Answer:
For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.
Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:
(x + y)2 = x2 + 2xy + y2 (Square of a sum)
(x − y)2 = x2 − 2xy + y2 (Square of a difference)
To find the roots of a quadratic equation in the form:
\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0,
follow these steps:
(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
(iv) Write the left side as a square and simplify the right side.
(v) Equate and solve.
Example 1
Find the roots of x2 + 10x − 4 = 0 using completing the square method.
Answer
Example 2
Solve 4x2 + x = 3 by completing the square.
Answer
Exercises
Solve the following quadratic equations by completing the square
Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s
2
+5s=3Answer
Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x
2
=3−4xAnswer
Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v
2
−6v−2=0Answer
Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0Answer
1. Solving Quadratic Equations by Factoring
3. The Quadratic Formula
can you say it in order
1 Calcula de la medio aritmética, la mediana
y la moda. Se analizó el IVA que se oplico
en diversos países europeos, a la compra de
obras de arte. Los resultados obtenidos
fueron los siguientes:
PAIS
España 0,16
Holia 0,20
Belgica 0,06
Holanda 0.06
Alemania 0,07
Portugal 0,17
Luxemburgo 0,06
Finlandia 0,22.
Answer:
Step-by-step explanation:
orms of volunteering can be applied to the different roles that people take within ... volunteer motivations and looks to develop a typology of sports volunteers. ... diversity for their effectiveness as a policy tool and for government support. ... International Journal of Sport Policy and Politics 4, 2, 187–200 . ... text, however. For .
Dan drives 23 miles to work every day. He works 5 days a week. How many miles does he travel to and from work over 52 weeks?
Answer:
Step-by-step explanation:
They make it sound like it is 23 miles one way.
2(23)5(52)
11960 miles
In the figure, kj and are opposite rays. 21 & 22 and KM
bisects NKL
Р
2
134
NM
L
What bisects ZJKN?
Answer:
P 2 134 2×384
Step-by-step explanation:
24×(345)3\
Find the surface area of the pyramid. The side lengths of the base are equal.
there are 3 sides and a bottom
the base is 12 and the height is 17
Five friends share 6 snacks equally.
How many fruit snacks will each friend get?
Answer:
A
Step-by-step explanation:
I need help on this question
Find the area of the semicircle. 10
Exact Area = 25pi square units
Approximate Area = 78.5 square units
The approximate value is found using pi = 3.14
====================================================
Explanation:
I think you meant to say "quarter circle" instead of "semicircle".
The area of a full circle with radius r = 10 is
A = pi*r^2
A = pi*10^2
A = pi*100
A = 100pi
But we only want one quarter of this. So we divide the full area by 4
(100pi)/4 = (100/4)pi = 25pi
The exact area in terms of pi is 25pi square units
If we used the approximation pi = 3.14, then we can say 25*pi = 25*3.14 = 78.5 is the approximate area
To get a better approximation, use more decimal digits in pi.
What is the area of the real bedroom?
Answer:
area of real bedroom = 32 cm²
hope it helps..
Answer:
Bedroom: 32 cm living room: 81 cm
Step-by-step explanation:
Bedroom: 4 x 8 = 32
Living room : 9 x 9 = 81
( if combining bedroom and living room, it’s 113 cm)(81 + 32 = 113)
Hope this helps
what form is the equation 12y=2x=24
Answer:
Step-by-step explanation:
Simplifying
12y + 2x = 24
Reorder the terms:
2x + 12y = 24
Solving
2x + 12y = 24
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12y' to each side of the equation.
2x + 12y + -12y = 24 + -12y
Combine like terms: 12y + -12y = 0
2x + 0 = 24 + -12y
2x = 24 + -12y
Divide each side by '2'.
x = 12 + -6y
Simplifying
x = 12 + -6y
Solve the following system of equations graphically on the set of axes below.
y= 2x-2
y= -x+7
Answer:
x=y + 2
2
y=2(x - 1)
Step-by-step explanation:
y=2 x -2
swap sides so that all variable terms are on the left hand side
2x - 2 =y
add 2 to both sides
2x = + 2
Divide both sides by 2.
2 x = y + 2
2. 2
Dividing by 2 undoes the multiplication by 2.
x = y + 2
2
Divide y +2 by 2.
x = y + 1
2
what is the percent of change from 85 to 64
Answer:
-24.71%
Step-by-step explanation:
what is the product of 3.54 and 3.7? show work / explain please!
What’s the slope of line 1
Answer:
the slope in line 1 is a
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
→ Utilise the gradient formula
(y₂ - y₁) ÷ (x₂ - x₁)
→ Substitute in the numbers
(2 - -6) ÷ (1--1)
→ Simplify
4
Jeffrey rented a car for spring break. It costs $100 to rent the car plus $8 per mile he was charged $1,316. How many miles did he drive.
