Answer: Factoring x2+8x+17
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +17
Step-1 : Multiply the coefficient of the first term by the constant 1 • 17 = 17
Step-2 : Find two factors of 17 whose sum equals the coefficient of the middle term, which is 8 .
-17 + -1 = -18
-1 + -17 = -18
1 + 17 = 18
17 + 1 = 18
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
1
:
x2 + 8x + 17 = 0
STEP
2
:
Parabola, Finding the Vertex:
2.1 Find the Vertex of y = x2+8x+17
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -4.0000
Plugging into the parabola formula -4.0000 for x we can calculate the y -coordinate :
y = 1.0 * -4.00 * -4.00 + 8.0 * -4.00 + 17.0
or y = 1.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2+8x+17
Axis of Symmetry (dashed) {x}={-4.00}
Vertex at {x,y} = {-4.00, 1.00}
Function has no real rootsvSolving x2+8x+17 = 0 by Completing The Square .
Subtract 17 from both side of the equation :
x2+8x = -17
Now the clever bit: Take the coefficient of x , which is 8 , divide by two, giving 4 , and finally square it giving 16
Add 16 to both sides of the equation :
On the right hand side we have :
-17 + 16 or, (-17/1)+(16/1)
The common denominator of the two fractions is 1 Adding (-17/1)+(16/1) gives -1/1
So adding to both sides we finally get :
x2+8x+16 = -1
Adding 16 has completed the left hand side into a perfect square :
x2+8x+16 =
(x+4) • (x+4) =
(x+4)2
Things which are equal to the same thing are also equal to one another. Since
x2+8x+16 = -1 and
x2+8x+16 = (x+4)2
then, according to the law of transitivity,
(x+4)2 = -1
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+4)2 is
(x+4)2/2 =
(x+4)1 =
x+4
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x+4 = √ -1
Subtract 4 from both sides to obtain:
x = -4 + √ -1
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Since a square root has two values, one positive and the other negative
x2 + 8x + 17 = 0
has two solutions:
x = -4 + √ 1 • i
or
x = -4 - √ 1 • i
Answer:
x=27
Step-by-step explanation:
I solved it myself and my result is (n+1)/n. Why is that 1/2 there? An explanation would be great if possible. Thanks!
Answer:
The product of (k + 1) series starts with 3 (because k = 2) and you need 2 to be multiplied to this in order to get (n + 1)!
Therefore you need to multiply 2 and 1/2 to make it right. 2 completes the factorial and 1/2 remains.
Hope it was clear explanation.
What is 5x5 cause I don’t know what it is
Answer:
25
Step-by-step explanation:
5 + 5 + 5 + 5 + 5 = 25
Answer:
25
Step-by-step explanation:
that the answer pick me brainliest plz
A restaurant wants to study how well its salads sell. If 10 of the salads sold were salads, how many total salads did the restaurant sell?
Answer:
Um... is this a joke it’s 10
Step-by-step explanation:
There are 18 black and 12 navy socks in your drawer. The room is dark and you
cannot turn on the light. What is the least number of socks that you have to take out of
your drawer to be certain that you have a pair of black socks?
The least number of socks that you have to take out of the drawer to be certain that you have a pair of the same color is 5 and the color is black.
Given that,
There are 18 black socks and 12 Navy socks in your drawer the room is dark and you cannot turn on the light.
We have to determine
What is the least number of socks that you have to take out of your drawer to be certain that you have a pair of black socks?
According to the question,
The following steps can be used in order to determine the least number of socks that you have to take out of the drawer:
The total number of blue socks is 18,
And the total number of navy socks is 12.
The probability that the socks come out is black socks is,
[tex]\rm P_b = \dfrac{18}{18+12}\\\\P_b= \dfrac{18}{30}\\\\P_b = \dfrac{3}{5}[/tex]
And the probability that the socks come out is navy socks is,
[tex]\rm P_n = \dfrac{12}{18+12}\\\\P_n= \dfrac{12}{30}\\\\P_n = \dfrac{2}{5}[/tex]
On comparing both the probability,
[tex]\rm P_b>P_n[/tex]
Hence, The least number of socks that you have to take out of the drawer to be certain that you have a pair of the same color is 5 and the color is black.
For more details refer to the link given below.
https://brainly.com/question/19200823
Answer:3
Step-by-step explanation:
I found this out because is you take 3 out you will get BLUE BLUE BLACK or BLACK BLACK BLUE or BLUE BLUE BLUE or BLACK BLACK BLACK
Hope that helps
please help I'm a week behind.Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object.
Help ASAP I’ll mark brainliest
Answer:
a
Step-by-step explanation:
a is positive
b is idek just scattered
c is a scattered correlation aswell
d is a negative correlation
Choose the graph that solves this system of equations.
y = 2x - 6
y = -4x + 3
The Option C is correct.
