Answer:
[tex]mnb^2 = ac(m+n)^2[/tex]
Step-by-step explanation:
Given
[tex]ax^2 +bx + c = 0[/tex]
Required
Condition that the roots is in m : n
Let the roots of the equation be represented as: mA and nA
A quadratic equation has the form:
[tex]x^2 + (sum\ of\ roots)x + (product\ of\ roots)=0[/tex]
or
[tex]x^2 - (\frac{b}{a})x + \frac{c}{a} = 0[/tex]
We have the roots to be mA and nA.
So, the sum is represented as:
[tex]Sum = mA + nA[/tex]
[tex]Sum = A(m + n)[/tex]
And the product is represented as:
[tex]Product = mA * nA[/tex]
[tex]Product = mnA^2[/tex]
By comparing:
[tex]x^2 + (sum\ of\ roots)x + (product\ of\ roots)=0[/tex]
with
[tex]x^2 - (\frac{b}{a})x + \frac{c}{a} = 0[/tex]
[tex]Sum = -\frac{b}{a}[/tex]
[tex]Product = \frac{c}{a}[/tex]
So, we have:
[tex]Sum = -\frac{b}{a}[/tex]
[tex]A(m + n) = -\frac{b}{a}[/tex]
Make A the subject:
[tex]A = \frac{-b}{a(m+n)}[/tex]
[tex]Product = \frac{c}{a}[/tex]
[tex]mnA^2 = \frac{c}{a}[/tex]
Substitute [tex]A = \frac{-b}{a(m+n)}[/tex]
[tex]mn(\frac{-b}{a(m+n)})^2 = \frac{c}{a}[/tex]
[tex]mn\frac{b^2}{a^2(m+n)^2} = \frac{c}{a}[/tex]
Multiply both sides by a
[tex]a * mn\frac{b^2}{a^2(m+n)^2} = \frac{c}{a} * a[/tex]
[tex]\frac{mnb^2}{a(m+n)^2} = c[/tex]
Cross Multiply:
[tex]mnb^2 = ac(m+n)^2[/tex]
Hence, the condition that the ratio is in m:n is
[tex]mnb^2 = ac(m+n)^2[/tex]
QUESTION: find the perimeter
Answer:
4g + 4
Step-by-step explanation:
Perimeter of a rectangle = 2(length + width)
Length = 0.7g + 2
Width = 1.3g
Plug in the values into the equation
Perimeter = 2(0.7g + 2 + 1.3g)
Perimeter = 2(0.7g + 1.3g + 2)
Perimeter = 2(2g + 2)
= 2*2g + 2*2
Perimeter = 4g + 4
Write the equation in point-slope form of the line that passes through the given point and has the given slope (4,-7); m= -1/4
Answer:
y + 7 = -1/4(x - 4)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Slope m = -1/4
Point (4, -7)
Step 2: Write Function
y + 7 = -1/4(x - 4)
Which expression is quivalent to this one ?
Answer:
third option 11
Step-by-step explanation:
Answer:
Second option: 1
Step-by-step explanation:
input it in a calculator, and the answer was 1
Factor the following 36k^2-1
answer
[tex] {36k}^{2} - 1[/tex]
using identity
[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
let a=6k and b=1
we get
[tex](6k + 1)(6k - 1)[/tex]
hope you are satisfied
Solve for b. -9/3 + b = -1 b = ___?
Answer:
2
Step-by-step explanation:
its 2 have a good day (:
I’m have trouble with this one
Answer:
y/cost=m/months/× x/cost per month+ b/ initial fee
Write two equivalent expressions to 9x + 27.
Answer:
3x+6x+27
9x+20+7
Step-by-step explanation:
just expand out the equation
Answer:
3(3x+9)
9(x+3)
Step-by-step explanation:
3(3x+9)= 9x+27
9(x+3)= 9x+27
Write the word sentence as an inequality.
A number y is no more than −8.
An inequality is
.
Answer:
y ≤ -8
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helppppppppppppppppppppppppppppppppp
1. Write an equivalent expression in standard form, and collect like terms(Combining like terms)
2. Express the answer from Part A as an equivalent expression in factored form.
Answer:
4x-10y
Step-by-step explanation:
Look at the pic...
Answer:
4x + 2y
Step-by-step explanation:
1. 4x - 3(x - 2y) + 1/2(6x - 8y)
4x - 3x + 6y + 3x - 4y
4x + 2y
2. 4x - 3(x - 2y) + (1/2)(6x - 8y) =
4x - 3x + 6y + 3x - 4y =
4x + y(6 - 4) = 4x + 2y = 2(2x + y)
I hope this helps
Line d passes through points (10, 10) and (7, 5). Line e is perpendicular to d. What is the slope of line e?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
(-3,-5)
Step-by-step explanation:
subtract y1 from y2 and you get -5. Now subtract x1 from x2 and you get -3. Now put the x value first and then the y value.
Answer:
m =5/3Step-by-step explanation:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(10,\:10\right),\\\:\left(x_2,\:y_2\right)=\left(7,\:5\right)\\\\m=\frac{5-10}{7-10}\\\\Simplify\\\\m = \frac{-5}{-3} \\\\m=\frac{5}{3}[/tex]
i want to know how to solve this cross number puzzle i know the answers but where do i put them
across
1) 10
2) 25
5)9
6)12
Plz help with math plzlzlzlzl
Solve for x: -2x + 1 = -6
This is a 2-step equation. We will solve it in 2 steps.