Answer:
152 miles
Step-by-step explanation:
Answer:
he drived around 300 mile
find x=, if x-5=10 HURRY!!!!
the area if a rectangle is 7 ¼ with leangth 2⁵/⁷ calculate its breadth
Answer:
Can u explain it one more time their is alot of spelling errors
Can someone help me please?! I’ll make you brainlest.
Maria had 6 feet of ribbon. She will cut the ribbon into pieces that are 2/3 of a foot long. How many pieces of ribbon will Maria have?please solve!
Answer:
2/3 x 9 = 18 divided by 3 = 6
answer is 9
Write the equation for this line in slope-intercept form.
y=-2x+?
A. -4
B. 2
C. -2
D. -1/2
Please explain as simply as you can I'm really struggling. Also will give brainly
Answer:
The answer is A. -4.
Step-by-step explanation:
The missing value you are looking for is the y-intercept or where the line crosses the y axis.
Nathan Reynolds bought a car for $15,000. He made a down payment of $3,000. Nathan secured a loan for the balance of the purchase price at 8 percent interest for four years.
determine the monthly payment and total interest
Answer:
1) The monthly payment is approximately $292.96
2) The total interest is approximately $2,061.84
Step-by-step explanation:
1) The financing method Nathan Reynolds applied to buy the car is given as follows;
The purchase price of the car = $15,000
The down payment made for the car = $3,000
The
The interest on the loan he took for the balance of the purchase price, R = 8%
The number of years for which he took the loan, n = 4 years = 48 months
We have;
The balance of the purchase price = (The purchase price of the car) - (The down payment made for the car)
∴ The balance of the purchase price = $15,000 - $3,000 = $12,000
The balance of the purchase price = $12,000 = The loan Nathan secured
The monthly payment on a loan is given by the following formula
[tex]A = P \times \dfrac{r \cdot (1 + r)^n}{(1 + r)^n - 1}[/tex]
Where;
A = The payment amount made monthly
P = The principal or loan amount = $12,000
r = The interest rate divided by 12 = R/12 = 8/12 = 2/3
n = The number of months the monthly payment will be made = 48 months
By plugging in the variable values, we get;
[tex]A = 12,000 \times \dfrac{\dfrac{2}{300} \times \left (1 + \dfrac{2}{300} \right ) ^{48}}{ \left (1 + \dfrac{2}{300} \right )^{48} - 1} = 292.955068099 \approx 292.96[/tex]
Therefore, the payment amount made monthly, A ≈ $292.96
2) The total payment made in the 48 months = A × 48 = 292.955068099 × 48 ≈ 14,061.84
The total payment made in the 48 months ≈ $14,061.84
The total interest = (The total payment made in the 48 months) - (The loan amount)
∴ The total interest = $14,061.84 - $12,000 ≈ $2,061.84
I need help with 4,5,6
Answer:
4. 3. 10
5. 1102.31
6. 17.37
Step-by-step explanation:
un pantalón se fabrica con 3/7de tela.¿Cuántos pantalones se pueden hacer con 36 metros de tela ?
Answer:
sam has egg plant seeds she puts the seed up her as/s hopeing for big egg plants to come out fast Forward 6 days in the past no egg plant are up her a/ss yet why is thath
Step-by-step explanation:
3x + 80 = 12x - 1
what’s the value of x ?
Answer:
9
Step-by-step explanation:
3x+80=12x-1
80=12x-3x-1
80=9x-1
9x=80+1
9x=81
x=81/9
x=9
Which value is greater 4/5 or 70%
Answer:
4/5
Step-by-step explanation:
4/5 = .8
70% = .7
Answer:
4/5
Step-by-step explanation:
April wrote two equations to represent this system of equations. She wrote: y = 5x +
I and y = 14x - 10. Do you agree or disagree with April?
Answer:
Disagree
Step-by-step explanation:
The lines are parallel, which means they have different y-intercepts but the same slope.
April's two equations have different slopes (5 and 14), so they do not properly represent two parallel lines.
Which side lengths represent the sides of a right triangle?
A)
1, 1, 2
B)
2, 3,5
C)
5, 12, 13
D)
7, 23, 25
Answer: the answer is C
Step-by-step explanation:
My friend is a math teacher
Hope this helps
please help ! 2.5 : 12.5 reduce the following into ratio of whole number.??
what is the classification of the triangle by its angles and by its sides??
ANSWER ASAP!!! PLS
Answer:
right triangle
Step-by-step explanation:
whenever there is a box in the corner it means its 90° and 90° is a right angle.
A rectangular paddock has perimeter 100 m. Find the width of the paddock if its length is 30 m.
Answer:
Step-by-step explanation:
W= L x 2/P
= 30 x 2/ 100
= 60 /100 = 0.6