System of equations:
Given equations are,
[tex]y = 2x - 6\\\\y= -4x + 3[/tex]
When we draw the graph of both equation of line.
Then these lines intersect at a point [tex](1.5,-3)[/tex].
So that option C is correct.
The correct graph is attached below.
Learn more about the system of equations here:
https://brainly.com/question/13729904
You buy a cell phone plan that gives you up to 1000 minutes of calling for $20 per month. During a particular month, you use only 100 minutes. What is your per-minute cost for that
month?
Answer:
20 cents
Step-by-step explanation:
In Exercises 3 and 4, find the values of x and y
plz help!!!
Answer:
x = 20°
y = 30
Step-by-step explanation:
The triangle given on close inspection, it is an equilateral triangle.
Each angle in an equilateral triangle is equal. Likewise, each side is equal.
Thus;
16 + y = 46
y = 46 - 16
y = 30
The triangle that has angle 80°, the other complete angle is 60° because it's an angle of an equilateral triangle.
Thus, the smaller angle there is;
180 - (80 + 60) = 40°
Because sum of angles in a triangle is 180°
Now, x + 40 = 60°
Since that's also an angle of an equilateral triangle.
x = 60 - 40
x = 20°
The value of length y is 30 and the value of angle x is 20 degrees and this can be determined by using the properties of an equilateral triangle.
Given :
The triangle ABC is given in the figure.
In an equilateral triangle, all angles are equal and therefore, each side is equal.
16 + y = 46
y = 46 - 16
y = 30
An angle in the triangle is given that is 80 degrees and angle C is 60 degrees because it is an angle of an equilateral triangle.
Applying sum of interior angles property:
80 + 60 + (60 - x) = 180
200 - x = 180
x = [tex]20^\circ[/tex]
For more information, refer to the link given below:
https://brainly.com/question/19237987
What is the midpoint of the segment with endpoints (-1,6) and (0,7)
Answer:
( -0.5 , 6.5 )
Step-by-step explanation:
It was 4:00 P.M. when John started mowing the lawn and it took him 50 minutes to finish. What time did John finish mowing the lawn?
Answer:
4:50 P.M.
Step-by-step explanation:
Sorry I don't know how to properly explain it but I just added 50 minutes to 4 o' clock to get the answer.
Hope this helps!
Maybe brainliest?
What is 120% of 180?
Step-by-step explanation:
[tex] \tt{120 \: \% \: of \: 180}[/tex]
Convert % to fraction. For that , Divide 120 by 100 :
⇢ [tex] \tt{ \frac{120}{100} \times 180 }[/tex]
Calculate
⇢ [tex] \tt{216}[/tex]
[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{216}}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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An office spends $375.00 per month on office supplies.
The manager wants the company to decrease office
supply costs by 16%. How much money would that save
each month?
Answer:
$51 saved.
Step-by-step explanation:
Well 12% of $425 is found by multiplying
(.12)(425) = $51 saved.
how is 3×3×3×3×3×3×3 written in exponential form
Answer:
7
Step-by-step explanation:
3 * 3 * 3 * 3 * 3 * 3 * 3 = [tex]3^{7}[/tex]
Answer:
3×3×3×3×3×3×3 is
Step-by-step explanation:
3 multiplied by itself 7 times will give you 3 to the 7th power.
What is the unit rate for this?
Time: 1, 2, 3, 4
Amount: 0.6, 1.2, 1.8, 2.4
Answer:
1:0.6
Step-by-step explanation:
-6y -8 = -18
can anyone solve this
Answer:
-6y -8 = -18
18-8=6y
10=6y
y=10/6=5/3
Answer:
-6y - 8 = -18
+ 8 +8
-------------------
-6y = -10
----- -----
-6 -6
10 divided by 6 is 5/3
so y is 5/3
The width of a rectangle is the length minus 4 units. The area of the rectangle is 12 units. What is the width, in units, of the rectangle?
Answer:
3
Step-by-step explanation:
Kate has some dimes and quarters. If she has 23 coins worth a total of $3.50, how many of each type of coin does she have?
23=d+q, d=23-q
350=10d+25q, using d from above
350=10(23-q)+25q
350=230-10q+25q
120=15q
q=120/15
q=8, and since d=23-q
d=23-8=15
So there are 15 dimes and 8 quarters
What is the domain and range of the relation?
Answer:
I think option c is answer
Jessica drank 3 1/2 glasses of water that was twice as much as her sister how many glasses did Jessica drink
What is the mode of 3, 3, 4, 5, 10?
Answer:
3
Step-by-step explanation:
The mode is the number that occurs most frequently in a set of numbers
Also:
I saw that this is your first question. Welcome to the Brainly community.
