The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 Blank space, fill in the answer
Provide the next step to derive the quadratic formula.
Answer Choices: (see image)
Answers
Answer:
b)
[tex]x^{2} +\frac{b}{a} x+(\frac{b}{2 a} )^{2} = \frac{-c}{a} + (\frac{b}{2 a}) ^{2}[/tex]
Step-by-step explanation:
Step(i):-
Given quadratic equation ax² + bx + c = 0
step(ii):-
ax² + bx = -c
Step(iii):-
Dividing 'a' on both sides , we get
[tex]\frac{ax^{2} +bx }{a} = \frac{-c}{a}[/tex]
[tex]x^{2} + \frac{bx}{a} = \frac{-c}{a}[/tex]
Step(iv):-
Adding [tex](\frac{b}{2 a} )^{2}[/tex] on both sides , we get
[tex]x^{2} +\frac{b}{a} x+(\frac{b}{2 a} )^{2} = \frac{-c}{a} + (\frac{b}{2 a}) ^{2}[/tex]
Answer:
B
Step-by-step explanation:
Related Questions
Which three programs or services are supported by taxes?
1. Fire Departments
2. Medicare
3. Public Education
4. Shopping Malls
5. Theaters
Answers
Answer:
Fire departments, Medicare, and public education.
Step-by-step explanation:
Our school gets $100,000 in donations from celebrities to buy Chromebooks for class learning. Each Chromebook costs $385 plus $20 insurance. what is the maximum number of Chromebook that we can buy for our students?
Answers
Answer: 246 laptops.
Step-by-step explanation: if they each each take 20 for insurance and 385 then its 405 title. hen you take 100,000 and divide it by 405 getting 246.91358. but you cant buy .91358 of a computer so you round down.
This green rug has a perimeter of 36 feet. The length is 3 + x and the width is 5. Write an expression that can be used to find the missing value of x. Combine like terms of your equation until it is the most simplified form. What is the value of x? Explain your reasoning.
Answers
Answer:
An equation for this would be : 36=3+x+3+X+5+5
the simplified version would be: 20=2x
The value of x = 10 feet
Step-by-step explanation:
Since perimeter is all the sides added together, and 36 ft is the perimeter,
think of a rectangle, 2 sides would be 3+x and the other 2 would be 5.
thus,
36=3+x+3+x+5+5
now add all like terms and you get 36=16+2x
subtracting 16 on both sides,
20=2x
dividing by 2 both sides,
x=10 feet.
In right triangle ABC, A = 15°, C=37, and ZC is the right angle. Solve the triangle. Round to the nearest tenth, if necessary.
Answers
Answer:
a= 9.58 units
b=35.74 units
Step-by-step explanation:
Determine the scale la
C
10 in
5 in
O A. 10
O B. 2
O c.
NI
O D. 5
Answers
Answer:
B.2
Step-by-step explanation:
To make ΔA'B'C' from ΔABC, we need to use t
he scale factor =|A'B'|/|AB|=10/5=2
PLEASEEEE HELPP!!!!!!!
Answers
Answer:
im not sure but 36
Step-by-step explanation:
A system of equations is given.
y= x^2 −9
y= −2x−1
What is one solution to the system of equations?
Answers
Answer:
(-4,7)
Explanation:
I graphed the two equations with a graphing tool.
The first equation forms a parabola.
The second equation is linear.
The graphed equations intercept at two points. Since the question asked for one, then one solution of the system is (-4,7).
Answer:
(- 4, 7 ) and (2, - 5 )
Step-by-step explanation:
Given the 2 equations
y = x² - 9 → (1)
y = - 2x - 1 → (2)
Substitute y = x² - 9 into (2)
x² - 9 = - 2x - 1 ( subtract - 2x - 1 from both sides )
x² + 2x - 8 = 0 ← in standard form
(x + 4)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
Substitute these values into (2) for corresponding values of y
x = - 4 → y = - 2(- 4) - 1 = 8 - 1 = 7 ⇒ (- 4, 7 )
x = 2 → y = - 2(2) - 1 = - 4 - 1 = - 5 ⇒ (2, - 5 )
Did I do this right not asking for answer unless I got it wrong
Answers
yes its right
there no need to ask any way
Click on the measure that is equivalent to 5 meters.
