Find x step by step (10 points)
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 -
A middle school mathematics teacher except a teaching position that pays 40,000 per year, each year the expected raise is $2000. How much total money with this teacher and teaching middle school math Mathematics over the first 30 years?
9514 1404 393
Answer:
$2,070,000
Step-by-step explanation:
The series of salaries has a first term of $40,000 and a common difference of $2,000. The sum of them is given by the formula ...
Sn = (2a1 +d(n -1))(n/2)
where a1 is the first term of the series, d is the common difference, and n is the number of terms.
In this problem, we have ...
a1 = 40,000; d = 2,000; n = 30
so the sum is ...
S30 = (2(40,000) +2,000(30 -1))(30/2) = (80,000 +58,000)(15)
S30 = 2,070,000
The teacher will earn $2,070,000 over 30 years on this salary schedule.
Britzy has $50 and wants to buy a new pair of basketball shoes.The shoes cost $45 and have 6% tax.Does britzy have enough money?
16. Mario has $15. He spends $6.25 on admission to the ice
skating rink, $2.95 to rent skates, and $1.65 each for 2 hot
chocolates. How much money does he have left?
Answer:
4.15
Step-by-step explanation:
Minus it all
15 minus 6.25 is 8.75
8.75 minus 2.95 equals 5.8
5.8 minus 1.65 equals 4.15
A t-shirt printing company charges a one-time setup fee, plus a charge to print each t-shirt. The math club had 75 t-shirts printed for a cost of $424. The science club had 50 t-shirts printed for a cost of $299. What is the cost of having 170 t-shirts printed? *
Answer:
$826.70
Step-by-step explanation:
If 75 t-shirts cost $ 424, it implies that the value of each shirt is $ 5.65 (424/75). Now, in the case of the 50 shirts, the total value is $ 299, with which the value of each unit is $ 5.98.
Thus, we can see that in an increase of 50% of the units (from 50 to 75), the discount is of the order of, as it arises from the following calculation:
5.98 = 100
5.65 = X
((5.65 x 100) / 5.98) = X
94.48 = X
Thus, since 100 - 94.48 is 5.52, the discount made for the 25 shirts is 0.22% each unit (5.52 / 25). Thus, in the case of printing 170 t-shirts, taking into account this tariff system, and taking as a base price that of 50 t-shirts at $ 299, a discount of 0.22% would be made on each of the 120 remaining t-shirts. Thus, 120 t-shirts at $ 717.6 (5.98 x 120) would be added to the initial $ 299, on which a 26.4% discount (0.22 x 120) would be applied, with which the final price would be $ 527.7 (717 x 0.736).
Thus, the total price of the shirts would be $ 826.7 (that is, adding the base price of $ 299 plus the price of the 120 extra shirts of $ 527.7).
Esther wants to solve the problem using an equation. Help her write an equation to determine how many text messages Lexie could send in any number of minutes.
Find the missing value in Kenny’s table.
Solve Esther’s equation. Will she get the same answer as Kenny?
What is Lexie’s unit rate? That is, how many text messages can she send in
minute
Answer2/0
Step-by-step explanation:
Factorise fully the following 2x+8
1.682 inches rounded to the nearest whole number is 1 inches?
Answer:
No, it is 2 inches because 6 rounds up.
Hope this helps and have a great day!
And please mark me brainliest if you can :)
What is the axis of symmetry for the following equation?
y=4x2-8x+9
Answer:x=1
Step-by-step explanation:
The x of the top of the parabola is:
x=-(-8)/(2*4)=1
x=1
Using quadratic function concepts, it is found that the axis of symmetry for the function is x = 1.
The standard quadratic function is modeled by:
[tex]y = ax^2 + bx + c[/tex]
And has axis of symmetry given by:
[tex]x = -\frac{b}{2a}[/tex]
In this problem, the function is:
[tex]y = 4x^2 - 8x + 9[/tex]
The coefficients are:
[tex]a = 4, b = -8, c = 9[/tex]
Then, the axis of symmetry is:
[tex]x = -\frac{b}{2a} = -\frac{(-8)}(2(4)} = 1[/tex]
A similar problem is given at https://brainly.com/question/24737967
Fill in the blanks below with the correct units
Answer:
a= ft is the unit
b=g(gram) is the unit
c= percent % is the answer
The GCF of 26 39 and 65
Omar is about to start his final semester of college, and he doesn't have enough money saved to afford the $750 he needs in books. He's 21, so he's going to open his own credit card to pay for the books, and then not use it again. His plan is to pay $100 per month toward his bill, until it's paid off. Which credit card offer is the best offer for Omar?
15*PLEASE ANSWER FAST VERY URGENT!!!!!
Answer:
25/15 - 12/15
Step-by-step explanation:
turn the mixed number to an improper fraction, then multiply the denominator and numerator by 5 to reach 15 and then 5 x 3 and 4 x 3 to get 12/15. I hope this helps
A garden is in the shape of a rectangle 90 m by 60 m.
Flowers are grown in 40% of the garden.
The rest of the garden is grass.
Work out the area of the garden that is grass.
Answer:
3240 sq meters
Step-by-step explanation:
Area of garden = 90*60= 5400 square meters.
Flowers grown on = 40%
So, grass grown on = (100 -40)% = 60%
60% of 5400 = 0.6*5400 = 3,240.
So, the area of the garden that is grass = 3,240 square meters
What is the volume of the figure? Enter the answer in the box.
Answer:
217,600
Step-by-step explanation:
Multiply all the sides
Please help. It’s not “yes, corresponding angles converse”
Answer:
Yes,Corresponding Angles
Step-by-step explanation:
any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.
Answer:
It is yes,corresponding angles
Step-by-step explanation:
Can y’all pls solve this
Answer:
1.
x=2+5x=0+7x=4x+1+37x=x+2+42.
x=2-33x=-2-4x=2x+7-5x=4x+6-7Solve the following equation.
1/3 k + 80 = 1/2 k + 120
Answer:
2; 3; 80; 1; -40; 1; -240 (answered from left to right then the next line)
Step-by-step explanation:
This is a question on fractions and solving algebraic equations. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Answer:
240
Step-by-step explanation:
k/3+80=k/2+120
K/3-k/2=120-80
3k-2k/6=40
K/6=40
K=240.
So the value of k is 240.
A country’s daily oil production can be approximated by q(t)=0.013t^2-0.6t+5.27
30POINTS
What is the value of x?
Answer:
look like the answer is 39
Step-by-step explanation:
Answer: your answer is y+b=39-dy 40=4=
80Step-by-step explanation:
f (x) = 20 - (1.27)
growth or decay ?
Answer:
Decay...? Read below
Step-by-step explanation:
Assuming you meant to put 20 - (1.27)x, it is decay. As the x increases, the y decreases, making it decay.
Solve: 4|x-1|+2=0
:{{{{{{{{{
2. The mean birth weight of a full term boy born in the US is 7.7 lbs, with standard deviation of 1.1 lbs. A. Find the probability that a boy born full term in the US weighs less than 7 lbs. B. Find the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs.
