Drag each tile to the correct box. Complete the sequence for deriving the quadratic formula using the quadratic equation in standard form, .
Answers
Answer:
see the picture
Step-by-step explanation:
By the below figure (6) is the initial equation
(1) next added (b/2a)^2 on both sides to make it whole square on left side which gives (4) in (4) both terms are added on the right side to make it (5)
then square root on both sides gives (2) and now taking b/2a to the right side gives the final quadratic formula (3)
We can obtain the quadratic formula from completing the square method as shown.
The quadratic formula is derived from the completing the square method as follows;
Given the quadratic equation;
[tex]ax^{2} + bx + c =0[/tex]
Dividing through by a we have;
[tex]x^{2} + \frac{b}{a} + \frac{c}{a} = 0[/tex]
Adding half of b to both sides of the equation, we have;
[tex](x + \frac{b}{a}) ^{2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]
Taking LCM of the right hand side;
[tex](x + \frac{b}{2a})^{2} = \frac{b^2 - 4ac}{4a^2}[/tex]
Making x the subject of the formula;
[tex]x = \frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]
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Related Questions
In 1903, the Wright brothers flew their first airplane. Sixty-six years later, a man walked on the moon. In which year did a man walk on the moon?
A. 1966
B. 1969
C. 1837
D. 1970
Answers
B. 1969
Step-by-step explanation:
Hope it helped you! :) (Please correct me if I'm wrong.)
1. It takes you 2 hours to travel 110 miles. How far can you travel in 5 hours?
Answers
Answer:
275 miles
Step-by-step explanation:
110/2 = 55 miles
you travel 55 miles an hour
multiply that by 5 to get your answer
equals 275 miles
Hope this is helpful.
Answer:
275 miles in 5 hours
Step-by-step explanation:
110/2 is 55. 55 is 1hour so multiply 55 times 5 and thats your answer.
-
How many solutions does the equation 2 + 6(x - 4) = 3x - 18 + 3x have?
A)0
B)1
C)2
D) Infinite
Answers
Answer:
C because it's a quadratic equation and it can be solved by factorization and completing the square method and also general formula
I suck at math help ill give brainliest
Answers
Answer:
3
Step-by-step explanation:
5x + 40 = 55
5x = 55 - 40
5x = 15
x = 15 / 5
x = 3
PLEASE HELP QUICK!!
what is the slope of this line?
Answers
I think it might be D
The cost of a pizza varies directly as the square of its radius. If a pizza with a 6 inch radius costs $8.00, how much should a pizza with an 11 inch radius cost? Round to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
14.7$
Find the slope of the line that passes through (1, 13) and (10, 6).
Answers
Answer:
-7/9
Step-by-step explanation:
Using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 6-13)/(10-1)
= -7/9
Find the value of X - triangle measurments
I WILL GIVE BRAINLIEST!
Answers
4x-20=60
4x=80
x=20
Answer:
x = 20Step-by-step explanation:
from how the sides are marked it is an equilateral triangle, to see it does not seem. assuming that it is equilateral it has 3 angles of 60 ° for which 4x - 20 = 60
4x - 20 = 60
4x = 80
x = 80 : 4
x = 20
-------------------
4 * 20 - 20 = 60°
what is the perimeter, in grid units, of a regular octagon that has one side with endpoints (-4, -3) and (-4, 8)
Answers
Answer:
88
Step-by-step explanation:
Let's find the length of one side. The perimeter will be 8 times that since it's a regular octagon.
[tex]d= \sqrt{(-4+(-4))^2+(8-(-3))^2} = \sqrt{0^2+(11)^2}= 11[/tex]
Perimeter has to be [tex]8\times 11 = 88[/tex]
For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f (x) = StartFraction 2 x Superscript m Baseline Over x a EndFraction a = –1, m = 0 a = 1, m = 0 a = –1, m = 1 a = 1, m = 1.
Answers
Answer:
C. a= -1, m=1
Step-by-step explanation:
hope i helped, have a great day :)
For the function f(x) = [tex]\frac{2x^m}{ x + a}[/tex], if the horizontal asymptote is at y = 2 and vertical asymptote is at x = 1, then a = -1 and m = 1.
What are Asymptotes of a Function?There are asymptotes like horizontal, vertical and oblique asymptotes.
Horizontal asymptote is the value of the function f(x) as x goes to ±∞, as long as this value is not infinity.
Vertical asymptotes are the values of x which are not in the domain of the function f(x). For a fractional expression it is found by letting the denominator equals zero.
The given function is,
f(x) = [tex]\frac{2x^m}{ x + a}[/tex]
Horizontal asymptote of this function is at y = 2.
lim x → ∞ f(x) = 2
lim x → ∞ [tex]\frac{2x^m}{ x + a}[/tex] = 2
Eliminate 'a' in the denominator, because as x tends to infinity a + x also tends to infinity.
lim x → ∞ [tex]\frac{2x^m}{ x }[/tex] = 2
For the left hand side to become 2, [tex]x^m[/tex] in the numerator and x in the denominator should get cancelled.
