sin(B) = a / sin(A)
b / sin(32°) = 11 / sin(47°)
b = (sin(32°) x 11) / sin(47°) <---- You would use this, so rewritten
11(sin(32))/sin(47) would be the expression, or answer B.)
BTW b = 7.970
Hope this helps!
What is the measure of ∠D ?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠D=
°
Answers
Remember: SOH-CAH-TOA!
Sine€ = O/H, Cosine€ = A/H, Tangent€ = O/A
O = opposite, H = hypotenuse, A = adjacent
TOA: tanD = O/A = 25/45 = 5/9 = 0.5556
Now use arc-tan feature of calculator:
[tex] { \tan(0.5556) }^{ - 1} = 29.0546 \\D= 29.05 \: degrees[/tex]
Answer:
[tex]m\angle D=29.05[/tex]
Step-by-step explanation:
We have been given an image of a right triangle and we are asked to find the measure of angle D.
We can see from our given triangle that the opposite side of angle D measures 25 ft and adjacent side of angle D is 45 ft.
Since we know that tangent represents the relation between the opposite and adjacent sides of a right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{tan}\angle D=\frac{25}{45}[/tex]
[tex]\angle D=\text{tan}^{-1}(\frac{25}{45})[/tex]
[tex]\angle D=29.054604099077[/tex]
Upon rounding our answer to nearest hundredth we will get,
[tex]\angle D\approx 29.05[/tex]
Therefore,the measure of angle D is 29.05 degrees.
Mrs. Gomez is sewing a dress for each of her four daughters. Each dress uses 2.25 yards of fabric, and the fabric costs $4.15 per yard. What will be the cost for fabric for all four dresses? Show your work, including labeling your answer with the appropriate units of measure.
Answers
Answer:
The cost for fabric for all four dresses is $37.35
Step-by-step explanation:
Each Dress requires fabric = 2.25 yards
Fabric required for 4 dresses = [tex]2.25 \times 4[/tex]
= [tex]9yards[/tex]
Cost of 1 yard fabric = $4.15
Cost of 9 yard fabric = [tex]4.15 \times 9[/tex]
= $37.35
Hence the cost for fabric for all four dresses is $37.35
MATH HELP. ^^
Answer the two pages below.
Answers
P = Principal Amount I =Interest Amount r = Rate of Interest per year in decimal; r = R/100 t = Time Periods involved