Answers
Answer:
[tex]\sqrt{(n-m)(n+m)}[/tex] & [tex]-\sqrt{(n-m)(n+m)}[/tex]
Step-by-step explanation:
1) Subtract [tex]m^{2}[/tex] from both sides. This should leave you with [tex]x^{2}=n^{2}-m^{2}[/tex].
2) Square root both sides. This should leave you with [tex]x=\sqrt{n^2-m^2}[/tex] & [tex]x=-\sqrt{n^2-m^2}[/tex].
You can stop here if this is what the problem is asking for. However, it is not fully simplified.
3) Factor the equation. This should leave you with [tex]\sqrt{(n-m)(n+m)}[/tex] & [tex]-\sqrt{(n-m)(n+m)}[/tex].
[tex]\boxed{\left \{ {{\sqrt{(n-m)(m+n)}} \atop {-\sqrt{(n-m)(m+n)}}} \right.}[/tex]
Solution Steps:- Steps using the quadratic formula -______________________________
1.) Subtract n² from both sides:[tex]n^2-n^2=0[/tex][tex]m^2-n^2=m^2-n^2[/tex]2.) Rewrite:This equation is in standard form: ax² + bx² + c = 0. Substitute 1 for a, 0 for b, and (m-n) (m+n) for c in the quadratic formula, [tex]\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}[/tex]:
[tex]x^2+m^2-n^2=0[/tex]2.a) Turns into:
[tex]x=\frac{0\frac{+}{}\sqrt{0^2-4(m-n)(m+n)}}{2}[/tex]3.) Square 0:[tex]0^2=0[/tex] (Also means it Cancels out.)4.) Take the square root of −4(m−n)(m+n):This just means combine them by squaring.
[tex]-4^2=2[/tex] (Half it, don't square it.)[tex](m-n)(m+n)^2=(n^2-m^2)[/tex]4a.) Our equation should look like this now:
[tex]x=\frac{0\frac{+}{}2\sqrt{(n^2-m^2)}}{2}[/tex]5.) Solve the equation using ±:Solve the equation [tex]x=\frac{0\frac{+}{}2\sqrt{(n^2-m^2)}}{2}[/tex]:
5a.) Solve the equation when ± is plus:
[tex]x=\sqrt{(n-m)(m+n)}[/tex]5b.) Solve the equation when ± is minus:
[tex]x=-\sqrt{(n-m)(m+n)}[/tex]______________________________
Hope this helps!
If you have any questions, or need help with anything else, feel free to ask! I'm happy to help!
- TotallyNotTrillex -
Related Questions
Show work for branliest
Which expression is equivalent to =
(4x^ 3 ) (2x)^-4
A. 1/(4x)
B. 4/x
C. 8/x
D. 128/x
Answers
(4x^3)(2x)^-4
Rewrite the equation
4x^3*2^-4 x^-4
Write in exponential form
2^2 x^3*2^-4 x^-4
2^-2 x^-1
Rewrite and change the power of -2 to a positive 2
1/2^2*1/x
1/4*1/x
1/4x
P.S the * represents multiplication, and in between some exponents I spaced them out, since I can’t write it properly on here without it looking like, for instance 2^2x^3 it’s suppose to be written together however it looks as if the exponent is 2x instead of being 2. You’d get the picture though.
WILL MAKE YOU BRAINLIEST FOR NO REASON IF YOU GIVE BEST RESPONSE
Answers
What is the partial fraction decomposition of
8x+19/(x+8)(x-1)?