⇒ [tex]x^m[/tex] = [tex]x[/tex]
⇒ m = 1
Vertical asymptote of the function is at x = 1.
Let x + a = 0
⇒ 1 + a = 0
⇒ a = -1
Hence we get the values a = -1 and m = 1 for the function f(x) = [tex]\frac{2x^m}{ x + a}[/tex] to have the horizontal asymptote at y = 2 and vertical asymptote at x = 1.
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How do you solve the equation 4a+b=12
Answers
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*a+b-(12)=0
Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 4a+b-12 = 0 and calculate its properties
Notice that when a = 0 the value of b is 12/1 so this line "cuts" the b axis at b=12.00000
b-intercept = 12/1 = 12.00000
When b = 0 the value of a is 3/1 Our line therefore "cuts" the a axis at a= 3.00000
a-intercept = 12/4 = 3
Slope is defined as the change in b divided by the change in a. We note that for a=0, the value of b is 12.000 and for a=2.000, the value of b is 4.000. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 4.000 - 12.000 = -8.000 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -8.000/2.000 = -4.000
Geometric figure: Straight Line
Slope = -8.000/2.000 = -4.000 a-intercept = 12/4 = 3 b-intercept = 12/1 = 12.00000Answer:
Step-by-step explanation:
Without having a numerical value for a (or b), you can't "solve this equation."
You can, however, solve it for either a or b, but not both.
For a: Subtract b from both sides. This results in 4a = 12 - b. Dividing both sides by 4 isolates a:
12 - b
a = --------------
4
For b: Subtract 4a from both sides. Then: b = 12 - 4a
Jessica has £600.
She gives 50% to her mother.
Jessica gives 10% to her brother.
She keeps the rest.
How much money does Jessica keep?
Answers
Answer:
she keeps 270
Step-by-step explanation:
have of 600 is 300 10 percent of 300 is 30
300-30 is 270
x^2 - 8x + 5 = 0
(a) find the value of the discriminant
(b) state the number and type of the roots (2 real, 2 imaginary/complex or 1 real).
Answers
√44
2 Real Roots
Step-by-step explanation:Looking at the image attached, the discriminant is the value under the square root.
In the equation given:
a = 1
b = -8
c = 5
The discriminant is therefore:
√(b²- 4ac) = √(-8²- (4*1*5)) = √(64-20) = √44
√44 is a positive number. Because it is positive, there must be 2 real roots.
If it were negative, there would be 2 imaginary roots.
If it were zero, there would be 1 real root.
a^1/2 x a^3/2 divide (a^3)^4
Answers
Answer:
3x
Step-by-step explanation:
Can someone please give me the (Answers) to this? ... please ...
I dentify the idlowing pairs. of angles.
1.<1 and <4
2.<1 and <5
3. <2 and <8
4.<4 and <5
5. <3 and <5
6.<3 and <6
7.<2 and <6
8.<1 and <8 /
/
<————-1——2—————>
3 / 4
5 / 6
<————————————>
7 / 8
/
Answers
1 / 2
<————---———————>
3 / 4
5 / 6
<————————————>
7 / 8
ANGLE TYPES: Vertical, Adjacent, Linear, Complementary, Supplementary, Co-Interior, Alternate Interior, Alternate Exterior, Corresponding,
ANSWERS:
1. Vertical
2. Corresponding
3. Supplementary
4. Alternate Interior
5. Co-Interior
6. Alternate Interior
7. Corresponding
8. Alternate Exterior
what is 15/4 as a whole number i've never been good at this and could us help
Answers
Answer:
3
Step-by-step explanation:
15/4=3 with a remainder of 3 . You take the 3 from your answer and it becomes the whole number.
Candy is sold out in 4 pound bags. How many full
Answers
need help with math
Answers
Ah sorry I got it wrong, dear
Explanation: 1/4 of grape juice as already in the bottle and then a mixture containing orange, grape and apple filled the bottle meaning the mixture was 3/4. If the mixture contained equal amounts of each juice it means 1/3 of each juice was in the mixture so 1/4 plus 1/4(the original amount of grape juice that was in the bottle before the mixture was added) is equal to 2/4 simplify that and you have 1/2
3m^2 + 5n; if m = -4 and n = -13
Answers
Answer:
3m^2 + 5n = 3
Step-by-step explanation:
3(16) + 5(-13) =
48 - 45 =
3
La casa de Camilo está a 4 cuadras a la derecha de la casa de Andrés, la casa de Rodrigo está a 2 cuadras a la izquierda de la casa Camilo ¿Cuántas cuadras hay entre las casas de Andrés y Rodrigo?.
Answers
La casa de Rodrigo está dos cuadras a la derecha de la casa de Andrés.
En esta pregunta, debemos leer el enunciado y obtener las ecuaciones equivalentes antes de obtener su solución. En este caso tenemos las siguientes dos ecuaciones:
(i) La casa de Camilo está a 4 cuadras a la derecha de la casa de Andrés.
[tex]c - a = 4[/tex] (1)
(ii) La casa de Rodrigo está a 2 cuadras a la izquierda de la casa de Camilo.