0 50 centimeters
50 millimeters
0 500 millimeters
0 500
centimeters
Answers
Answer:
500 cm
Step-by-step explanation:
100 cm is equal to 1 meter. *5 is 5 meters or 500 cm
Sorry if I'm wrong. I don't think I am but there is always a possibility
Answer:
Step-by-step explanation:
100cm = 1 meter so therefore 5 meters = 500cm
Explain how to determine if the two expressions are
equivalent using x = 6 and x = 10.
8x + 40
8(x + 5)
Answers
Answer:
If both expressions have the same value after substituting and simplifying for x = 6 and x = 10, then they are equivalent. Substitute 6 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 88. Now, substitute 10 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 120. Therefore, the expressions are equivalent.
Step-by-step explanation:
got it right!
The two expressions are equivalent.
Important information:
The given expressions are [tex]8x+40[/tex] and [tex]8(x+5)[/tex].The given values are [tex]x=6[/tex] and [tex]x=10[/tex].Equivalent Expressions:The values of both expression for [tex]x=6[/tex] are:
[tex]8(6)+40=48+40[/tex]
[tex]8(6)+40=88[/tex]
And
[tex]8(6+5)=8(11)[/tex]
[tex]8(6+5)=88[/tex]
The values of both expression for [tex]x=10[/tex] are:
[tex]8(10)+40=80+40[/tex]
[tex]8(10)+40=120[/tex]
And
[tex]8(10+5)=8(15)[/tex]
[tex]8(10+5)=120[/tex]
Since the values of both expressions are equal for each of the values [tex]x=6[/tex] and [tex]x=10[/tex]. Therefore, the two expressions are equivalent.
Find out more about 'Equivalent Expressions' here:
https://brainly.com/question/10628562
pi owns a cornfield and has placed fences around four polls, A, B, C, D that delimit the edges of the field. He needs to drive around the field every day to check whether anybody has tried to break in. The four poles are located at:
A (-2,1)
B (3,-11)
C (-2,-23)
D (-7,-11)
How many miles will pi drive if he starts at pole A and drives around the entire border of the field?
(please show the work)
Answers
Answer:
52 miles
Step-by-step explanation:
A to B:
sqrt( (3 - (-2))^2 + (-11 - 1)^2 )
sqrt( (5)^2 + (-12)^2 )
sqrt( 25 + 144 )
sqrt( 169 )
13
B to C:
sqrt( (-2 - 3)^2 + (-23 - (-11))^2 )
sqrt( (-5)^2 + (-12)^2 )
sqrt( 25 + 144 )
sqrt( 169 )
13
C to D:
sqrt( (-7 - (-2))^2 + (-11 - (-23))^2 )
sqrt( (-5)^2 + (12)^2 )
sqrt( 25 + 144 )
sqrt( 169 )
13
D to A:
sqrt( (-2 - (-7))^2 + (1 - (-11))^2 )
sqrt( (5)^2 + (12)^2 )
sqrt( 25 + 144 )
sqrt( 169 )
13
Adding:
13 + 13 + 13 + 13
52
Renan found the sum (4.2x + 3) + (5.7x – 2) + (5 – 2.6x), as shown.
4.2x + 3 + 5.7x – 2 + 5 – 2.6x
4.2x + 5.7x + 2.6x + 3 – 2 + 5
(4.2 + 5.7 + 2.6)x + 3 – 2 + 5
12.5x + 6
Answers
Answer:
He used the commutative property incorrectly.
Step-by-step explanation:
Answer:
a is correct
Step-by-step explanation:
If f(x) = 3x2 + 2 and g(x) = -5x +3, find f(g(x)).