Answers
Answer:
8x+19/(x+8)(x-1)= 5/(x+8) + 3/(x-1)
Step-by-step explanation:
Step one:
given the expression
8x+19/(x+8)(x-1)
in partial fraction the expression is
8x+19/(x+8)(x-1)= A/(x+8) + B/(x-1)
8x+19/(x+8)(x-1)= A(x-1)+B(x+8)/(x+8)(x-1)
equating the numerator we have
8x+19=A(x-1)+B(x+8)-------------------------1
to find A put x=-8 in eqn 1
8(-8)+19=A(-8-1)+B(-8+8)
-64+19=-9A
-45=-9A
A=45/9
A=5
to find B put x=1 in eqn 1
8(1)+19=A(1-1)+B(1+8)
8+19=9B
27=9B
B=27/9
B=3
The partial fraction decomposition
8x+19/(x+8)(x-1)= 5/(x+8) + 3/(x-1)
Answer:
Option-B
Step-by-step explanation:
edge
Consider functions f and g.
What is the value of ?
The words don't actually matter, it is the picture that has the question.
Answers
Answer:
we get [tex]\mathbf{(g \ o \ f)(4)=9}[/tex]
Option C is correct.
Step-by-step explanation:
We are given:
[tex]f(x)=-x^3\\g(x)= |\frac{1}{8}x-1|[/tex]
We need to find (g о f)(4)
For finding (g о f)(4) we will first find g(f(x)) i.e putting value of f(x) inside g(x) and then put x=4
[tex](g \ o \ f)(x)=g(f(x))\\(g \ o \ f)(x)=|\frac{1}{8}(-x^3)-1 |[/tex]
Now, putting x=4
[tex](g \ o \ f)(x)=|\frac{1}{8}(-x^3)-1 |\\Put \ x=4\\(g \ o \ f)(4)=|\frac{1}{8}(-(4)^3)-1 |\\(g \ o \ f)(4)=|\frac{1}{8}(-64)-1 |\\(g \ o \ f)(4)=|-8-1 |\\(g \ o \ f)(4)=|-9| \\\\We \ will \ use \ absolute \ value \ i.e \ 9 \\(g \ o \ f)(4)=9[/tex]
So, we get [tex]\mathbf{(g \ o \ f)(4)=9}[/tex]
Option C is correct
Answer:
c is correct answer
just use formula
Ebony's bank balance first reached $400 on Day 4. The last day her balance was $400 was Day 8. Look at the picture. Brainliest Answer. Only answer if your 100% sure .
Answers
Answer:
It stays true because it stays the same amount so B would be the correct answer.
Step-by-step explanation:
5. Write what the three missing digits could be in this calculation.
__x_=378
Answers
So it could be. 9 x 42 = 378
2 x 189
3 x 126
Here are a few, and there’s plenty more. Hope this helps!! ;)
Plz help this is khan and I don’t remember how to do this
Answers
it could be a I’m not sure
Explanation
I am kind of stuck on this question could someone explain and answer this question I would really appreciate it :)
Answers
Answer:
First one
Step-by-step explanation:
Supplementary angles basically means which angles added together equals 180 degrees, 180 degrees is also a straight line.
So the answer would be the first one because both the angles added together is 180.
how do you write the algebraic notation when the scale factor is 3
Answers
Answer:(2 * 3, 1 * 3)
Step-by-step explanation:
just need help with a. please helppp
Answers
Answer:
Domain: [tex]-5\leq x\leq 4[/tex]
Range: [tex]-5\leq y\leq 5\\[/tex]
Function: yes
Step-by-step explanation:
Domain is all possible x values. In this function, domain would be: [tex]-5\leq x\leq 4[/tex]
Range is all possible y values. In this function, range would be: [tex]-5\leq y\leq 5[/tex]
This is a function because it passes the vertical line test.
A leaking pond loses 20 gallons of water in 35 hours. How many gallons of water will it lose in 47 hours?
Answers
(20/35) * 47 = around 27 gallons in 47 hours
Lines j and k are parallel and cut by a transversal t. If m<1 = 4x – 20 and m<6 = 5x – 25, what is m<2?
Answers
Answer:
Step-by-step explanation:
m<2 = 5.
because if you subtract 5x from 4x and that equals -1x. then you add 20 to -25 that equals -5. then you divided -5 by the -1x and you get 5.
