Here are two steps from the derivation of the quadratic formula (picture included)
what took place between the first step and the second step?
A. factoring a perfect square trinomial
B. completing the square
C. taking the square root of both sides
Answers
The mathematical operation which took place between the first step and the second step from the derivation of the quadratic formula is: B. completing the square.
What is a quadratic equation?A quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
The derivation of quadratic formula.Mathematically, the quadratic formula can be derived as follows:
x² + b/ax +c/a = 0
x² + b/ax = -c/a
x² + b/ax + (b/2a)² = - c/a + (b/2a)² [completing the square]
(x + b/2a)² = b²/4a² - c/a
x + b/2a = √(b²/4a² - c/a)
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
In conclusion, the step which is shown in the image above for the derivation of the quadratic formula was derived by using completing the square method.
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Answer: THE CORRECT ANSWER IS Factoring a perfect square trinomial
Step-by-step explanation:
Related Questions
45% of the population of a town are men and 35% are women. If the number
of children is 30,000, find the number of men.
Answers
Answer:
67,500 men
Step-by-step explanation:
Percent of children = 20% (.2)
30,000 x 5 = 150,000 (Total pop.)
150,000-30,000 = 120,000 (Pop. minus children)
.35 (Percent of women) x 150,000 =52,500
120,000-52,500 = 67,500
Answer:
67,500
Step-by-step explanation:
20 percent of the population is children. 45 percent is men. If children population is 30000, you multiply by 2 to get 40 percent. That means that if men were 40 percent, men population would be 60000. When you add another 5 percent to get 45 percent, it makes 67500 men.
Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at (6,3). Which point on the y-axis could be on the edge of the circle of the distance from the center of the circle to the edge is 10
Answers
Good evening
Answer:
(0 , 5) and (0 , 11)Step-by-step explanation:
Suppose M(x , y) is a point of the circle of center (6,3) and radius 10 and M is also a point of the y-axis then the coordonates of M should verify these two equations at the same time:
[tex]\left \{ {(x-6)^{2} +(y-3)^2=10^{2} } \atop {x=0}} \right.[/tex]
Then
(0-6)² + (y-3)² = 100
then
36 + (y-3)² = 100
then
(y-3)² = 100 - 36
= 64
then
|y-3| = 8
then
y - 3 = 8 or y - 3 = -8
then
y = 11 or y = 5
then the only points that are on the edge of the circle and on y-axis are:
(0 , 5) and (0 , 11).
:)
Answer:
(0, –5)
Step-by-step explanation:
If you don't see this option there is another option, (0 , 11) is also correct
The data on ages at which a sample of 35 fathers had their first child show a mean 25.43 and standard deviation 5.19. Define the population parameter of interest in this context.
Answers
Answer:
Step-by-step explanation:
A population parameter describes an entire population; a particular characteristic of an entire population. A value that describes the entire population. In this context, the population parameter is looking into the average ages of fathers when they had their first child, but this value is not given. The mean given here is the sample statistic.
Since, the population studied here is a very large population (all fathers), you have a statistic. But sometimes, if the population is very small and groups are small enough to measure, you have a parameter.
Dexter mows his law every 12 days and washes his windows every 30 days. He mowed his lawn and washed his windows today.How many days from now will it be until he mows his lawn and washes the windows on the same day
Answers
Answer:
60 days
Step-by-step explanation:
To find when the two actions will happen together again, we just need to find the least common multiple of 12 and 30.
To do this, first we factor them in prime numbers:
12 = 2 * 2 * 3
30 = 2 * 3 * 5
Now we choose one of them and add the prime factors that the number chosen does not have from the other.
If we choose 30, we should add a number 2, so 2 * 30 = 60
If we choose 12, we should add a number 5, so 12 * 5 = 60
So after 60 days Dexter will mow his lawn and wash the windows on the same day.
Plz Help meee!!!
Factor the Trinomial
x^2+12x+27
Answers
Answer:
(x + 9)(x + 3)
Step-by-step explanation:
Factor 27 so that the factors, when combined, will equal 12:
x² + 12x + 27
x 9
x 3
(x + 9)(x + 3) is your answer.
Check: Use the FOIL method. Multiply the first two terms, the outside terms, the inside terms, and then the last two terms. Combine like terms:
(x + 9)(x + 3) = x² + 3x + 9x + 27 = x² + 12x + 27 (√)
~
Answer:
(x+9)(x+3)
Step-by-step explanation:
first of all, you should learn this properly, because you'll have to go back to this over and over again. anyways
you need to find two numbers so that it adds up to 12, but also multiplies to 27.
The numbers 9 and 3 fit the situation
So you add 9x and 3x because it's the same thing as 12x. you're just splitting up the term 12x into two other terms.
so now it looks like x^2 + 9x + 3x + 27. now you factor the first two terms and last two terms
x ( x + 9 ) <---factor of first two terms
3 ( x + 9) <---factor of last two terms
x(x+9)+3(x+9)
you notice that (x+9) is common in both factorized parts
so, you add x and 3 from the outside
and you get (x +3 ) (x+9)
Place parentheses around one operation and two numbers to make this equation true. Then solve it, showing all of your steps. 64 - 8 + 12 x 2 + 9 = 188
Answers
Answer:
64 - 8 + 12 x (2 + 9) = 188
Step-by-step explanation:
64 - 8 + 12 x 2 + 9 = 188
Putting parentheses around two numbers and one operation:
64 - 8 + 12 x (2 + 9) = 188
Following the BODMAS principle
Solving the bracket or parentheses first
(2 + 9) = 11
64 - 8 + 12 × 11
Then multiplication:
12 × 11 = 132
64 - 8 + 132
Then addition:
-8 + 132 = 124
64 + 124 = 188
Hence the proof
can anybody spare dome time to help me?
Answers
Answer:
y = x² -8x + 16
Step-by-step explanation:
y = (x -4)^2
y = (x -4) * (x -4)
use the FOIL method
y = x*x -4x -4x +16
y = x² -8x + 16
Question 28
Let be an angle in quadrant such that.
Find the exact values of and.
Answers
Answer:
see explanation
Step-by-step explanation:
Since Θ is an angle in the third quadrant, then secΘ < 0 and tanΘ > 0
Using the identity
sec x = [tex]\frac{1}{cosx}[/tex] , then
cos x = - [tex]\sqrt{1-sin^2x}[/tex]
= - [tex]\sqrt{1-(-3/5)^2}[/tex] = - [tex]\sqrt{1-\frac{9}{25} }[/tex] = - [tex]\sqrt{\frac{16}{25} }[/tex] = - [tex]\frac{4}{5}[/tex], thus
secΘ = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]
---------------------------
Using the identity
tan x = [tex]\frac{sinx}{cosx}[/tex] , then
tanΘ = [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex] = - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex] = [tex]\frac{3}{4}[/tex]
The value of sec(x) is (5/4) and tan(x) will be (-3)(4).
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.
The six trigonometric ratios are the source of all fundamental trigonometric identities.
The given value of sin (x) is ( -3 / 5 ). The values of sec(x) and tan(x) will be calculated as below:-
sec(x) = 1 / cos(x)
[tex]cosx = \sqrt{1-sin^2x}[/tex]
[tex]cosx = \sqrt{1-(\dfrac{-3}{5})^2}[/tex]
cos(x) = 4 / 5
sec(x) = 1 / ( 4 / 5 ) = ( 5/ 4)
The value of tan(x) will be calculated as:-
tan(x) = sin(x)/cos(x) = ( -3 / 5 ) / (4 / 5 )
tan(x) = (-3/4)
Therefore, the value of sec(x) is (5/4) and tan(x) will be (-3)(4).
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How long is Y Z?
