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)
\(x^{2} +\frac{b}{a} x+(\frac{b}{2 a} )^{2} = \frac{-c}{a} + (\frac{b}{2 a}) ^{2}\)
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
\(\frac{ax^{2} +bx }{a} = \frac{-c}{a}\)
\(x^{2} + \frac{bx}{a} = \frac{-c}{a}\)
Step(iv):-
Adding \((\frac{b}{2 a} )^{2}\) on both sides , we get
\(x^{2} +\frac{b}{a} x+(\frac{b}{2 a} )^{2} = \frac{-c}{a} + (\frac{b}{2 a}) ^{2}\)
Answer:
B
Step-by-step explanation:
Related Questions
Translate the sentence into an equation. Two less than the product of 5 and a number equals 9. Use the variable c for the unknown number.
Answers
Answer:
The equation is: \(5c-2=9\)
Step-by-step explanation:
Since 2 less than the product of 5 and a number c is equal to 9, it follows:
\(5c-2=9\)
do you know the answer to this
Answers
Answer:468
Step-by-step explanation:
PLSSS HELP ONLY EVENS ALL 100 points + brainlist NEED HELP ASAP
Answers
Answer:
do u still need
Step-by-step explanation:
you have to write a discussion on this can someone help
Answers
Determine if the statement below is always true, sometimes true, or never true.
When x is a nonzero integer, the quantity −3x will be negative.
Answers
Using a proportion, how can we find 12% of 125? Please show your proportion set up and all work. HELP ME ASAPPPPPPPPP THE CORRECT ANWSER GETS A BRAINLIST I HAVE 3MINS SOMEONE PLEASE!!!!!
Answers
Answer: 15
Step-by-step explanation:
Write 12% as a fraction: 12/100
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have: 12/100 of 125.
12/100 × 125
If you are using a calculator, enter 12÷100×125 which will give you 15 as the answer.
A restaurant serves you a 16-fluid ounce glass of juice that is 30% ice. How many fluid ounces of juice do you actually get? Show all of your work
Answers
to solve how much ice there is you need to do 16 • .30, which would get you 4.8
Now you need to subtract 4.8 from 16, since the 4.8 is the amount of ice in the glass of juice.
So you would actually get 11.2 ounces of juice.
Graph the parabola.
y=x^2-4x+2
Answers
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Vertex:
(2,−2)
Focus:
(2,−74)
Axis of Symmetry:
x=2
One angle of a triangle measures 125°. The other two angles are in a ratio of 2:9. What are the measures of those two angles?
Answers
Answer:
The 2 angles are 10 and 45 degrees.
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
180 - 125 = 55
Add the ratios 2+9 = 11
Divide the left over angels by the ratio: 55/11 = 5
Now multiply 5 by each side of the ratio:
2:9
2*5 = 10
9*5 = 45
So the 2 angles are 10 and 45 degrees.
To check, add up all the angels : 10 + 45 + 125 = 180
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Answers
Answer:
answer is 0.19in^3
Step-by-step explanation:
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I will mark as brainliest for the correct answers given
Thankyou!!
Answers
Answer:
(C) 10
Step-by-step explanation:
The numbers inside are the difference between the numbers outside.
Look at the left figure.
6 = 10 - 4
8 = 18 - 10
14 = 18 - 4
Look at the middle figure to confirm this also works there.
Now apply it to the right figure.
? = 15 - 5
? = 10
Answer: (C) 10
Pls help me! And thank you
Answers
Answer:
38°
General Formulas and Concepts:
Geometry
Vertical Angles Theorem - vertical angles are congruentStep-by-step explanation:
From the graph given, we see that angle x° and angle 38° are vertical.
Therefore, using the Vertical Angles Theorem, we can say that they are congruent and x = 38°.
Interpreting graphs of functions
Correct answers only thank you very much
A weight is attached to a spring, which moves up and down as a function of time.
p(t) gives the position of the weight at time (t). Position is in centimeters, and time is in seconds.
Complete the following sentences based on the graph of the function.
15 points
Answers
Answer:
non-linear401/2Step-by-step explanation:
This is a non-linear function specifically it is an oscillating functionThe initial position of the weight occurs at t=0 and from the graph we see that at t=0, the weight position is 40 centimetersThe weight is said to reach equilibrium when its position is at 0 cm. From the graph we can see that the function first reaches 0 cm at t=0.5 seconds or at t= 1/2 secondGiven b(x) = \+4, what is b(-10)?
A.) -10
B.) -6
C.) 6
D.) 14
which one?
Answers
Answer:
B.) -6
Step-by-step explanation:
b(x) = x + 4
b(-10) = -10 + 4
b(-10) = -6
Answer:
-6
Step-by-step explanation:
Renting bowling shoes costs $5. Bowling costs $4 per game. Which equation can be used to find y, the total cost of bowling, if x represents the number of games played.
y = 5x + 4
y = 5 + 4x
y = 5x + 4x
y = 5x - 4
Answers
Answer:
the answer is y=5+4x
Step-by-step explanation:
the indepedndennt variable is 5, since that is the cost of the shoes. you wont be needing a new pair of shoes for every game, therefore it stays constant. 4x represents the number of games times the cost. 4 being the cost per game, x being the amount of games
If two lines are parallel, then the alternate interior angles are__________.
A. supplementary
B. congruent
Answers
Answer:
The answer in the blank is congruent.
:)
Answer:
Congruent
Step-by-step explanation:
Hope this helps!
HELP PLEASE-
Convert 25 kilometers ran in 10 hours to a unit rate. Use the label kilometers per hour (kph).
Answers
Answer:
Step-by-step explanation:
Speed is distance divided by time. Simply put, if you drove 60 kilometres for one hour, it would look like this: Speed = distance (60 km) / time (1 hour) = 60km/h. Let's take a more complex example: what's the average speed if you covered 425.5km in 5 hours 22 minutes and 30 seconds?
Simply divide 60 by your pace. When you aren't using whole hours in the calculation, convert the number to minutes, then multiply the result by 60 minutes per hour to get miles per hour or kilometers per hour.
let S be the distance from Los Angeles to new York. The distance to Omaha is half of the distance from Los Angeles to new York. Write an expression for the distance to Omaha
NEED FAST
Answers
1/2s=x
Explanation:
It’s really easy. I just used critical thinking.
find the slope please it would help so much
Answers
Answer:
1. 1/-4
4. 4
Step-by-step explanation:
Formula of slope of 2 lines: x2-x1/y2-y1. Using this value we got the answer.
hope this helps
Please help, screenshot!
Answers
Answer:
4/7
Step-by-step explanation:
class total = 21
chance of picking one of 12 boys out of 21.
12/21 which can be simpilfied to 4/7
9 girls + 12 boys = 21
Boys/total = 12/21
12/21 divided by 3 = 4/7
A wheel with a diameter of 21 inches is rolling on a farm. After 100 revolutions, approximately how many inches has the wheel traveled? Use 22/7 for pi
Answers
Answer:69420
Step-by-step explanation:
if you go 21 inches down a 100 inch slope you will be 79 inches
7th grade math I'll give brainliest
Answers
Answer:
Step-by-step explanation:
Rise over run is the slope, m
m=2/5
a) the slope is 2/5 = .4 which is below the boundary guideline. So no this is not with in carpenter's guidelines
b) the image below show a line with slope 2/5 but with intercept 3
c) the stairs can be draw on the line with rise 2 run 5 from the line. see image
d)equation is in image
2.
a) count the squares
horizontal distance =3
vertical distance =3
b) slope is vertical distance over horizontal distance so m= 3/3 =1
How much interest is earned on $2,078.24 at 0.6% for eight years?
$1096.99
$109.96
$199.76
$99.76
Answers
Answer:
109.96
Step-by-step explanation:
I got about 109 so it rounds to 109.96
Explanation
The amount x the number of years
2078.24x8= 16625.92
The total x the interest rate
16625.92 x 0.6%= 99.75552
Estimate
99.75552≈ $99.7
ivan and jeff buy a package of 8 pen for 4.00. ivan want 5 of the pen. how many should ivan pay?
Answers
Answer:
$2.50
Step-by-step explanation:
Let's set up a proportion using the following setup.
price / pens = price / pens
We know that it costs $4.00 for 8 pens.
$4.00 / 8 pens = price / pens
We don't know how much it costs for 5 pens. Therefore, we can say it costs $x for 5 pens.
$4.00 / 8 pens = $x / 5 pens
4/8=x/5
We want to solve for x (the cost for 5 pens). Therefore, we must get x by itself on one side of the equation. x is being divided by 5. The inverse of division is multiplication, so multiply both sides of the equation by 5.
5*(4/8)=(x/5)*5
5*(4/8)=x
5*0.5=x
2.5=x
x= $2.50
Ivan should pay $2.50 for 5 pens.
Answer:
4.00
Step-by-step explanation:
Consider a sequence given by the formula a n = a n -1 − 5, where a1 = 12 and n ≥ 2.