Lois is four times as old as her son Don. The sum of their ages is 40. How old is Don?
a.Create an equation that can be used to solve this problem.
b.How old is Don?
Answers
Explanation :
Lois = 4 (Don)
L+ D = 40
4D+D=40
5D=40
D=8
Read the description of f below, and then use the drop-down menus to complete an explanation of why f is or not a function. Help
Answers
Answer:
can you add the dropdown menu? hard to answer without the dropdown
Step-by-step explanation:
Answer:
hope this helps!
Step-by-step explanation:
Please help me out. Thanks
Answers
Answer:
61
Step-by-step explanation:
Rectangle area=
[tex]60 \times 40 = 2400yd ^{2} [/tex]
The area at the right
[tex](\pi \times 20^{2} ) \div 2 = 628yd^{2}[/tex]
Total area = 2400+628=3028yd^2
Now you have to find the quantity of grass seed needed (1pound for every 50yd square)
3028/50=60.56 (which is almost 61)
solve 2x to the second power - 8x = -7
Answers
Answer:
[tex]x=4+\sqrt{2}/2, x=x=4-\sqrt{2}/2[/tex]
Step-by-step explanation:
Just the image below.
Answers
Answer:
Step-by-step explanation:
I'm answering this silly thing only because it seems to have an expected answer
B: is about the only answer you cannot give.
C and D are Both open ended at 15 which doesn't allow you to say that the first acceptable answer is 16
The only answer you can pick is A. The amount starts at 15 and you keep going until you hit 70. That doesn't mean you have to stop. It just means that it represents what he desires to make.
If Paul’s savings are 25% more than Janet’s savings,
What percentage of Paul
savings are Janet’s savings
(A) 25 %
(B). 50%
(C) 75%
(D) 80%
Answers
What is the sum of 347+645=
Answers
Answer:
347 + 645 = 992
Step-by-step explanation:
347
+645
922
PLEASE HELP
Alvin's age is three times Elga's age. The sum of their ages is 52. What is Elga's age?
Answers
Answer:
A = 3E
A + E = 56
3E + E = 56
4E = 56
E = 14
Elga is 14 years old.
Step-by-step explanation:
Could you please mark me as the brainliest answer
Answer:
Step-by-step explanation:
17.33
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School Brented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? *
Answers
Answer:
ANSWER: each van carries 18 people and each bus can transport 59 people.
Step-by-step explanation:
Let x = number of vans
y = number of buses
Then x + 6y = 372
4x + 12y = 780
Multiply the first equation by -4: -4x - 24y = -1488
4x + 12y = 780
Adding the equations, we get -12y = -708
y = 59
Substitute for y in the equation x + 6y = 372:
x + 6(59) = 372
x + 354 = 372
x = 18
Completely factor the expression.
Answers
Answer:
x(8xsquare+6x-20)
Step-by-step explanation:
Answer:
[tex]x(2x+4)(4x-5)[/tex]
Step-by-step explanation:
[tex]x(8x^{2} +6x-20)\\x(2x+4)(4x-5)[/tex]
What is the result of 4 divided by one-half? A number line going from 0 to 4. 2 8 12 16
Answers
Answer:
2
4/.5 = 2
Therefore, your answer is 2, or A. Hope this helped!
Answer:
the answer is B) 8
Step-by-step explanation:
hope this helped sorry if it didn't and if it's wrong sorry for that also.
(GIVING BRAINLIEST AND EXTRA POINTS!!!)
Solve the equation using equivalent fractions. SHOW YOUR WORK.
13/14 - 1/7 + 1/2
Answers
Answer:
1 2/7 or 9/7
Step-by-step explanation:
First subtract 13/4-1/7=11/14
Then take the answer we subtract so we can add it 11/14+1/2= 1 2/7
HELP ASAP ! PLEASE I LOVE YOU MAY GOD BLESS YOU <3 :)
Answers
I can't answer the first question because you need to draw lines from one number to another and I'm not sure how to type that. The answer to the second question is choice 1.