The mode of the data set 3, 3, 4, 5, 10 is 3
What is mode?"It the value that appears most frequently in a data set.""A data set may have one mode, more than one mode, or no mode at all."For given question,
We have been given a set of data.
3, 3, 4, 5, 10
The frequency of each value in the data set is:
Value Frequency
3 2
4 1
5 1
10 1
We can observe that, 3 appears most frequently in a data set.
Therefore, the mode of the data set 3, 3, 4, 5, 10 is 3
Learn more about the mode of the data set here:
https://brainly.com/question/6813742
#SPJ2
if log x (8x-3) - logx 4=2 the value of x is ___ and ____
the answer is not 1/2 and 3/2. I've already tried that and it is wrong.
Find the mean for each set of data, weights of cats at a pet store in pounds: 5,4,10,7,6
Answer:
6.4
Step-by-step explanation:
add all numbers together then divide by 5
Kaylee invested $830 in an account paying an interest rate of 6.6% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,260?
Answer:
t≈6
Plug values into A=P(1+r/n)^nt
Escribe el término "punto, línea, plano o superficie" según corresponda a la descripción a la que se hace referencia.
La pantalla de un cine.
Una cuerda tensa.
La punta de un lápiz
Una hoja de papel
La antena de un automóvil
La marca en la piel después de aplicar una vacuna
Un campo de fútbol
El doblez de un folder
La percepción de una estrella en el cielo
El cristal de una ventana
Punto:
La punta de un lápiz.Línea:
Una cuerda tensa.La antena de un automóvil.Plano:
La pantalla de un cine.Una hoja de papel.El cristal de una ventana.Superficie:
La marca en la piel después de aplicar una vacuna.Un campo de fútbol.El doblez de un folder.GeometríaEl punto es una entidad que tiene una posición, pero no tiene dimensiones (largo, ancho o alto). Por lo tanto, es de dimensión cero, es decir, adimensional. Contiene el significado de lugar, de existencia, pero no tiene elementos mensurables, es decir, no se puede medir.
En contextos geométricos, una línea es un cuerpo unidimensional de forma y longitud arbitrarias. Todos los objetos unidimensionales, como cuerdas, líneas rectas, mitades y perímetros, son líneas. Se cree que una línea se forma cuando un punto de dimensión cero se mueve en el espacio y forma una línea infinita de múltiples puntos.
Intuitivamente, el concepto de plano se puede describir como una superficie perfectamente recta (es decir, sin curvatura ni cavidad) y lisa, que tiene volumen cero y ocupa solo las dos dimensiones del espacio tridimensional.
La superficie de un objeto se refiere a una superficie bidimensional, que separa el objeto de otros objetos y del entorno. En topología, la superficie es una dimensión bidimensional.
Aprenda más sobre geometría en https://brainly.com/question/4637858
Which of the following best describes why the Hours of Service Regulations were put into place?
To minimize the number of vehicles on the road at night
To reduce the number of accidents caused by fatigue
To protect the rights of shippers
Answer:
To reduce the number of accidents caused by fatigue
Step-by-step explanation:
I don't know if its right
PLEASE HELP ;-; Ill GIVE BRAINLY
What is the solution to the following system of equations? Explain how you know.
Answer:
-3,1
Step-by-step explanation:
When you are doing Systems Of Equations using a graph, the point where the lines intersect is your answer
15. Which of the following sets of quantum numbers are allowed
a) n=1, 1 = 0 and m=0
c) n=1,1=0 and m = +1
b) n=2, 1 = 2 and m =+ 1
d) n = 2, 1= 2 and m = 0
Answer:
I'm not exactly sure but its 3 am here so it might be wrong but ima go with d
The Super Lotto Plus game consists of a player selecting five different numbers from 1 to 47 and a mega number from 1 to 27 (the order is unimportant and the mega number need not be different from the other numbers). (11) What is the probability of all five numbers and the mega number matching the winning numbers
Answer:
1/41416353 probability of all five numbers and the mega number matching the winning numbers
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order of the numbers is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Probability of the five numbers matching:
Desired outcomes: 1 -> the matching numbers
Total outcomes: 5 from a set of 47. So
[tex]T = C_{47,5} = \frac{47!}{5!(47-5)!} = 1533939[/tex]
Probability:
[tex]p_{S} = \frac{1}{1533939}[/tex]
Probability of the mega number matching:
1 from a set of 27. So
[tex]p_M = \frac{1}{27}[/tex]
Probability of both matching:
Independent events, so we multiply the probabilities:
[tex]p = p_S*p_M = \frac{1}{1533939}*\frac{1}{27} = \frac{1}{41416353}[/tex]
1/41416353 probability of all five numbers and the mega number matching the winning numbers
Find the slope of the line passing through each of the following pairs of points (0,7), (0,-8)
Answer:
Step-by-step explanation:
Answer:
The answer is unidentified
Step-by-step explanation:
I checked ;)