Create an explicit formula of the sequence. Use the explicit formula to find of the
sequence. Give your answer in the answer space.
a100
Answers
Answer:
a= n+6 n
Step-by-step explanation:
n=an−1−5
Step 1: Flip the equation.
an−6=n
Step 2: Add 6 to both sides.
an−6+6=n+6
an=n+6
Step 3: Divide both sides by n.
an n = n+6 n a= n+6 n
Describe how the data is dispersed in a box plot with the following data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.
AND PLEASE ACTUALLY EXPLAIN/DESCRIBE!
Answers
In a box plot, also known as a box-and-whisker plot, the data is dispersed and represented visually to provide a summary of the distribution and key characteristics of the dataset. Let's describe how the data is dispersed in the box plot for the given data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.
1. Median (Q2): The median represents the middle value of the dataset when arranged in ascending order. In this case, the median is around 27 or 28, as it lies between the values 27 and 30.2. Lower Quartile (Q1): The lower quartile marks the boundary between the lower 25% of the data and the upper 75%. It is located approximately around 22 or 23, as it falls between the values 21 and 24.3. Upper Quartile (Q3): The upper quartile marks the boundary between the lower 75% of the data and the upper 25%. It is located around 34 or 35, as it lies between the values 33 and 36.4. Interquartile Range (IQR): The IQR is the range between the upper and lower quartiles (Q3 - Q1). In this case, the IQR is approximately 12 (35 - 23).5. Whiskers: The whiskers represent the range of the data excluding any outliers. They extend from the lower quartile (Q1) to the minimum value and from the upper quartile (Q3) to the maximum value. However, in some cases, the whiskers can also be defined based on certain criteria, such as 1.5 times the IQR. Outliers, if present, are depicted as individual data points beyond the whiskers.6. Outliers: Outliers are data points that significantly deviate from the rest of the dataset. In this case, there are no clear outliers based on the data provided.7. Box: The box in the box plot spans from the lower quartile (Q1) to the upper quartile (Q3) and represents the middle 50% of the data. In this case, the box spans approximately from 23 to 35.By observing the box plot, we can see that the data is moderately dispersed, with the majority of values concentrated around the median. The range of the data is approximately 20 to 38, with some variability within the dataset.
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Minimum value: 18
First quartile (Q1): 22
Median: 29
Third quartile (Q3): 36
Maximum value: 38
The box plot is created using these values. A box is drawn from Q1 to Q3 with a line inside the box at the median. Whiskers are drawn from the box to the minimum and maximum values. Any data points beyond the whiskers are plotted as individual points.
In this box plot, the data is dispersed fairly evenly, with no outliers beyond the whiskers. The box is centered around the median, indicating that the data is roughly symmetric. The lower half of the data is slightly more spread out than the upper half, as indicated by the longer whisker on the left side of the box. Overall, the box plot shows that the data is relatively consistent, with no extreme values.
Which triangle is correctly labeled?
Answers
Option (b) Is the answer
Hope it helps you
The answer is Option (B)
Reason
The Hypotenuse is always on the Opposite side of the Right Angle.
This is only seen in Option (B)
Learn more about Hypotenuse and Legs here
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The function rule for the input/output table is to divide by 3. What number completes the table?
Answers
Answer:
2
Step-by-step explanation:
divide 6 by 3 and you get 2 or do nine lines:
3, 6, 9,
12, 15, 18,
21, 24, 27
and then count how many 3s it took to get to 6, so in this case it is 2.
Question 3...............
Answers
Answer:
18 in.
Step-by-step explanation:
because if we divide
\((32 \times 18 \times 16 ) \div (24 \times 16 \times x = 18\)
hope it helps you if you like answer please mark brainliest
Answer:
18 in
Step-by-step explanation:
Which measurements is/are greater than 3 meters 12 feet 3 yards 86 inches key: 1 foot=.305 meters
3ft=1 yard
12=1 foot
Answers
3 meters is equivalent to 9 feet.
3 yards is equal to 9 feet which is equal to 3 meters
86 inches is equivalent to 7 feet, less than 9 feet.
12 feet is greater than 3 meters.
Hence, it is \(12\) feet.
What is the yard?
A unit of measurement of length equal to \(3\) feet or approximately \(0.914\)meter.
As per the given information,
\(3\) meters is equals to \(9\) feet, \(3\) yards is equal to \(9\) feet which is equal to \(3\) meters and \(86\) inches is equivalent to \(7\) feet, less than \(9\) feet.
So, \(12\) feet is greater than \(3\) meters.
Hence, it is \(12\) feet.
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