Answer:
A
The value is [tex]P( X < 7 ) =0.26226[/tex]
B
The value is [tex]P( X < 7 ) = 0.00073[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 7.7 lbs[/tex]
The standard deviation is [tex]\sigma = 1.1 \ lbs[/tex]
The sample size is n = 25
Generally the probability that a boy born full term in the US weighs less than 7 lbs is mathematically represented as
[tex]P( X < 7 ) = P( \frac{X - \mu }{\sigma} < \frac{7 - 7.7 }{1.1 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P( X < 7 ) = P(Z <- 0.6364 )[/tex]
From the z table the area under the normal curve to the left corresponding to -0.6364 is
[tex]P(Z <- 0.6364 ) =0.26226[/tex]
=> [tex]P( X < 7 ) =0.26226[/tex]
Generally the standard error of mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{ 1.1 }{\sqrt{25} }[/tex]
=> [tex]\sigma_{x} = 0.22[/tex]
Generally the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs is mathematically represented as
[tex]P( \= X < 7 ) = P( \frac{\= X - \mu }{\sigma_{x}} < \frac{7 - 7.7 }{ 0.22 } )[/tex]
=> [tex]P( X < 7 ) = P(Z <- 3.1818 )[/tex]
From the z table the area under the normal curve to the left corresponding to -3.1818 is
=> [tex]P(Z <- 3.1818 ) = 0.00073[/tex]
=> [tex]P( X < 7 ) = 0.00073[/tex]
Find the area of the circle.
Answer:
50.24 centimeters squared
Step-by-step explanation:
The diameter (d) is 8 which means the radius is 4 (8/2)
we use the formula pi x radius^2
It says to use 3.14 for pi
so the equation is 3.14(4)^2=3.14 x 16 = 50.24
Answer:
50.24 centimeters squared
Step-by-step explanation:
i just took the test
Convert the rate 25 miles per hour to feet per second
Answer:
36.67 feet / second
Step-by-step explanation:We will be using Dimensional Analysis to solve this question
We are given the rate: 25 miles / hour
Converting the Miles to feet:
We know that 1 mile = 5280 feet
So, we can say that [tex]\frac{5280 feet}{1 mile}[/tex] = 1
Multiplying the Given rate by 1:
[tex]\frac{25 miles}{Hour}[/tex] * 1
(multiplying by 1 will not change the actual value of the expression)
[tex]\frac{25 miles}{Hour}[/tex] * [tex]\frac{5280 feet}{1 mile}[/tex] (since 5280 feet/ 1 mile = 1)
here, the 'mile' will cancel out and we will get:
[tex]\frac{25 * 5280 feet }{Hour }[/tex]
[tex]\frac{132000 feet}{Hour}[/tex]
Converting the Hours to Seconds:
We know that 1 hour = 3600 seconds
So, we can say that:
[tex]\frac{1 Hour}{3600 seconds}[/tex] = 1
Multiplying the Rate by 1:
[tex]\frac{132000 feet}{1 Hour} * 1[/tex]
(multiplying by 1 will not change the actual value of the expression)
[tex]\frac{132000 feet}{1 Hour} * \frac{1 Hour}{3600 seconds}[/tex] (since 1 hour / 3600 seconds = 1)
Here, the 'Hour' in the numerator and the denominator will cancel out to make:
[tex]\frac{132000 feet}{3600 seconds}[/tex]
which can be simplified to:
[tex]\frac{36.67 feet}{second}[/tex]
Therefore, 25 mph can also be written as 36.67 feet per second
FInd the area of the circle
Answer:
A = 12.56 m²
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASGeometry
Area of a Circle: A = πr²d = 2rStep-by-step explanation:
Step 1: Define
d = 4 m
Step 2: Find r
Substitute: 4 = 2rIsolate r: 2 = rRewrite: r = 2 mStep 3: Find Area
Substitute: A = π(2)²Substitute: A = (3.14)(2)²Evaluate: A = (3.14)(4)Multiply: A = 12.56 m²find the equation of the line shown
Answer:
y = x + 1
Step-by-step explanation:
find slope (y2-y1)/(x2-x1)
pick 2 points (0,1) and (1,2)
(2-1)/(1-0) = 1/1 = 1
Since (0,1) you know that y intercept is 1
the equation in slope intercept form: y = x + 1
In △LMN, S is the centroid. If NP=69 find SP.
Answer:
maybe in the 70s actually
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
The centroid divides each median in a ratio of 2:1.
Help! This is due today and I don’t know nothing
Answer:
1.A
2.A
3.B
4.B
Step-by-step explanation:
That the answer
What is the measure of ABC?
Answer:
D i think
Step-by-step explanation: