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
A light house worker is tracking a boat that is 5 km south of her. She is also tracking a boat
that is 6 km from the tower located 70° east of north. To the nearest kilometer, how
far apart are the two boats?
A. 7 km
B. 9 km
C. 8 km
D. 16 kM
Answer:
cccccccccccccccccccccccccccccc c
I generally need help
Answer:
24 units²
Step-by-step explanation:
4(12)/2=24
whyyyyyy does math suck help meeee plzz
Answer:
3 1/2
Step-by-step explanation:
the equation is 7/8x4/1 and can be rewritten as 7x4/8x1 = 28/8 which simplifies to 3 4/8 or 3 1/2
You deposit $500 in an account that earns 6.5% annual interest compounded yearly. Write a function that represents the balance y (in dollars) after x years.
Answer:
f(x)=.65+y
Step-by-step explanation:
.
The function for compound interest is A = 500 ( 1.065 )ˣ
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the compound interest amount be represented as A
Now , the interest rate r = 6.5 %
The number of times the interest is applied = yearly
The principal amount P = $ 500
n = 1 ( compounded yearly )
t = x ( number of years )
So, the function that represents the balance y (in dollars) after x years is:
y ( x ) = 500 ( 1 + 0.065/1 )ˣ
On simplifying , we get
y ( x ) = 500 ( 1.065 )ˣ
Hence , the function is A = 500 ( 1.065 )ˣ
To learn more about compound interest click :
https://brainly.com/question/21270833
#SPJ2
Mare has a monthly cell phone plan that has a fixed charge of $12 per month plus
$0.30 per text message. Marie wants to spend no more than $40 per month on her
call phone. Which inequality represents the number of text messages, X, that Marie
Please hurry
You need to multiply the cost per text message by the number of messages (x) add that to the fixed charge.
The total of those need to be less than or equal to the amount she wants to spend.
The equation would be written as:
0.30x + 12 <= 40
I dont really understand this question, can anyone help me out?
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Angles.
Complementary angles sum up together to become 90°.
Supplementary Angles sum up together to become 180°.
hence,
1.) Ans ==>Angle ABC and Angle NMP
2.) Ans ==> angle ABC and angle EFG
How can I solve this question?
draw a rectangle triangle :
sin B=8/17 that means that de biggest side are 17 ("hipotenusa"), and another side is 8. Applying de theorem of pythagoras:
[tex]17^{2} =8^{2} +x^{2} \\x^{2} =17^{2} -8^{2}\\x=\sqrt{17^{2} -8^{2}} \\x=5\sqrt{5}[/tex]
factor out the gcf 12y³+10y²
Answer:
Find the prime factors of each term in order to find the greatest common factor (GCF).
2y^2
Factoring out the greatest common factor (GCF)To factor the GCF out of a polynomial, we do the following: Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.
Step-by-step explanation:
Hope it is helpful.....
The y-intercept is 2.
Question 1 options:
True
False
Answer:
false. the y-intercept is -2.
Which answer choice correctly identifies the missing information in the problem? Joey and Kirk are in the 6th grade. Kirk is 5 feet 4 inches tall. Joey is 4 feet 8 inches tall. How much taller is Kirk than Joey?
Answer:Kirk is taller than Joey by 8 inches
Step-by-step explanation:
Step 1
Kirk's height is given as =5 feet 4 inches tall.
Joey's height 4 feet 8 inches tall
Difference in height = 5 feet 4 inches
- 4 feet 8 inches
=
Step 2
Bear in mind that 12 inches = 1 feet . Now,8 cannot be subtracted from 4 , so we borrow 1 feet from 5feet, which is equivalent to 12 inches and add to inches so it becomes
4 feet (12+4)inches = 4 feet 16inches
- 4 feet 8 inches - 4 feet 8 inches
= 8 inches
Therefore Kirk is taller than Joey by 8 inches
what do you observe about the form of the equation of any circle whose center is at the point of origin
Ce clasă ești sa văd daca te pot ajuta
f (x) = 2x g(x) = 4x + 5 Find f (x) + 3g(x)
Answer:
f(x) + 3g(x) = 14x + 15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = 2x
g(x) = 4x + 5
Step 2: Find
Substitute in functions: 2x + 3(4x + 5)[Distributive Property] Distribute 3: 2x + 12x + 15Combine like terms: 14x + 15x^2+17x+4=0 find the discriminant.
[
1
What is the distance between the points (-4, -8) and (10,-8)?
Need help
Answer:
2
Step-by-step explanation:
√(-8-8)^2 +(10+4)^2=
✓-32+28
✓4
=2
Question: 2 out of 10
~!¡! Volume !¡!~
(Pleaaase go try to answer the first one- )
Answer:
B) 2,340
Step-by-step explanation:
Find and reduce -4/7 x 2/3
What is the answer to this?
Answer:
-8/21
Step-by-step explanation:
I’m confused about this problem
x= arctan (114/180)
=32.34744..
rounded to the nearest tenth =32.3
Step-by-step explanation:
At 6:00 A.M., the temperature was 10º below zero. During the day, the temperature rose an average of 2º per hour. If h represents the number of hours since 6:00 A.M., which equation represents the temperature T?
Answer:
t=-10+2h
Step-by-step explanation:
How do I write a phrase in words as an algebraic expression for 8/d?
Answer:
The quotient of 8 and d.
Step-by-step explanation:
I hope this helps you have a wonderful day! :D
give all relationships between angle 1 and angle 2 select all that apply
Answer:
vertical maybe if try it and see
Help me please!!!!!!
Answer:
(2,8)
Step-by-step explanation:
I'm not so sure but if I were answering I would have picked (2,8)
Answer the photo below thanks
Answer:
x=50
Step-by-step explanation:
65+65=130
180-130=50
Answer:
50 is the answer
Step-by-step explanation:
this is a isosceles triangle having 65 and 65
then 65 + 65 + x = 180 property of traingle
130 + x = 180
x = 180- 130 = 50
The part that's cut off it says To the nearest tenth of a percent, what's percent...
and is the answer 3.3?
Answer:
Yes you are correct.
El alcance de tangente
Answer: ¿Qué significa alcance tangente? ¡Lo busqué y no dice nada!
Step-by-step explanation:
There is an unknown number of people at the table at the
beginning of lunch. Then...
3 more people joined the group.
Then the entire group divided into 2 groups, and
one group left and went outside,
of the total students were left in the lunchroom
5 people joined the group in the lunchroom.
The total number of people in the lunchroom at the
end of lunch was 10
a. Write the equation you can create to show this situation.
b. How many people were at the table at the beginning of lunch? Explain how you know.
Answer:
11 hours ago u prob dont need it
Step-by-step explanation:
123456
flora has a summer job where she earns $9.50 per hour. At this company, employees get a 10% raise after working for 400 hours. If flora works 640 hours over the summer, how much money will she make?
25a² -4b²+28bc-49c² factorize
Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula,
Step-by-step explanation:
= 25 a²- ( 4b²- 28bc +49c²)
=. 25a²- {( 2b)²- 2(2b)(7c)+ (7)²}
= 25a²- { (2b - 7c)²}
= (5a)²- (2b -7c)²
= { 5a -(2b-7c)} { 5a+ ( 2b-7c)}
= ( 5a - 2b +7c) ( 5a +2b - 7c)
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
plz you find it useful plz mark my answer as brainlist.
what 2/5(10x + 3/4) - 2x?
Answer:
2x + 3/10
Step-by-step explanation:
2/5 (10x + 3/4) - 2x = 4x + 3/10 - 2x = 2x + 3/10
HELP I NEED HELP ASAP
A. Day 4 to Day 6
B. Day 8 to Day 10
C. Day 6 to Day 8
D. Day 10 to Day 12
Answer:
b
Step-by-step explanation:
trust i did it already
Answer:
the answer is B
Step-by-step explanation:
I just had that question
does anyone know the answer to 5(2t+3)=75 that can tell me how to find the answer not just the answer
Answer: Let me know if this helps.
Step-by-step explanation:
5(2t+3)=75 Distribute the 5 using multiplication. 5x2t and 5x3
10t+15=75 Subtract 15 because you need to get the t by itself.
10t = 60 Now divide by 10 to get t by itself. 10/10 and 60/10.
t = 6 Answer.
Answer:
t=6
Step-by-step explanation:
It's all about get t on one side of the equation, and so everything else on the other side of the equation.
The first thing we want to get rid of is the 5. The 5 is multiplied by (2t+3), so to get rid of it, we divide both sides by five (divide both sides since they must remain equal):
(5(2t+3))/5=75/5
2t+3=15
The next thing we can get rid of is the 3. Subtract 3 from both sides:
2t+3-3=15-3
2t=12
Now, we get rid of the 2. Divide both sides by 2:
2t/2=12/2
t=6