[tex]-2x + 1 = -6\\\\-2x = -7\\\\x = \frac{7}{2}[/tex]
The solution for this equation is x = [tex]\frac{7}{2}[/tex].
Factor an 8 from the expression: 32 + 40b
Draw the reflection of the figure over the line shown .
Don claims that the trianlges are congruent by SAS triangle congruence criterion because a sequence of rigid motions carries \triangle ABC△ABC onto \triangle DEF△DEF. Select all that can be used to support Don's claim.
A -a rotation of 30^o30 clockwise about vertex A, follwed by a translation that carries AB to DE, and a reflection over AC.
B- a rotation of 30^o30 clockwise about vertex A, follwed by a translation that carries AB to DE, and a reflection over AB.
C- a rotation of 90^o90 counterclockwise about vertex A, follwed by a translation that carries AC to DF, and a reflection over AC.
D- a rotation of 90^o90 counterclockwise about vertex A, follwed by a translation that carries AC to DF, and a reflection over AB.
Answer:
The triangles would match if you chose D
the price of a calculater has decreased from $200 to $150. What is the percentage of decrease?
Answer:
25%
Step-by-step explanation:
200-150=50
50/200=0.25
have a nice day!
Write and solve an equation to find x and also find the measure of angle EHF.
Which of the following functions best describes this graph?
A. y = (x-1)(x+3)
B. y =x^2-x+5
C. y = (x+1)(x+1)
D. y=x^2-5x+6
Simplify. Your answer should contain only positive exponents
Answer:
Simplify what though? i would answer u but plz put what im supposed to simplify
Step-by-step explanation:
Pleaseee help meee....
Answer:
its 90 bc the angle has a square (tbh I'm just guessing
Use a system of equations to solve the following problem:
I NEED THIS ANSWER ASAP PLEASE
Answer:
0,7
Step-by-step explanation:
by graphing
please help! struggling a lot.
Answer:
x=2<br/>y=1
Step-by-step explanation:
\left\{ \begin{array} { l } { 4 x + y = 9 } \\ { 3 x - 2 y = 4 } \end{array} \right.
4x+y=9,3x-2y=4
4x+y=9
4x=-y+9
x=\frac{1}{4}\left(-y+9\right)
x=-\frac{1}{4}y+\frac{9}{4}
3\left(-\frac{1}{4}y+\frac{9}{4}\right)-2y=4
-\frac{3}{4}y+\frac{27}{4}-2y=4
-\frac{11}{4}y+\frac{27}{4}=4
-\frac{11}{4}y=-\frac{11}{4}
y=1
x=\frac{-1+9}{4}
x=2
x=2,y=1
Sarah and three friends enter a story writing contest. They win the contest and receive a cash
prize. Each person on the team received $21.25. How much money did the team win
altogether
Show work please
Answer:
85
Step-by-step explanation:
21.25 times 4 (Sarah and 3 friends) equals 85
PLS HELP ILL GIVE BRAINLEIST !!!!!!
15)Big Bird is making wedding favors for Jack and Jill. He can create 3 vases
every hour. He already had 2 vases in his storage area (7 pts)
a Write an equation to model this situation:
b. Graph Big Bird's vases. Be sure to label the axes appropriately
Watch the scales on the axes!!!
hours
vases
12
10
1
2
3
4
6+
4
2
O
i
3
Answer:
y=3x+2
Step-by-step explanation:
For a the equation is y=3x+2 because he makes 3 every hour (3x) and he already has 2 (+2).
For the graph you replace x with any number and solve. Plot the point.
Then you do it again but with a different x.
Finally you draw a straight line trough the 2 points.
I WILL MARK BRAINIEST
PLEASE HELP ASAP ITS DUE
Answer:
The star has rotational symmetry of order 5.
Step-by-step explanation:
SAT QUESTION!!!
Jayden has been reading a 275-page book for English class. On average, he has read about 10 pages in 15 minutes. With a deadline looming, Jayden realizes that he won't finish in time unless he skims through the rest of the book. If he skims the book, he can cover 15 pages in 10 minutes. If it takes Jayden 5 hours and 50 minutes to finish the book (reading and skimming combined), how many pages did Jayden have to skim through?
WITH STEPSSS
Step-by-step explanation:
Let x be the number of pages that were skimmed through.
Time taken to skim through = 10 * (x/15) = 2/3 x min.
Time taken to read through = 15 * [(275-x)/10] = 1.5(275-x) min.
We have 2/3 x + 1.5(275-x) = 350.
Therefore 412.5 - 5/6 x = 350 and x = 75.
Answer:8pages
Step-by-step explanation:
10minutes/350minutes×275=7.85~8pages
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 1350 cubic centimeters when the pressure is 250 millimeters of mercury (mm Hg), find the volume when the pressure is 450mm Hg.
The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1.5 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard.
Answer:
(3.5, 9.5)
Step-by-step explanation:
μ=6.5
σ=1
In a certain Algebra 2 class of 27 students, 18 of them play basketball and 16
of them play baseball. There are 3 students who play neither sport. What is
the probability that a student chosen randomly from the class plays
basketball or baseball?
Answer:
The probability is 0.89 or 89%
Step-by-step explanation:
Probability
There are n=27 students in a certain Algebra 2 class. 18 out of them play basketball and 16 of them play baseball.
We also know 3 students play neither sport. This leaves 27-3=24 students playing sports.
The probability that a randomly chosen student plays basketball or baseball is:
[tex]\displastyle p=\frac{24}{27}[/tex]
Simplifying:
[tex]\displastyle p=\frac{8}{9}=0.89[/tex]
The probability is 0.89 or 89%