PLEASE HELP ME
Answers
Answer:
Option 2: 75x^2 -90x + 29
Step-by-step explanation:
f(g(x))
f(-5x+3) = 3(-5x+3)^2 + 2
= 3 (25x^2 - 30x +9) +2
= 75x^2 - 90x+ 27 + 2
f(g(x)) = 75x^2 - 90x + 29
Please Explain step - by - step!
Answers
Answer:
use PEMDAS
Step-by-step explanation:
start with doing what's in the parenthesis 3+2 = 5
7+4^3-3-5^2
then do ur exponents
7+64-3-25
then do you addition and subtraction left tto right
71-3-25
68-25
43
ur answer is 43
I would greatly appreciate it if you helped me out
Answers
Answer:no correlation
If each square unit represents 3 square feet what is the area of the patio in square feet
Answers
Answer:
563
Step-by-step explanation:
find the area of each figure . only 3 questions ! 30 pts awarded to u for answering !! thanks !
Answers
Answer:
Number 1 is 391 Number 2 is 663 Number 3 is 12 or 18
Step-by-step explanation:
Trisha and Malia went to the mall with their mom. Trisha spent $15.60 on a pair of sunglasses. Malia spent $29.80 more than Trisha on a new handbag. Their mom spent 2.5 times as much as Malia on an espresso machine for their kitchen. How much money did their mom spend on the espresso machine?
Answers
Answer:
$113.50
Step-by-step explanation
add $15.60 + $29.80 = $45.40multiply $45.40 x 2.5 = $113.50
The amount of money there mom spent on the expresso machine is $113.5
How to form equation and solve for the variable?Trisha spent $15.60 on a pair of sunglasses.
Malia spent $29.80 more than Trisha on a new handbag.
Therefore,
Malia expenses = 29.80 + 15.60 = $45.4
Their mom spent 2.5 times as much as Malia on an espresso machine for their kitchen. Therefore,
Mom expenses = 2.5(45.4)
Mom expenses = $113.5
Therefore, there mom spent a total of $113.5 on the expresso machine
learn more on equation here: https://brainly.com/question/21506399
A.) $203,000.00
B.) $177,000.00
C.) $207,000.00
D.) $197,000.00
Swell Computers is preparing to market a new microchip to upgrade computers already purchased by consumers. Management sees a huge potential for sales since people will not have to purchase a whole new computer system to have access to the latest technology, just this chip. The company has already determined that it can produce these chips for $8 each, with a $5000 start-up cost. Projections indicated that sales of x chips will generate a revenue of R(x)=200x-0.01x^2. How much profit do they hope to make on the first 1000 chips sold?
Answers
Answer:
A?
Step-by-step explanation:
What is the slope of the line joining (5,9) and (-2, 9)?
Answers
Answer:
0
Step-by-step explanation:
We can find the slope by
m = (y2-y1)/ (x2-x1)
= (9-9)/(-2-5)
0 /-7
0
Answer:
y=9
Step-by-step explanation:
both y are on 9 so the only things similar and the only line they are on is y=9
Find the zeros of the function. Write the smaller solution first, and the larger solution second. f(x)=-3x^2 +75f(x)=−3x 2 +75f, left parenthesis, x, right parenthesis, equals, minus, 3, x, squared, plus, 75 \text{smaller }x =smaller x=start text, s, m, a, l, l, e, r, space, end text, x, equals \text{larger } x =larger x=start text, l, a, r, g, e, r, space, end text, x, equals
Answers
Answer:
Smaller x= -5Larger x=5Step-by-step explanation:
Given the function [tex]f(x)=-3x^2 +75[/tex]
The zeros of the function are the values of x for which f(x)=0.
[tex]f(x)=-3x^2 +75=0\\-3x^2 +75=0\\-3(x^2-25)=0\\$Divide both sides by -3\\x^2-25=0\\$Add 25 to both sides\\x^2-25+25=0+25\\x^2=25\\$Take the square root \\\sqrt{x^2}=\pm \sqrt{25}\\ x=\pm 5[/tex]
The zeros of f(x) are therefore 5 and -5.
