Solve each quadratic equation by factoring.
Show steps pls
8x^2 - 4x = 2x +9
Answers
Answer:
hope these help........
Answer:
[tex]x = \frac{-3}{4}[/tex] or [tex]x = \frac{3}{2}[/tex]
Step-by-step explanation:
[tex]8x^{2} - 4x = 2x +9[/tex]
Okay, let's put everything on one side.
[tex]8x^{2} -4x-2x-9=0[/tex]
As you can see we can subtract -4x from -2x now leaving us with -6x.
[tex]8x^{2} -6x-9=0[/tex]
Now there are multiple ways to solve a polynomial, but we can go with a way to factor them the easy way. We need to multiply the leading coefficient with the ending term because there is no common number we can factor out of these guys.
[tex]8(-9)=-72[/tex]
We multiplied 8 and -9 together which gave us -72. With this, we need to find two numbers that add to the middle term, -6, but will multiply to -72. This is going to be 6 and -12. Now we are going to replace the middle coefficient with those two numbers.
[tex]8x^{2} + 6x - 12x- 9= 0[/tex]
(Keep in mind the equation has not changed)
Now we are going to do something called factoring by grouping, with the first two terms, 8x^2 and 6x we take out the GCF (greatest common factor):
[tex]2x(4x+3)[/tex]
so let's do the same between the last two.
[tex]-3(4x+3)[/tex]
So when putting them together we have,
[tex]2x(4x+3)-3(4x+3)=0[/tex]
Now let's factor here, (4x+3) can be taken out and 2x as well as -3 can be put together.
[tex](4x+3) (2x-3)=0[/tex]
Then we set these factors to zero to get our x answer:
[tex]4x+3=0[/tex]
[tex]2x-3=0[/tex]
And we solve, which leaves us with:
[tex]x = \frac{-3}{4}[/tex] or [tex]x = \frac{3}{2}[/tex]
Related Questions
Joey built a skateboarding ramp. The base of the ramp along the ground is 13 feet, and the top of the ramp is 7 feet off the ground. What is the length of the ramp's incline?
Answers
Answer:
14.77 feet
Step-by-step explanation:
Using the pythagoras theorem to get the length of the ramp
l² = 13² + 7²
l is the length of the ramp
l² = 169 + 49
l² = 218
l = √218
l = 14.77 feet
Hence the length of the ram is 14.77 feet
4 + x/7 =2
Solve
a -14. b 10. c 12 d 42
Answers
Answer:
-14
Step-by-step explanation:
4 + x/7 =2
x/7= -2
x= -2 * 7
x=
-14
Please help me out with this one, I don't know how to do this one
Answers
Answer:
3/14 or about 21%
Step-by-step explanation:
Just divide the number of black cars by the total number of cars.
15/70 = 3/14
at the grocery sale you want to buy 4 and 9 tenths lb of cheese what decimal should the digital scale show
Answers
Answer:
4.9 lb
Step-by-step explanation:
Tenths are the first place after the decimal point.
(marking brainliest or however you spell it)
may someone help me on this? please?? thank you if you tried to help!
Answers
Answer:
6.4
Step-by-step explanation:
To do this you just have to multiply 40 by 2 to get 80 and than divide by 12.5 and you get 6.4
factorise x^3 - 5x
please help, would be greatful
Answers
x(x^2-5)
D. Solve the following problems:
in a 100 kilometer trip, jojo uses 12 liters of gasoline, how many liters of gasoline will he use on a trop of 350 kilometers?
Answers
Step-by-step explanation:
100 = 12
300 + 50 = 36 + 6 = 42 L
the volume of cylinder can be 1.5litre and area of its base is 77 . find its height
Answers
Answer:
20.07 cm³
Step-by-step explanation:
Volume of Cylinder = 1.54 liters = 1540 cm³.
Area of its base = 77 cm².
πr² = 77
(22/7) * r² = 77
r = 4.94
Now,
Volume of cylinder = πr²h
⇒ 1540 = (22/7) * (4.94)² * h
⇒ h = 20.07 cm³
Directions - Identify the key components, create an exponential equation, then answer the questions.
Exponential Form: y=a.6, a is the starting value, b is the base (rate).
In a small town, the stray dog population is rapidly increasing there are currently 15 stray dogs, and it is estimated that the population will triple every year.
How many dogs will there be after 1 year? 2 years? 3 years?
1) a =
4) Dogs after 1 years =
2) b =
5) Dogs after 2 years =
3) Equation:
6) Dogs after 3 years =
Answers
Answer:
Directions - Identify the key components, create an exponential equation, then answer the questions.