Answer:
1) draw a colored in dot right above 0 with an arrow connected to it that points to the left of the graph
2) draw a white uncolored in dot right above 12 connected to an arrow that points to the left of the graph
6) draw a colored in dot right above -4 with an arrow connected to it that points to the right of the graph
7) draw a colored in dot right above 2 with an arrow connected to it that points to the left of the graph
For question 1 on the second image, the answer is Option 1. We would color in the dot right above 36 because the child an be 36 inches and still ride the ride, and we would leave the dot right above 48 uncolored because in order to ride the ride the child must be less than 48 inches they cannot be 48 inches or taller if they want to ride the ride.
Step-by-step explanation:
The inequality for the first question can be simplified to p [tex]\leq \\[/tex] 0, so just draw a colored in dot right above 0 with an arrow connected to it that points to the left of the graph (indicating that all values of p are less than or equal to 0)
The inequality for the second equation can be simplified to g < 12, so just draw a white uncolored in dot right above 12 connected to an arrow that points to the left of the graph (indicating that all values of g are less than 12)
The inequality for the problem that says 6), can be simplified to -4 [tex]\leq \\[/tex] c, so just draw a colored in dot right above -4 with an arrow connected to it that points to the right of the graph (indicating that all values of c are equal to or greater than -4)
The inequality for the problem that says 7), can be simplified to j [tex]\geq[/tex] 2, so just draw a colored in dot right above 2 with an arrow connected to it that points to the left of the graph (indicating that all values of j are equal to or greater than 2)
what is the value of 4/5(8+7)-2/3(8+7)
Answers
Answer:
The answer is 2.
Hope this helps and if you could mark this as brainliest. Thanks!
The question is below (This an order of operation question)
Answers
Step-by-step explanation:
i am 90% sure this is correct
Answer:
Step-by-step explanation:
Do multiplication first since it comes before the division in this equation
1/5 · 1/2 = 1/10
Plug this value back into the equation
1/2 - 1/10 + 2/5 ÷ 7/10
Divide 2/5 by 7/10
4/7
Plug this value back into the equation
1/2 - 1/10 + 4/7
Subtract 1/10 from 1/2
2/5
Plug this value back into the equation
2/5 + 4/7
Add.
34/35
Hope this helps :)
Please consider Brainliest :)
In the equilateral triangle below, x =
and the length of each side is
units.
3x + 6
9x – 12
6x - 3
Answers
Step-by-step explanation:
3x+6+9x-12+6x-3=180
15x-9=180
x-9=12
x=21
A dog that weighs 14 pounds should eat 1 5/8 cups of a certain type of dog food per day. How much of the same type of dog food should be fed, per day, to a dog who weighs 26 pounds?
PLEASE HELP!!!!!!!!
Answers
(13/8)/14 = .116 or 13/112
.116 (26) = 3.016 or 169/56
9514 1404 393
Answer:
3 1/56 cups
Step-by-step explanation:
Apparently, you're to assume that the amount of food is supposed to be proportional to weight. If x is the amount of food for the 26-pound dog, then ...
cups/weight = (1 5/8)/14 = x/26
Multiplying by 26 we have ...
x = (26)(13/8)/14 = 338/112 . . . cups
x = 3 1/56 cups ≈ 3.02 cups
About 3.02 cups of the same type of food should be fed to a 26-pound dog.
Which of the following angle pairs are alternate interior angles? Choose all that apply. (2 points)
A. Angles 1 and 4
B. Angles 8 and 6
C. Angles 5 and 6
D. Angles 2 and 3
E. Angles 8 and 7
F. Angles 3 and 6
Answers
Answer:
A. Angles 1 and 4
D. Angles 2 and 3
Step-by-step explanation:
Alternate interior angles are a pair of angles which alternate each other lying on either side of the transversal but within the two parallel lines that is cut across by the transversal.
In the diagram above, the following are alternate interior angles:
<1 and <4,
<2 and <3
Answer:
A and D
Step-by-step explanation: