Answer:
As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains.
The quadratic formula is useful for solving equations of the form ax² + bx + c = 0.
We have,
The quadratic formula is useful for solving equations of the form
ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
This formula allows us to find the solutions (or roots) for quadratic equations when factoring or other methods may not be readily applicable or efficient.
The quadratic formula states that for any quadratic equation of the form ax² + bx + c = 0, the solutions can be found using the following formula:
x = (-b ± √(b² - 4ac)) / (2a)
The quadratic formula is particularly useful when:
The quadratic equation cannot be factored easily or at all.
The coefficients a, b, and c are known or can be easily determined.
The equation is in standard quadratic form, where the highest power of x is 2 and the coefficients are real numbers.
The desired solutions are required in an exact form or as precise decimal approximations.
The quadratic formula provides a straightforward method to find the solutions of a quadratic equation in various contexts, such as mathematics, physics, engineering, and other fields where quadratic equations arise.
Thus,
The quadratic formula is useful for solving equations of the form
ax² + bx + c = 0.
Learn more about equations here:
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"A freely falling object experiences gravity. The value of gravity is 9.8 m/s2 or 980 cm/s2. The equation that describes the distance an object falls from rest under the influence of gravity is?"
Answer:
S =4.9t²
Step-by-step explanation:
Using the equation of motion
S =ut+1/2gt²
u is the initial speed = 0m/s
t is the time
g I the acceleration due to gravity = 9.8m/s²
S is the distance of the object
Substitute
S = 0(t)+1/2 (9.8)t²
S = 0+4.9t²
S = 4.9t²
Hence thee equation that describes the distance an object falls from rest under the influence of gravity is S = 4.9t²
Please help , will mark brainliest
Answer:
Should be 360
Step-by-step explanation:
Jim is building a model airplane. The scale is 1 in: 40 ft. The actual wingspan of the plane is 211 feet. How long will wings of the model be?
in isosceles trapezoid EFGH, FG parallel EH, FG=10, GH=12, and ∠E=60. Find the area of EFGH.
Answer:
22√3 units squared
Step-by-step explanation:
1) Draw the trapezoid
2) Notice you have to find the height to find the area of the trapezoid
3) Notice it is a 30 60 90 triangle when you draw the line to find the height
4) Solve for the 30 60 90 triangle and you get the height to be 2√3
5) Solve for the area of the trapezoid using this formula A= 1/2 h ( b1 + b2)
6) Fill in the numbers for the equation A= 1/2∙ 2√3 ( 10 + 12)
7) Keep aside the 1/2 for now
8) Simplify equation 2√3 + 22 or 2√3 + (10 + 12)
9) Simplify further 44√3
10) Now bring back the 1/2 and put it in the equation 1/2∙ 44√3
11) Simplify to get 22√3
12) 22√3 is the area of the trapezoid
13) 22√3 units squared is the final answer
I will put a my drawing of the trapezoid for reference and this is what I used to solve the question.
If you want to know how I solved the 30 60 90 triangle please let me know.
Sorry I was one week late I just saw it today.
:D
What is the value of b and the value of c? Picture of triangle down below.
b=
c=
Answer:
b = 73
c = 34
Step-by-step explanation:
<T and <R are equal because they are opposite equal sides.
So b = 73°
Every triangle has 180 degrees
b + c + 73 = 180
73 + c + 73 = 180
146 + c = 180
c = 180 - 146
c = 34
The Science Club went on a two-day field trip. The first day the members paid $40 for transportation plus $19 per ticket to the planetarium. The second day they paid $90 for transportation plus $16 per ticket to the geology museum. Write an expression to represent the total cost for two days for the n members of the club.
Answer:
total cost = $130 + $35n
Step-by-step explanation:
Cost incurred on the first day.
Fixed cost = $40. this amount is fixed because it does not depend on the number of students that take the trip
variable cost = $19n. It is variable because it depends on the number of students that take the trip. the more the club members that take the trip, the higher the cost
Total cost on the first day = $40 + $19n
Cost incurred on the second day
Fixed cost = $90. this amount is fixed because it does not depend on the number of students that take the trip
variable cost = $16n. It is variable because it depends on the number of students that take the trip. the more the club members that take the trip, the higher the cost
Total cost on the second day = $90 + $16n
Total cost incurred would be the sum of the two costs incurred on the two days
total cost = $40 + $19n + $90 + $16n
= $130 + $35n
10) A jeweler has a pendant for sale for $150. If she
charges her customer $10.50 for sales tax, what
is the percent of sales tax?
(A) 6%
(B) 7%
(C) 8%
(D) 9%
Answer:
the right answer is option B) 7percent
Pete and his sister, Sophie, play the game Space Mission Commander on their video game console. Pete has already completed 27 missions. Sophie has only completed 13 missions. From now on, Pete plans to complete 3 missions per week. Meanwhile, Sophie plans to complete 5 missions per week.
Step-by-step explanation:
Pete has already completed 27 missions. Pete plans to complete 3 missions per week
Let x represents weeks
Games completed = 3x + 27
Sophie has only completed 13 missions. Sophie plans to complete 5 missions per week.
Games completed = 5x + 13
3x + 27 = 5x + 13
27 - 13 = 5x - 3x
2x = 14
x = 7
By the seventh week, they would have completed equal number of games,
A group of 5 friends is out to dinner. Each of the friends will order the dinner special, and they
have a coupon for $10 off the entire bill. Which equation can be used to find the total cost of
all the dinners after the coupon is applied?
10d - 5 = 0
100 + 5 = 0
5d + 10 = 0
5d - 10 = 0
I NEED HELP BUT I DONT HAVE THE FREE TRIAL THING
Answer:
5d-10 =0
Step-by-step explanation:
Answer: 5d - 10 = C
-tay
The question says “the system below has been solved by graphing. How many solutions does it have?”