Smaller x= -5Larger x=5Solve the inequalities 4y+7>27
Answers
Answer:
y>5
Step-by-step explanation:
4y>20
y>5
Step-by-step explanation:
4y+7>27
4y+7-7>27-7
4y>20
(4y÷4 )>20÷4
y>5
What is the measure of
Answers
Answer:
x = 37
Step-by-step explanation:
The large angle is a right angle so it equals 90 degrees
53+x = 90
Subtract 53 from each side
53+x-53 = 90-53
x = 37
Answer:
37
Step-by-step explanation:
90-53=37
Find the missing angle. *
70°
?
40°
40 degrees
100 degrees
25 degrees
70 degrees
Answers
Answer:
70
Step-by-step explanation:
A triangle angles add up to 180 so you add up 70 and 40 and then subtract that answer from 180 and you get 70
Answer:
70 degrees.
All three sides of a triangle added together will equal 180 degrees. If 70 and 40 are added together then you get 110. Then you subtract the total 180 and the two angles that equal 110. You get 70 degrees, which is your missing angle.
HELP ME PLEASEEEE :,(
Answers
Step-by-step explanation:
[tex]{a}^{2} = b + 6 [/tex]
[tex]b = {a}^{2} - 6[/tex]
The temperature in Petersburg was recorded over a period of four
hours. The equation y= - 4x +35 describes the temperature over
this time, where y is the temperature in degrees Fahrenheit (°F) and x
is the number of hours since measurements started. Which of the
following statements correctly describes the temperature?
of QUESTIONS
It was -4°F when the temperature was first measured, and it is rising by
35 degrees per hour.
It was -4°F after four hours, and it is rising by 35 degrees per hour.
It was 35°F after four hours, and it is dropping by 4 degrees per hour.
It was 35°F when the temperature was first measured, and it is dropping
by 4 degrees per hour.
Answers
Answer:
x = 35/4
Step-by-step explanation:
Geometry pls help I have 5 more questions
Answers
Answer:
[tex]193.14m^2[/tex]
Step-by-step explanation:
Rectangle
[tex]A=wl\\=15.3*11.1\\=169.83m^2[/tex]
Triangle
[tex]A=\frac{ab}{2} \\=\frac{11.1*4.2}{2}\\ =23.31m^2[/tex]
Add both together
[tex]169.83+23.31\\=193.14m^2[/tex]
Landon scores 80% on his math test. if there are 40 problems how many did he get correct
Answers
The right answer is 32.
Look at the attached picture
Hope it will help you
Good luck on your assignment
Yoko earns 48 dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Yoko earns in a week if she sells B books. Write an equation relating A to B. Then use this equation to find the amount of money Yoko earns if she sells 21 books.
Answers
Answer:61
Step-by-step explanation: 48 +21 = 61
What is the sum?
StartFraction x Over x + 3 EndFraction + StartFraction 3 Over x + 3 EndFraction + 2 Over x + 3 EndFraction
Five-thirds
StartFraction x + 5 Over x + 3 EndFraction
StartFraction x + 5 Over 3 x + 27 EndFraction
StartFraction 6 x Over x + 3 EndFraction
Answers
Answer:
x+5/X+3 is the right answer I can conform this as i just took the edge test.
Step-by-step explanation:
The sum of given expression is x+5/x+3. Therefore, option B is the correct answer.
What is addition of algebraic expression?Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.
The given expression is x/x+3 + 3/x+3 + 2/x+3.
Here, denominators of all the fractions are same, which is x+3
Now, x/x+3 + 3/x+3 + 2/x+3
= (x+3+2)/x+3
= x+5/x+3
Therefore, the sum is x+5/x+3.
Learn more about the addition of algebraic expressions here:
https://brainly.com/question/21443100.
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