Exponential Form: y=a\cdot b^{x},\ a\ is\ the\ \textit{starting}\ \textit{value},\ b\ is\ the\ base\ (rate).\y=a⋅b
x
, a is the starting value, b is the base (rate).
In a small town, the stray dog population is rapidly increasing. there are currently 15 stray dogs, and it is estimated that the population will triple every year. How many dogs will there be after 1 year? 2 years? 3 years?
1) a = 15
4) Dogs after 1 years = 45
2) b = 3
5) Dogs after 2 years = 135
3) Equation:
y= 15 ×3x
6) Dogs after 3 years =
405
Step-by-step explanation:
In a standard deck of cards, what is the probability of drawing a card with the suit of clubs?
Answer (round) to the hundredth place value.
Answers
Answer:
[tex]\frac{1}{4}[/tex]
= 0.25
Step-by-step explanation:
In a standard deck of cards, there are 52 cards. The standard deck of cards also has 13 clubs. Probability is;
[tex]\frac{wanted- outcomes}{total- outcomes}[/tex]
The wanted outcomes is a clubs, the total outcomes are the total number of cards in the deck, hence;
[tex]\frac{13}{52}[/tex]
Simplify;
[tex]\frac{1}{4}[/tex]
Point S is on line segment \overline{RT}
. Given ST=3x-8,ST=3x−8, RT=4x,RT=4x, and RS=4x-7,RS=4x−7, determine the numerical length of \overline{RT}.
RT
.
.
Answers
Answer:
RT = 20
Step-by-step explanation:
Point S is on line segment
R------------S------------T
RS + ST = RT
Given
ST=3x-8
RT=4x
RS=4x-7,
Step 1
We find x
4x - 7 + 3x - 8 = 4x
4x + 3x -7 - 8 = 4x
7x - 15 = 4x
7x - 4x = 15
3x = 15
x = 15/3
x = 5
Step 2
We find RT
RT = 4x
x = 5
RT = 4 × 5
RT = 20
The numerical length of RT is 20
Can someone help me ASAP!!
Answers
Answer:
UR in trouble
Step-by-step explanation:
Look, the First order is the biggest force in the galaxy.
Now, it is gonna send a star destroyer to ur house and blow it up.
Deon has taken a car loan for $1800. To pay the loan off in 12 months, how much would he have to pay per month?
Variable: x = amount to pay per month
Answers
Answer:
$150 per month
Step-by-step explanation:
If you divided 1800 by 12 you will get 150 so therefore he needs to pay $150 per month.
8c-72=-2(6x-9)-4c fast
Answers
Answer:
2c+15/2
Step-by-step explanation:
What is m∠N?
A. 19°
B. 68°
C. 95°
D. 112°
Answers
Answer:
B.68.......................
HELP HELP HELP POINTS GIVEN POINTS GIVENN
Answers
All except for the leg
URGENT! PLEASE HELP ME!
Martin had read 70% of a book. He has 3 more pages to finish. How many pages are there in the book?
Answers
Answer:
15
Step-by-step explanation:
15x3=70
Answer:
5.1 pages
Step-by-step explanation:
70% of 3 is 2.1 and 2.1 + 3 = 5.1
The lines AB and CB intersect at B
(a) Find the co-ordinates of the midpoint of AB
(b) Find the equation of the line CB
Answers
Step-by-step explanation:
Soln
given,
from the figure
coordinate of B is (5,3),
A(7,0) and C(0,4)
A. solution
let, M(x,y) be the mid point of AB
A(7,0) = (x1,y1)
B(5,3) = (x2,y2)
we know
x = (x2+x1)/2
or, x = (5+7)/2
or, x = 12/2
or, x = 6
and for y
y = (y2+y1)/2
or, y = (3+0)/2
or, y = 3/2
therefore M(x,y) = (6,3/2)
B. solution
let,
C(0,4) = (x1,y1)
B(5,3) = (x2,y2)
equation of line is ;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
or, (y - 4)/(x -0) = (3 - 4)/(5 - 0)
or, (y - 4)/(x - 0) = -1 / 5
by cross multiply
or, 5×(y - 4) = -1×(x)
or, 5y - 20 = -x
or, x + 5y = 20 is the required equation.
There are 15 fruits in a bowl and 3 of them are apples. What percent of the fruits in the bowl are apples?
Answers
Answer:
20 percent of them
Step-by-step explanation:
3/15=1/5=20%
i need the answerrrrrrrrrrrrrrrrrrrrrrrrrrrr
Answers
Answer:
The first number is zero, and the second number is 17
Step-by-step explanation:
If we triple the first number (which is zero), it would still equal zero. Then, if you double the second number the answer would be 34.
have a good day!! :)
) Luci Lulu opened a cookie store in the mall. She found that the relationship between the price of a cookie, p, and the number of cookies sold, x, is given by the linear relationship x = −2000 p + 4000 . Find the maximum revenue Luci can make selling cookies in one day
Answers
Answer:
The maximum revenue Luci can make selling cookies in one day is $4,004,000.
Step-by-step explanation:
Given;
x = −2000 p + 4000 ..................... (1)
Revenue = xp
Revenue = (−2000 p + 4000)p =
Revenue = −2000p^2 + 4000p .................... (2)
The price at which Luci will the maximum profit can be calculated by finding the derivative of equation (2), equating to 0, and then solve for p as follows:
−4000p + 4000 = 0
4000 = 4000p
p = 4000 / 4000
p = 1
This implies that the price at which Luci will the maximum profit is $1.
Substituting p = 1 into equation (2) to obtain the maximum revenue Luci can make selling cookies in one day, we have:
Revenue = (−2000 * 1)^2 + (4000 * 1)
Revenue = −2000^2 + 4000
Revenue = 4,000,000 + 4000
Revenue = 4,004,000
Therefore, the maximum revenue Luci can make selling cookies in one day is $4,004,000.
A square has a side length of 13 meters. What is the area of the square?
If the dimensions of the square are doubled, what will be the area of the new square?
Answers
Answer:
Area of original = 169m^2
Area of new = 676m^2
Step-by-step explanation:
Area of a square = (length of side)^2
13^2 = 13 * 13 = 169
If the dimension is doubled:
(2*13)^2 = 26^2 = 676
Answer:
G00D LuCk
Step-by-step explanation:
Feel free to fail
The answer and the step by step explanation pleasee
Answers
Answer:
C
Step-by-step explanation:
Given
V = lwh ( isolate w by dividing both sides by lh )
[tex]\frac{V}{lh}[/tex] = w → C
Given z1 =9+9/3i and z2 = 2+/3i, what is z2-z1?
8+7/3i
-7-8/3i
7+ 10/3i
-7+ 10/3i
Answers
Answer:
z2 - z1 = 7/3i
Step-by-step explanation:
Given the following complex number:
z1 = 9+i/3i
z2 = 2+i/3i,
Taking the difference
z2 - z1 = 9+i/3i - (2+i))/3i)
z2-z1 = (9+i-(2+i))/31
z2 - z1 = 9+i -2-i/3i
z2-z1 = 9-2/3i
z2 - z1 = 7/3i
Note that the complex number given was not properly written and the ones used were assumed. Same procedure an be used for other complex numbers that might be given.
Ana uses Talk-A-Lot and Peter uses Talk-to-Me. Each company charges
the same amount per hour of talk time, however Ana and Peter will never
be charged the same amount. Write a system of equations that could
represent the situation. Explain.
Answers
Answer:
They both talk for a different amount of time
how fast was a plane flying if it traveled 40 kilometers in 30 minutes
Answers
Answer:
80 km/hr
Step-by-step explanation:
0.5 hour = 30 min
40 km in 30 min
80km in 60 min
Below are a picture of parallel railroad tracks intersecting the parallel edges of a road.
Find x
Answers
9.5=25/t+(-8) helppppppppp
Answers
Answer:
437.5Step-by-step explanation:
I will REALLY answer your question :)
9.5 = 25/t + -8
The first step here is to simplify t + -8. If you add a negative of something, you also subtract. This can be rewritten as:
9.5 = 25/t - 8
Now, we need to add 8 to undo the subtraction.
17.5 = 25/t
Now, to undo the division, we will multiply the whole equation by 25.
17.5 x 25 = 437.5
x + 4 =7
Solve the equation for the value of the variable show all work someone please help
Answers
Answer:
x = 3
Step-by-step explanation:
x + 4 = 7 ( isolate x by subtracting 4 from both sides )
x = 3
if u substitute 3 for x, 3+4=7
you could also do 7-4 to get x which is 3 :)
Which linear equation can be used to represent a line perpendicular to Line W passing through point (-3,-2)?
line is x=8 on graph PLEASE HELP!
Answers
Answer:
x=-3
hope this helps!!:)
Step-by-step explanation: