Answer:
X=4 or X=-2
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8
Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is -2 .
-8 + 1 = -7
-4 + 2 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 2
x2 - 4x + 2x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
2 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-4)
Which is the desired factorization
Equation at the end of step
1
:
(x + 2) • (x - 4) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2
Solving a Single Variable Equation:
2.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
Supplement : Solving Quadratic Equation Directly
Solving x2-2x-8 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = x2-2x-8
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 1.0000
Plugging into the parabola formula 1.0000 for x we can calculate the y -coordinate :
y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 8.0
or y = -9.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-2x-8
Axis of Symmetry (dashed) {x}={ 1.00}
Vertex at {x,y} = { 1.00,-9.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = { 4.00, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving x2-2x-8 = 0 by Completing The Square .
Add 8 to both side of the equation :
x2-2x = 8
Now the clever bit: Take the coefficient of x , which is 2 , divide by two, giving 1 , and finally square it giving 1
Add 1 to both sides of the equation :
On the right hand side we have :
8 + 1 or, (8/1)+(1/1)
The common denominator of the two fractions is 1 Adding (8/1)+(1/1) gives 9/1
So adding to both sides we finally get :
x2-2x+1 = 9
Adding 1 has completed the left hand side into a perfect square :
x2-2x+1 =
(x-1) • (x-1) =
(x-1)2
Things which are equal to the same thing are also equal to one another. Since
x2-2x+1 = 9 and
x2-2x+1 = (x-1)2
then, according to the law of transitivity,
(x-1)2 = 9
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-1)2 is
(x-1)2/2 =
(x-1)1 =
x-1
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-1 = √ 9
Add 1 to both sides to obtain:
x = 1 + √ 9
Since a square root has two values, one positive and the other negative
x2 - 2x - 8 = 0
has two solutions:
x = 1 + √ 9
or
x = 1 - √ 9
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2-2x-8 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -2
C = -8
Accordingly, B2 - 4AC =
4 - (-32) =
36
Applying the quadratic formula :
2 ± √ 36
x = —————
2
Can √ 36 be simplified ?
Yes! The prime factorization of 36 is
2•2•3•3
√ 36 = √ 2•2•3•3 =2•3•√ 1 =
± 6 • √ 1 =
± 6
So now we are looking at:
x = ( 2 ± 6) / 2
Two real solutions:
x =(2+√36)/2=1+3= 4.000
or:
x =(2-√36)/2=1-3= -2.000
Solve the system of equations by the addition method.
[tex]\left \{ {{\frac{x}{2}-y=7 } \atop {-\frac{x}{7}+\frac{2y}{7}= -2 }} \right. <=>\left \{ {{\frac{x}{2}.2-2y=2.7} \atop {-\frac{x}{7}.7+\frac{2y}{7}.7= -2.7}} \right. <=>\left \{ {{x-2y=14} \atop {-x+2y=-14}} \right. <=>\left \{ {{0x=0} \atop {y={\frac{x}{2}-7}} \right.[/tex]
ANSWER: B
ok done. Thank to me :>
Integer solution
x= 2n, y=n-7, nEZ
real solution or you can use inverse operation to have addition
y= x/2-7 y=x[multiplied by] 2+7
oh and for the first one the choice is A the second one im sorry im not sure
10 points. Thank you :)
Answer:
I believe it's A
Step-by-step explanation:
Answer:
i think C. 10(5x-3) is answer
Jordan bikes at a speed of 8 2/3 mph. How many miles will he bike in 2/3 of an hour?
Answer:
26.87 miles
Step-by-step explanation:
Answer: 5 7/9
Step-by-step explanation:
Find The Area Of The Arrow Above Question Answered
Answer:
30 inches
Step-by-step explanation
because the other triangle is the same and its 30inches
PLEASE HELP GIVING BRAINLIEST
Answer:
Minus 4 from 16 = 12
12 is 3/10ths of the number. So, divide it by three. This is 4 and then you do 4*10 = 40
I think this is correct
Answer: X = 6
Step-by-step explanation:
Sorry i'm asking for so much help tonight/morning, i just rlly need to get this finished and i still don't completely understand this. Plz help me with this? Thanks in advance
Answer:
Read below
1. 270
2. 277
Step-by-step explanation:
I'm not too sure which answer you're looking for but I'll try to answer all of them :).
First of all, we can consider them in percentage form first.
If the first sale price is marked down by 30%, it is now 70%.
For the second, the price is marked down by 20% first, so 80%.
And then another 10% on top of the 80%. 10% of 80 is 8, so the second one is marked down 80-8, or 72%.
As we can clearly see, 72% is greater than 70% so the first deal( 30% off ) would give you a cheaper price
Now we move on to the actual prices.
First one is 70% of the original price, 70% of $385 is $269.5.
Second one is 72% of original price, 72% of $385 is $277.2
Don't forget to round to the nearest dollar!
1. 270
2. 277
Hopefully this helps! If I did it wrong feel free to tell me ;-;
Also lol relatable my works due tmr and i dont feel like doing it either ://
Hi, I need some help with the last question of the first problem and the answer to the second page.
Answer:
46.9 for the first one
Step-by-step explanation:
So sorry if i'm wrong <3
Write an equation for the constant of proportionality.
Answer:
they r all multiple by 3
Step-by-step explanation:
2×3=6
4×3=12
6×3=18
8×3=24
10×3=30
Answer:
Step-by-step explanation:
as hotdogs (x) increase by 2 the cost (y) increases by 6
6/2 = 3/1 = 3
y = 3x
PLS HELP ME!!!!!!! URGENT!
Answer:
A
Step-by-step explanation:
Your final bill is $51.28. This includes a 12% tip. What was the bill without tip?
Answer:
$45.13
Step-by-step explanation:
what is 12% of 51.28 change 12% to a decimal by moving two spaces to left =0.12. multiple by 51.28= 6.15 that is the amount of the tip then subtract it from 51.28-6.15= $45.13 original amount before the tip.
I don't understand this.
859 ÷ 3 = (286.3333333...) 286 R 1
The quotient (integer division) of 859/3 equals 286; the remainder (“left over”) is 1.
hope this helpss
p.s. can you mark me as the brainliest?
GIVING BRAINLIEST!! FAST-
Answer:
c'estla A
Step-by-step explanation:
You buy 3.18 pounds of apples, 1.25 pounds of pears, and 2.67 pounds of oranges. What is your total bill rounded to the nearest cent?
Answer:
318125267
Step-by-step explanation:
-_-...............that is the answer
3.17 pounds of apples
1.25 pounds of pears2
2.56 pounds of oranges
add = 7.98
rounded = 7.42, (or anything close. I am really bad at rounding decimals)
A 6-pack of beaded necklaces costs $12.78. What is the unit price?
$____ per necklace
Please help!! will give brainliest to the correct answer!!
Thanks,
:)
The unit price for 1 pack of beaded necklaces is $2.13.
What is unit price?The unit price refers to the price per unit of measures, such as price per pound, quart, ounce, or other units of weight or volume of the food package.
Given that a 6-pack of beaded necklaces costs $12.78.
We need to find the unit price, for the same.
So the unit price will be calculated by dividing the total cost by number of packets,
= 12.78/6 = 2.13
Hence the unit price for 1 pack of beaded necklaces is $2.13.
Learn more about unit price click;
https://brainly.com/question/10706678
#SPJ2
What is the distance from City A to City C?
A. 12 km
B. 18 km
C. 20 km
D. 30 km
Answer:
30
Step-by-step explanation:
the whole thing is 47 so you take away 17 because thats the starting point of c to d so then you have ur answer hope this helped :))))))))))
Answer:
It is D
Step-by-step explanation:
You just do this
[tex]47 - 17 = 30[/tex]
Which equation best represents the line?
y = 3x + 3
y = 1/2x − 3
y = 1/2x + 3
y = 3x + 1/2
Answer:
the third one, y = 1/2x + 3
Answer:
y = 1/2x + 3
Step-by-step explanation:
The y intercept is 3 and the slope is 1/2.
If the population of an ant hill doubles every 10 days and there are currently 100 ants living in the ant hill, what will the ant hill population be in 20 days?
Answer:
400
Step-by-step explanation:
The current number is 100, it doubles every ten days, and you're asking what the size will be in twenty days.
Beginning:
100 ants (ten days pass)
100 x 2 = 200
Middle:
10 of the 20 days have passed
Your new number is 200 ants
End:
200 ants (ten days pass)
Since every ten days the size doubles: 200 x 2 = 400
400 ants after 20 days
1. a circular table with a radius of 18 inches is going to be covered with 2 in2 tiles. how many tiles will be needed to cover the top?
2. Mr Jones wants to add a cement path around his new pool. the pool has a radius of 7 feet. the cement path will be 1 foot wide and go all the way around the pool. what is the square footage of the path?
Answer:
9 is the required answer
Can You Solve This?
(if you can't see what it says the question is: "Using given algebra tiles, write an expression that is equivalent to the quantity represented in the model below" )
Answer: move the icons thing to the box in your choice I think
SOLVE FOR P
(1) 4 x p x .5= 12
(2) 0.03 x p x 18= 2.7
Answer:
1-24 (I dont know about 2)
Step-by-step explanation:
0.5 x 24 = 12
A copy machine can print 480 copies every 4 minutes. A teacher printed 720 copies. How long did it take to print?
Answer:
6 minutes
Step-by-step explanation:
every minute is 120
720/120=6
Two teams working together can finish a job in 8 days. if the first team works alone for two days and the second team works alone for 5 days, 5/8 of the total work still remains. How many days will it take each team to finish the work alone?
x is the days that the first team finishes the work alone (x>8)
y --------------------------second-----------------------------------------(y>8)
In a day:
The first team finishes 1/x (the work) The second team finishes 1/y (the work) Two teams working together finish 1/8 (the work)⇒ [tex]\frac{1}{x}+ \frac{1}{y} =\frac{1}{8}[/tex] (1)
If the first team works alone for two days and the second team works alone for 5 days, 5/8 of the total work still remains:
⇒ [tex]\frac{2}{x}+\frac{5}{y}=\frac{3}{8}[/tex] (2)
(1),(2) ⇒ [tex]\left \{ {{\frac{1}{x}+ \frac{1}{y} =\frac{1}{8}} \atop {\frac{2}{x}+\frac{5}{y}=\frac{3}{8}}} \right. <=>\left \{ {{x=16} \atop {y=24}} \right.[/tex]
It'll take the first team 16 days and the second team 24 days to finish the work alone
ok done. Thank to me :>
Marielle is cutting equal-sized strips of ribbon for her scrapbook. She has 59 inches of ribbon. if she cuts 8 equal-sized pieces of ribbon, how long will each piece of ribbon be?
Answer:
7 .375
Step-by-step explanation:
what is (0.25) x (1.4)
Answer:
0.35
tep-by-step explanation:
During a period of extreme cold, the average daily temperature dropped decreased by 112°F day. How many days did it take for the temperature to decrease by 9°F? Which equation would you use to find the solution?
A x + 112 = 9x + 112 = 9
B x − 112 =−9x − 112 =−9
C −112x = −9−112x = −9
D 112x = 9
It takes about 4 days for the temperature to decrease by 9°F.
An equation is an expression that shows the relationship between two or more variables or numbers.
Let x represent the number of days. Given that the temperature drop decreased by 1 1/2°F each day (- 1 1/2), for it to decrease by 9°F (-9):
-1 1/2 * x = -9
-1.5x = - 9
x = 4 days
It takes about 4 days for the temperature to decrease by 9°F.
eeeeeeee help!!!1!1!11
Answer:
no because order of operations requires division to be done before addition, she should divide 18252 by n then add
Step-by-step explanation:
PLS I NEED HELP ASAP
Answer:
(-13.5, 4.5)
Step-by-step explanation:
What is 110% of 160?
The first person to answer gets Brainliest
Answer:
176 Basically find whats 10% of 160 and then add that to 160 and there is your answer
- 1/9x+2.4=6 what is x
A pet store is having a pet fish sale. Lauren bought b balas and c catfish. Write an algebraic expression to represent the total cost of the fish. Use the chart to answer the question.