Answer:
Infinitely many solutions
Step-by-step explanation:
3x+y=1
15x+5y=5
Step: Solve3x+y=1 for y:
3x + y +−3 x = 1 + −3x (Add -3x to both sides)
y=−3x+1
Step: Substitute−3x+1 for y in 15x+5y=5:
15x+5y=5
15x+5(−3x+1)=5
5=5(Simplify both sides of the equation)
5+−5=5+−5(Add -5 to both sides)
0=0
so there are infinite solutions
The right rectangular prism shown below is made of equal-sized cubes. The side length of each cube is 2 1/2 inches. What is the volume in cubic inches, of the right rectangular prism?
The image of the right rectangular prism is missing, so i have attached it.
Answer:
volume of the right rectangular prism = 625 in³
Step-by-step explanation:
The rectangular prism is made of equal-sized cubes. Thus, let's first find the volume of 1 cube.
Formula for volume of one cube is;
V = a³
where
a is the length of one side of the cube
We are told that this length is 2½ inches
Thus;
a = 2½ = 5/2 inches
>> V = (5/2)³
>> V = 125/8 in³
Now, in the rectangular prism attached, if we count the number of cubes we have, it is equal to 40 cubes
Therefore, the volume of the prism is;
Volume of one cube × 40
>> volume of the prism = (125/8) × 40
volume of the prism = 625 in³
What is the diameter of a circle with a radius of 7 inches
Answer:
14
Step-by-step explanation:
the diameter is the radius multiplied by 2
HELP ASAP ASAP EXTRA POINTS
Answer:
The slope is -2
Step-by-step explanation:
HURRY!
An auto shop has 2 used vehicles for sale, 1 car and 1 truck. The truck is 3 years older than the car but 7 years older than one-half the car's age. How many years old is the car? 7 year old 7 year old 8 years old 8 years old 9 years old 9 years old 10 years old
Simplify: 7(-2x - 3) *
-14x - 21
-14x - 3
14x - 21
14x - 3
help pls lollll
10th grade mathematics
Answer:
I think it's a because
12÷42= 3.5
and
56÷16=3.5
so
10×3.5=35
Step-by-step explanation:
please help a girl out:
What is your favorite sport? Sample is chosen from people attending
games
Answer:volleyball
Step-by-step explanation:
Answer:
My fav sport is badminton...
Step-by-step explanation:
Hope it's help u
If wrong then sry sry
Alberto is considering taking a job with a company where the sequence {$50,000; $50,700; $51,400; $52,100; $52,800} represents the salary schedule for the first five years of employment. If the pattern continues, what can Alberto expect to earn in his sixth year of employment?
Answer:
$53,500 is the answer.
Step-by-step explanation:
The question is an Arithmetic Progression of common difference (d) = 700
a₁ = $50,000
a₂ = $50,700
d = $700
sixth year can be written as,
a₆ = a + 5d
a₆ = 50,000 + 5 × 700
a₆ = 50,000 + 3,500
a₆ = 53,500
therefore, Alberto will earn $53,500 in his sixth year of employment.
His salery grows by 700 per year, as you can see. This can be represented as [tex]700x+50000[/tex], where 50,000 represents the starting wage, 700 represents the annual increase, and [tex]x[/tex] represents the year (starting from 0). So, if you want to know his wage in his sixth year of employment, simply substitute 5 for [tex]x[/tex]. Note that [tex]x[/tex] is the number of years minus one. As a result, the answer is [tex]700(5)+50000=53500[/tex].
Can someone help me with this?
Answer:
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
Step-by-step explanation:
is this a right triangle 6,12,8
Answer:
No it is a obtuse triangle
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
Álgebra 1.
Calculate the slope
Answer:
slope: -1/4x
Step-by-step explanation:
i hope this helps :)
What is the square root of 4586
Answer:
67.72
Step-by-step explanation:
Answer:
57.68*
Step-by-step explanation:
Dont really know how to explain....
An isosceles triangle has an angle that measures 102°. Which other angles could be in that isosceles triangle?
Answer:
(180-102)/2 = 39° each (remaining 2)
HELP ASAP!!!!!!!!! 30 POINTS + BRAINLIEST!!!!!!!!
Answer:
Step-by-step explanation:
Pls help, for 10 points!
Answer:
I think 9 but dont quote me on it
Answer:
2
Step-by-step explanation:
in khan academy i put 9 because thats what the last person said here but it was wrong and the correct answer was 2 so its 2 for sure.
30 POINTS PLEASE HELP ASAP !!!
Answer:
1: x = 29
2: Angle C is 93 degrees
Step-by-step explanation:
For 1 angle C has to equal 93 degrees since 52 + 35 = 87 and 180 - 87 = 93, and a triangles interior angles add up to 180 degrees.
From there create an equation: 3(x + 2) = 93 then solve
3x + 6 = 93
-6 from both sides
3x = 87
/3 from both sides
x = 29
For 2 just plug in x (29)
3(29 + 2)
87 + 6
93
Sergio passes by a bike store on Monday and sees his dream bike in the window. It cost 120 . He passes by on Wednesday and is thrilled to see that is marked down by 1/4 . What is the new price of the bike
Answer:
90
Step-by-step explanation:
120 - (120/4)
120 - 30 = 90
Help me with this problem please!
Answer:
Step-by-step explanation:
i can barely see that maybe re upload a better picture and someone will help
GIVING BRAINLIEST FOR CORRECT ANSWER<3
Answer: 75 percent
Step-by-step explanation: I'm pretty sure