[tex]r - c = -2[/tex] (2)
Si sumamos (1) con (2), entonces obtenemos la siguiente ecuación entre las casas de Andrés y Rodrigo:
[tex]r - a = 2[/tex]
En síntesis, la casa de Rodrigo está dos cuadras a la derecha de la casa de Andrés.
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Find a trinomial for the area of the rectangular rug shown on the right whose sides are x+2 feet and 3x-1 feet.
Answers
The trinomial for the rectangular rug is 3x² + 5x - 2
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.
A trinomial is a polynomial with three terms.
The area of a rectangle = length * width
Area of rectangle = (x + 2) * (3x - 1) = 3x² + 6x - x - 2
Area of rectangle = 3x² + 5x - 2
The trinomial for the rectangular rug is 3x² + 5x - 2
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To the nearest tenth, what is the BEST estimate of the value 5√10
Answers
Answer:
15.8 i think
Step-by-step explanation:
What is (-i)^3
A. -i
B. i
C. -1
D.1
Answers
Answer:
i
Step-by-step explanation:
=> -i³
=> (-1 . i )³
=> -1³ . i³
=> -1 [ i² . i ]
=> -1 [ (√-1)² . i ]
=> -1 [ -1 . i ]
=> i
Answer:
B: i
Step-by-step explanation:
Algebric explanation: as long as you remember power rules you should be good:
[tex](-i)^3 = (-1)^3\times i^3 = -1 \times i^2\times i= (-1)\times(-1)\times i=1i[/tex]
Geometric explanation: In the complex plane you can think "multiplying by i" as "rotate 1/4 counterclockwise". [tex](-1)^3[/tex] is a real number, and it's simply [tex]-1[/tex]. Rotate that ccw once, you're at [tex]-i[/tex]. Again, and you're at 1. third time (is really the charm!) you end up at [tex]i[/tex].
Polar explanation Courtesy of euler's identity.
[tex](-i)^3 = (e^{-\frac{\pi}2i})^3=e^{-\frac32\pi i}= cos (-\frac32\pi)+isin(-\frac32\pi) = 0+i(1)= i[/tex]
what is 84 divided by -12
Answers
Answer:
-7
Step-by-step explanation:
Answer:
-7
Step-by-step expla
-7 times -12 is 84
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
N
Step-by-step explanation:
Answer:
n
Step-by-step explanation:
Show all work
which of the following lines is parallel to 2y=3x-1?
a. y = 1/2x - 1
b. 2y = x - 3
c. 4y = 6x + 8
d. y = 3x + 4
e. 3y = 2x - 3
Answers
Answer:
c. 4y=6x+8
Step-by-step explanation:
For lines to be parallel, they must have the same slope. To solve this problem, we need to isolate the y on one side of the equation (putting the equation into slope intercept form).
The equation itself must be divided by 2 to do that. We end up with y=1.5x-0.5. We need to find another equation that has 1.5 as the slope.
b. y=0.5x-1.5
c. y=1.5x+2
d. y=3x+4
e. y=2/3x-1
As we can see, the only other equation with a slope of 1.5 is C. Therefore, C is our answer.
Select all ratios equivalent to 3:5
Answers
15/25 18/30 21/35 24/40
27/45 30/50 33/55 36/60
39/65 42/70 45/75 48/80
51/85 54/90 57/95 60/100
63/105 66/110 69/115 72/120
75/125 78/130 81/135 84/140
87/145 90/150 93/155 96/160
99/165 102/170 105/175 108/180
111/185 114/190 117/195 120/200
123/205 126/210 129/215 132/220
135/225 138/230 141/235 144/240
147/245 150/250 153/255 156/260 159/265 162/270 165/275 168/280
171/285 174/290 177/295 180/300
183/305 186/310 189/315 192/320
195/325 198/330 201/335 204/340
207/345 210/350 213/355 216/360
219/365 222/370 225/375 228/380
231/385 234/390 237/395 240/400
243/405 246/410 249/415 252/420
255/425 258/430 261/435 264/440
267/445 270/450 273/455 276/460 279/465 282/470 285/475 288/480
291/485 294/490 297/495 300/500
Ratios can also be written in fraction form
What is the soultion to the following system of equations
{x+4y=-22
{3x-7y=29
Answers
Answer:
y= -1/4x - 11/2
y= 3/7x - 29/7
Write an equation of the line with the given slope and y-intercept: m = 2, b = negative three-fourths a. y = negative 2 x + three-fourths b. y = 2 x minus three-fourths c. y = negative 2 x minus three-fourths d. y = 2 x + three-fourths
Answers
Answer:
y = 2x - 3/4 Answer b
Step-by-step explanation:
slope intercept form is
y = mx + b
m is the slope = 2
b is the y-intercept = -3/4
therefor
y = 2x - 3/4 Answer b
Can someone please explain how to find the answer please.
Answers
Answer:
36 / 21 = h / 168 so h = 168 (12 / 7)
Step-by-step explanation:
i dont know how to explain it