Any help will be appreciated thank you
Answers
Answer:
This is a special triangle. It is a 30 60 90 degree triangle. I would google more about it. I don't have much more time to work it out. I hope this helps. Have a great rest of your day!
please help me asap!!!!! 4x^{2} -144
Answers
Answer:
x=6
Step-by-step explanation:
First you square root the whole problem to get
2x-12=0
then you add 12 to both sides
2x=12
then you divide both sides by two to get
x=6
30 POINTS!!! NEED HELP!!!!
Write the expansion for the series described by the summation notation. *
Captionless Image
a) 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100+ 121 + 144
b) 16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121
c) 16 + 9 + 5 + 0 + 1 + 4 + 25 + 25 + 36 + 49 + 64 + 81 + 100 + 121
d) None of the above
Answers
Answer:
b) 16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121
Step-by-step explanation:
[tex] \Sigma_{k=1}^{16} (k - 5)^2 \\
= (1- 5)^2 + (2- 5)^2 + (3- 5)^2 + \\ (4- 5)^2 + (5- 5)^2 + (6- 5)^2 \\+ (7- 5)^2 + (8- 5)^2 + (9- 5)^2 \\+ (10- 5)^2 + (11- 5)^2 + (12- 5)^2 \\+ (13- 5)^2 + (14- 5)^2 + (15- 5)^2\\ + (16- 5)^2 \\\\
=(-4)^2 + (-3)^2 + (-2)^2 + (-1)^2 + (0)^2 \\+ (1)^2 + (2)^2 + (3)^2 + (4)^2 + (5)^2 \\+ (6)^2 + (7)^2 + (8)^2 + (9)^2 + (10)^2 + \\ (11)^2 \\\\
=16 + 9 + 4 + 1 + 0 + 1 + 4 + 9 + 16 + 25 \\+ 36 + 49+ 64 + 81 + 100 + 121[/tex]
Hong reads 18 chapters of a book in 6 hours. What is his rate in chapters per hour?
Answers
Answer:
3 chapters/hour
Step-by-step explanation:
18 chaps. / 6 hours =3
solve 6n + 12 - 8n = 22
Answers
Answer:
n = -5
Explanation:
6n + 12 − 8n = 22
[ Simplify both sides of the equation ]
6n + 12 − 8n =22
6n + 12 + −8n = 22
(6n + −8n) + (12) = 22 [Combine Like Terms]
−2n + 12 = 22
−2n + 12 =22
[ Subtract 12 from both sides ]
−2n + 12 − 12 = 22 − 12
−2n = 10
[ Divide both sides by -2 ]
-2n / -2 = 10 / -2
n = -5
Answer:
n = -5
Step-by-step explanation:
6n + 12 - 8n = 22
Combine like terms
-2n +12 = 22
Subtract 12 from each side
-2n +12-12 = 22-12
-2n =10
Divide each side by -2
-2n/-2 = 10/-2
n = -5
FIND (-8/3)+(-1/4)+(-11/6)+3/8-3
PLEASE HELP ME......YOU WILL 15 POINTS FOR ANSWERING THIS QUESTION.....
Answers
Answer:
-7 3/8
Step-by-step explanation:
The least common denominator of 3, 4, 6, and 8 is 24; converting all of our fractions to that denominator and solving, we have
[tex]-\frac{8}{3}+\left(-\frac{1}{4}\right)+\left(-\frac{11}{6}\right)+\frac{3}{8}-3\\=-\frac{64}{24}+\left(-\frac{6}{24}\right)+\left(-\frac{44}{24}\right)+\frac{9}{24}-3\\\\=\frac{-64+(-6)+(-44)+9}{24} -3\\\\=\frac{-70+(-44)+9}{24} -3\\\\=\frac{-114+9}{24} -3\\\\=\frac{-105}{24}-3 \\\\=\frac{-35}{8}-3\\ \\=-4\frac{3}{8}-3\\\\=-7\frac{3}{8}[/tex]
So our solution is -7 3/8
Solve the following system of equations using elimination (addition)
5x - 6y = - 32
3x + 6y = 48
Answers
Answer:
x = 2
y = 6 1/3
Step-by-step explanation:
5x - 6y = -32
3x + 6y = 48
-----------------
8x = 16
x = 2
5(2) - 6y = 48
10 - 6y = 48
-6y = 48 - 10
-6y = 38
y = 6 1/3
This is a very important opinion question. Answer however you want to lol
1. Whats the best burger place, ice cream place, and groceery store you have ever been to?
2. Whats the best sugary treat and where can you buy it.
3. Your favorite word (ex. potato)
Answers
Answer:
1. In & Out, Jeremiah's Ice cream, and Costco
2. Circus Peanuts, at a local grocer (Publix, Winn-Dixie)
3. Irrationally
Step-by-step explanation:
What’s the value of x in this equation? -4x=6
Answers
Answer: I believe it would be -1.5
Step-by-step explanation: You would divide both sides of the equation by -4 which would give you x = -1.5
Hope this helps!!!
SMART PEOPLE HELP ASAP
Answers
Answer:
Step-by-step explanation:
Area of this shape is L*W*H
All dimensions are given, now you just have to multiply it
turn all fractions into improper fractions
10 3/8 = 83/8
1 3/4 = 7/4
2 1/2 = 5/2
[tex]\frac{83}{8}[/tex] * [tex]\frac{7}{4}[/tex] * [tex]\frac{5}{2}[/tex] = ?
= 2905/64 =
app. 45.39
Chris tried to rewrite the expression \left( 4^{-2} \cdot 4^{-3} \right)^{3}(4 −2 ⋅4 −3 ) 3 left parenthesis, 4, start superscript, minus, 2, end superscript, dot, 4, start superscript, minus, 3, end superscript, right parenthesis, cubed. \begin{aligned} &\phantom{=}\left( 4^{-2} \cdot 4^{-3} \right)^{3} \\\\ &=\left( 4^{-5} \right)^{3}&\text{Step } 1 \\\\ &=4^{-2}&\text{Step } 2 \\\\ &=\dfrac{1}{4^{2}}&\text{Step } 3 \end{aligned} =(4 −2 ⋅4 −3 ) 3 =(4 −5 ) 3 =4 −2 = 4 2 1 Step 1 Step 2 Step 3 Did Chris make a mistake? If so, in which step? Choose 1 answer: Choose 1 answer: (Choice A) A Chris did not make a mistake. (Choice B) B Chris made a mistake in Step 1. (Choice C) C Chris made a mistake in Step 2. (Choice D) D Chris made a mistake in Step 3.
Answers
Answer: Chris made a mistake in step 2
(It was in Khan Academy)
Answer:
Chris made a mistake in step 2.
Step-by-step explanation:
I was solving this problem just now and I searched it up here. Now I got the answer :)
Find the volume of the figure. Use 3.14 for pi.
Answers
Answer:
10082.36cm²
Step-by-step explanation:
The formula for volume of a cone: V = [(3.14) r²](h/3)
Steps:
1. Find the value of the radius: 1/2 of the diameter (26/2) = 13cm
2. Find the value of the height: 31cm
3. Plugin: [(3.14) 13²] (31/3)
Solve for the volume of the cone:
a) 13² = 169
b) 169(pi) = 530.66
c) 530.66 (31/3) = 530.66 (10.3333)
Volume of cone: 5483.31
The formula for volume of hemisphere is 1/2[(4/3)3.14{r³}]
Steps:
1. Find the value of the radius: 13cm
2. Solve for the volume of the hemisphere
1. 13x13x13 = 2197
2. 2197 (3.14) = 6898.58
3. (4/3) 6896.58 = 9198.1067
4. (1/2) 9198.1067 = 4599.05
Add the two volumes together:
4599.05+5483.31 = 10082.36cm²
This took forever since I used the google calculator, but it got done after forever! Hope this helps!
The Volume of the figure is 10,082.53 cm³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
Volume is a three-dimensional quantity used to calculate a solid shape's capacity.
We have a cone surmounted by Hemisphere.
So, Volume of Figure
= Volume of Cone + Volume of Hemisphere
= 1/3 πr²h + 2/3 πr³
= 1/3 x 3.14 x 13 x 13 x 31 + 2/3 x 3.14 x 13 x 13 x 13
= 5,483.48 + 4,599.05
= 10,082.53 cm³
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plzzzzzzzzzzzzzzaaaaaaaaaa
Answers
Answer:
A
Step-by-step explanation:
[tex]3x^2+5x+2=0[/tex]
[tex]x=\dfrac{-5\pm \sqrt{5^2-4(2)(3)}}{6}=\dfrac{-5\pm 1}{6}=-\dfrac{2}{3}, -1[/tex]
Therefore, the answer is choice A. Hope this helps!
The student council sold 362 rolls of wrapping paper for a fundraiser. If they raised $4,706, what was the cost of one roll of wrapping paper
Answers
Answer:
13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
What is the completely factored form of f(x)= x^3 -2x^2-5x+6?
Answers
Answer:The answer is X^2(x+5) +2(2x+3)
Step-by-step explanation: give the equation f(x)=x^3+5x^2+4x-6
Factoring out the common items we have
=X^2(x+5) +2(2x+3)
Enter a simplified polynomial expression for the area of a parallelogram whose base is (x + 8) units and whose height is (x − 2) units.
The area of the parallelogram is ? square units.
Answers
Answer:
[tex]\\x^{2}[/tex]+6x-16
Step-by-step explanation:
x^2 is exponent 2.
Answer:
(x+8)(x-2) = a
a = x^2 -2x + 8x - 16
Area = x^2 + 6x - 16
May someone please help me
Answers
hi buddy i can help you with this
Rafael has $230 in his savings account. He used 20% of his money to buy a video game. what was the cost of the video game?
Answers
Answer:
46
Step-by-step explanation:
turn the percentage into a fraction
so 20% is equal to 2/10.
230 is the whole number so multiply is by the numerator which is 2
230 x 2=460
and divide it by the denominator which is 10
460/10=46
plz Wegnerkolmp2741o or right awsers plzzzzzzzzzzzzzzzzzz any one
Answers
Answer:
A. (z+9) (z+8)
Step-by-step explanation:
Answer:
(z+8)(z+9)
Step-by-step explanation:
The first step is to look at the signs. All the signs are positive so we know that the signs in our factored equation will be positive as well. This tells us that we just need to find what factors of 72 can add up to 17. So, we can get 72 with 36 times 2, 24 times 3, 18 times 4, 12 times 6, and 8 times 9. 36 + 2 does not equal 17, 24 + 3 does not equal 17, 18 + 4 does not, 12 + 6 does not, and 8 + 9 does! So since 8+9=17, we can plug those in. So we take our normal factor form (a variable + or - a number)(a variable + or - a number). Our variable is z, and our signs are positive, and our numbers are 8 and 9. To check use FOIL (multiply the First, Outer, Inner, then Last terms and combine like terms to see if you get your original problem.
Slope and y-intercept of the function y= -5x+4.
Answers
Answer:Slope is -5. y-intercept is 4
Step-by-step explanation:
y=mx+c m=slope y-intercept=c
y=-5x+4
Comparing both equations we m=-5 and c=4 meaning slope =-5 y-intercept=4
How do you write 7.01 in scientific notation?
Answers
Answer:
7.01×10'0
snap. Jona_Fl16
Answer: 7.01×10^0
Step-by-step explanation:
7.01×10^0=7.01
7.01*1
7.01
Francine has a piece of wood that is five 5 5/12 feet long she uses three 3 1/4 feet of the wood from a science project how much for just Francine have left.
Answers
Answer:
4/3 ft
Corrected question;
Francine has a piece of wood that is five 5/12 feet long she uses three 1/4 feet of the wood from a science project how much for just Francine have left.
Step-by-step explanation:
Given;
Francine has a piece of wood that is five 5/12 feet long.
Total amount of wood T = 5 × 5/12 ft = 25/12 ft
she uses three 1/4 feet of the wood from a science project.
Amount of wood Used U = 3 × 1/4 = 3/4 ft
The amount of wood left equals the total amount of wood minus the amount of wood used;
The amount of wood left L = T - U = 25/12 - 3/4
L = 25/12 - 9/12
L = 16/12
L = 4/3 ft
